#ifndef `MINCERHFILE' #define MINCERHFILE "1" * * This is the mincer system as adapted to version 3 of FORM. * All necessary files are included in the file mincer.h * All local variables have names that start with mnc to avoid namespace problems. * When needed one should use replace_ to change external names to internal ones. * All procedures are included here as well. * The only variables that have external names are: * S D,ep,z3,z4,z5,z6,zz5; * CF acc; * V P,Q,p1,p2,p3,p4,p5,p6,p7,p8; * I mu,nu,ka,la,ro,si,ga,alfa,beta,MU,NU,KA,RO,SI,mmu,nnu; * S cw1,cw2,cw3; * S cf,ca,nf,nc,[cf-ca/2],[cf-ca],[dabc^2/n]; * CF Glonel; * S ab,a,[alfas/pi]; * used in total and other renormalizations. * * Conversion by J. Vermaseren 2-may-2000. * *--#[ Declarations : #define OLDTWO "1" #define EXTRARED "1" #define LATRANS "0" #define BEPATH "0" #define O1PATH "0" #define INNOTABL "11" #define NOSPEC "0" S D,[D-4],ep(:6),[1-ep/2]; dimension D:[D-4]; AutoDeclare Index mnci,mncj,mu,nu,ka,la,ro,si,ga; AutoDeclare Vector Q,P,mncp,mncq; AutoDeclare Symbol mnce,mncx,mncy,mncsgn,mnck,D; V p1,p2,p3,p4,p5,p6,p7,p8; V [P+Q],[P+p1],[P+p2],[P+p3],[P+p4],[P+p5],[P+p6],[P+p7],[P+p8]; V [P-Q],[P-p1],[P-p2],[P-p3],[P-p4],[P-p5],[P-p6],[P-p7],[P-p8]; set mncpp18:p1,p2,p3,p4,p5,p6,p7,p8; set mncpQ18:p1,p2,p3,p4,p5,p6,p7,p8,Q; set [mncpp18]:[P+p1],[P+p2],[P+p3],[P+p4],[P+p5],[P+p6],[P+p7],[P+p8]; set [-mncpp18]:[P-p1],[P-p2],[P-p3],[P-p4],[P-p5],[P-p6],[P-p7],[P-p8]; set mncee18:mnce1,mnce2,mnce3,mnce4,mnce5,mnce6,mnce7,mnce8; set [mncPp]:[P+p1],[P+p2],[P+p3],[P+p4],[P+p5],[P+p6],[P+p7],[P+p8],[P+Q], [P-p1],[P-p2],[P-p3],[P-p4],[P-p5],[P-p6],[P-p7],[P-p8],[P-Q]; set mncPcenter:[P+p7],[P+p2],[P+p8],[P-p7],[P-p2],[P-p8]; set mncpcenter:p7,p2,p8; set [mncx18]:mncx1,mncx2,mncx3,mncx4,mncx5,mncx6,mncx7,mncx8; S z3,z4,z5,z6,zz5; S mncs,mncj; S mncexp11,mncexp10,mncexp20,mncG311,mncF321,mncint1,mncint2,mncint3; S mncN1,mncN2,mncN3,mncA,mncB,mncm; I alfa,beta; I MU,NU,KA,RO,SI,mmu,nnu; S mncxi; S cw1,cw2,cw3; S cf,ca,nf,nc,[cf-ca/2],[cf-ca],[dabc^2/n]; S mncfermi1,mncfermi2,mncfermi3,mncghost1,mncghost2,mncghost3,mncgluon1,mncgluon2,mncgluon3; F mncS,mncSS,mncSSS; S ab,[(mu^2/Q.Q)^ep],a,[ln(mu^2/Q.Q)],[alfas/pi]; CF mncv2gi,mncV3G,mncv3g,mncv3gi,mncV4G,mncv4g,mncv4gi,mncDg,mncDs,Glonel,mncVgh,mncDgh,mncDL,mncVv; CF mncv2gp,mncv2gc,mncv3gp,mncv3gc,mncv4gp,mncv4gc; CF mncG,mncdeno,mncpo,mncpoinv,mncaccm,mncftri; F mncdel,mncdd,mncfp; S mncproexp; CF mncepexp,mncpropxp,mncnaar,mncsumm1,mncsumm2,mncsumm3; T mncFQ,mncFFPP; CF acc; #ifndef `SCHEME' #define SCHEME "1" #endif *--#] Declarations : *--#[ Procedures : *--#[ benz : #procedure benz(P1,P2,P3,P4,P5,P6,P7,P8,Q) * * Reduction procedure for three loop graphs of the BE or benz type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<------<-\ * P1 / \ P2 / \ P3 * / \ / \ * / P6 v ^ P7 \ * / \ / \ * Q --<-- \ / --<-- Q * \ | / * \ v P8 / * \ | / * P5 \ | / P4 * \---->------->----/ * * We start with reducing the dotproducts in the numerator to sums * of denominators. Only one dotproduct is irreducible: Q.P2 * The easiest reduction (and quite fast) is by writing everything * in terms of Q,P1,P2,P3 and use vertex identities and P8 = P3-P1 * to write the few remaining dotproducts in terms of denominators. * * Routine coded by J.A.M.Vermaseren 8-jul-1990, modified 13-nov-1990. * * id `P4'.P?!{,`P4'} = `P3'.P-'Q'.P; * id `P5'.P?!{,`P5'} = `P1'.P-'Q'.P; *#call ACCU(Benz momenta 1) * id `P6'.P?!{,`P6'} = `P2'.P-`P1'.P; *#call ACCU(Benz momenta 2) * id `P7'.P?!{,`P7'} = `P2'.P-`P3'.P; *#call ACCU(Benz momenta 3) * id `P8'.P?!{,`P8'} = `P3'.P-`P1'.P; *#call ACCU(Benz momenta 4) id 'Q'.`P1' = `P1'.`P1'/2+'Q'.'Q'/2-`P5'.`P5'/2; #call ACCU(Benz scalar 1) id 'Q'.`P3' = `P3'.`P3'/2+'Q'.'Q'/2-`P4'.`P4'/2; #call ACCU(Benz scalar 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P6'.`P6'/2; #call ACCU(Benz scalar 3) id `P2'.`P3' = `P2'.`P2'/2+`P3'.`P3'/2-`P7'.`P7'/2; #call ACCU(Benz scalar 4) id `P1'.`P3' = `P1'.`P1'/2+`P3'.`P3'/2-`P8'.`P8'/2; #call ACCU(Benz scalar 5) if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ); #call triangle(`P2',`P6',`P7',`P1',`P3') endif; * #endprocedure *--#] benz : *--#[ benzbar : #procedure benzbar(P1,P2,P3,P4,P5,P6,P7,Q) * * Reduction procedure for three loop graphs of the BEbar or benz-bar type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<------<-\ * P1 / | P2 | \ P3 * / \ / \ * / P6 | | P7 \ * / \ / \ * Q --<-- v ^ --<-- Q * \ \ / / * \ | | / * \ \ / / * P5 \ | / P4 * \---->------->----/ * * * Note that from the ladder graphs we can have powers of p7.p8 (P6.P7) * Here they can be written as a fake (P6-P7)^2 * Such a (P6-P7)^2 isn't affected by the transformations here. * It is better than writing it as (P3-P1)^2 because then we would * generate positive powers of P1.P1 and P3.P3 in the end. * * Coded by J.A.M. Vermaseren, 13-nov-1990. * id `P6'.`P7' = `P6'.`P6'/2+`P7'.`P7'/2-mncx8/2; if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7') > 0 ); #call triangle(`P2',`P6',`P7',`P1',`P3') endif; id mncx8 = `P6'.`P6' + `P7'.`P7' - 2*`P6'.`P7'; #endprocedure *--#] benzbar : *--#[ benzbu : #procedure benzbu(P1,P2,P3,P4,P5,P6,P7,Q) * * Reduction procedure for three loop graphs of the BU or benz-bu type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<-------------<-\ * P1 / | \ P6 * / ^ P4 \ * / | \ * / P2 | \ * Q --<-- ----->------| --<-- Q * \ | / * \ | / * \ v P5 / * P3 \ | / P7 * \---->------->----/ * * The main complication is to make sure that no loop momentum * survives in the numerator (Q.P4 and Q.P5 are independent objects) * Because this is a service routine it is best if the calling * routine takes care of that. * BU is BE with 1 or 3 missing. * * Procedure coded by J.A.M. Vermaseren, 13-nov-1990. * if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7') > 0 ); if ( count(`P6'.`P6',1) > count(`P7'.`P7',1) ); #call triangle(`P4',`P2',`P1',`P5',`P6') else; #call triangle(`P5',`P2',`P3',`P4',`P7') endif; endif; * #endprocedure *--#] benzbu : *--#[ benzred : #procedure benzred(P1,P2,P3,P4,P5,P6,P7,P8,Q) * * Reduction procedure for three loop graphs of the BE or benz type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<------<-\ * P1 / \ P2 / \ P3 * / \ / \ * / P6 v ^ P7 \ * / \ / \ * `Q' --<-- \ / --<-- `Q' * \ | / * \ v P8 / * \ | / * P5 \ | / P4 * \---->------->----/ * * We start with reducing the dotproducts in the numerator to sums * of denominators. Only one dotproduct is irreducible: `Q'.P2 * The easiest reduction (and quite fast) is by writing everything * in terms of `Q',P1,P2,P3 and use vertex identities and P8 = P3-P1 * to write the few remaining dotproducts in terms of denominators. * * Routine coded by J.A.M.Vermaseren 8-jul-1990, modified 13-nov-1990. * BEPATH added 21-dec-1994 to improve efficiency. * #ifndef `BEPATH' if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU2(AB `P1'.`P3' `P1'.`P1' `P3'.`P3' `P8'.`P8',Benz scalar 0) id `P1'.`P3' = `P1'.`P1'/2+`P3'.`P3'/2-`P8'.`P8'/2; #call ACCU2(AB `P2'.`P3' `P2'.`P2' `P3'.`P3' `P7'.`P7',Benz scalar 1) id `P2'.`P3' = `P2'.`P2'/2+`P3'.`P3'/2-`P7'.`P7'/2; #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P6'.`P6',Benz scalar 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P6'.`P6'/2; #call ACCU2(AB `Q'.`P1' `P1'.`P1' `Q'.`Q' `P5'.`P5',Benz scalar 3) id `Q'.`P1' = `P1'.`P1'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `Q'.`P3' `P3'.`P3' `Q'.`Q' `P4'.`P4',Benz scalar 4) id `Q'.`P3' = `P3'.`P3'/2+`Q'.`Q'/2-`P4'.`P4'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 5) #else #if `BEPATH' == 0 if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU2(AB `P1'.`P3' `P1'.`P1' `P3'.`P3' `P8'.`P8',Benz scalar 0 \(0\)) id `P1'.`P3' = `P1'.`P1'/2+`P3'.`P3'/2-`P8'.`P8'/2; #call ACCU2(AB `P2'.`P3' `P2'.`P2' `P3'.`P3' `P7'.`P7',Benz scalar 1 \(0\)) id `P2'.`P3' = `P2'.`P2'/2+`P3'.`P3'/2-`P7'.`P7'/2; #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P6'.`P6',Benz scalar 2 \(0\)) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P6'.`P6'/2; #call ACCU2(AB `Q'.`P1' `P1'.`P1' `Q'.`Q' `P5'.`P5',Benz scalar 3 \(0\)) id `Q'.`P1' = `P1'.`P1'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `Q'.`P3' `P3'.`P3' `Q'.`Q' `P4'.`P4',Benz scalar 4 \(0\)) id `Q'.`P3' = `P3'.`P3'/2+`Q'.`Q'/2-`P4'.`P4'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 5 \(0\)) #endif #if `BEPATH' == 1 #call ACCU2(AB `Q'.`P1' `P1'.`P1' `Q'.`Q' `P5'.`P5',Benz scalar 0 \(1\)) id `Q'.`P1' = `P1'.`P1'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `P1'.`P6' `P2'.`P2' `P1'.`P1' `P6'.`P6',Benz scalar 1 \(1\)) id `P1'.`P6' = `P2'.`P2'/2-`P1'.`P1'/2-`P6'.`P6'/2; #call ACCU2(AB `P6'.`P8' `P6'.`P6' `P8'.`P8' `P7'.`P7',Benz scalar 2 \(1\)) id `P6'.`P8' = `P6'.`P6'/2+`P8'.`P8'/2-`P7'.`P7'/2; #call ACCU2(AB `P1'.`P8' `P3'.`P3' `P1'.`P1' `P8'.`P8',Benz scalar 3 \(1\)) id `P1'.`P8' = `P3'.`P3'/2-`P1'.`P1'/2-`P8'.`P8'/2; #call ACCU2(AB `Q'.`P8' `P3'.`P3' `P4'.`P4' `P1'.`P1' `P5'.`P5',Benz scalar 4 \(1\)) id `Q'.`P8' = `P3'.`P3'/2-`P4'.`P4'/2-`P1'.`P1'/2+`P5'.`P5'/2; #call ACCU2(AB `Q'.`P6' `Q'.`P2' `Q'.`Q' `P1'.`P1' `P5'.`P5',Benz scalar 5 \(1\)) id `Q'.`P6' = `Q'.`P2'-`Q'.`Q'/2-`P1'.`P1'/2+`P5'.`P5'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6', `P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6', `P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6', `P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 6 \(1\)) #endif #if `BEPATH' == 2 #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P6'.`P6',Benz scalar 0 \(2\)) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P6'.`P6'/2; #call ACCU2(AB `P2'.`P7' `P2'.`P2' `P7'.`P7' `P3'.`P3',Benz scalar 1 \(2\)) id `P2'.`P7' = `P2'.`P2'/2+`P7'.`P7'/2-`P3'.`P3'/2; #call ACCU2(AB `Q'.`P1' `P1'.`P1' `Q'.`Q' `P5'.`P5',Benz scalar 2 \(2\)) id `Q'.`P1' = `P1'.`P1'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `Q'.`P7' `Q'.`P2' `Q'.`Q' `P3'.`P3' `P4'.`P4',Benz scalar 3 \(2\)) id `Q'.`P7' = `Q'.`P2'-`Q'.`Q'/2-`P3'.`P3'/2+`P4'.`P4'/2; #call ACCU2(AB `P1'.`P7' `P2'.`P2' `P6'.`P6' `P3'.`P3' `P8'.`P8',Benz scalar 4 \(2\)) id `P1'.`P7' = `P2'.`P2'/2-`P6'.`P6'/2-`P3'.`P3'/2+`P8'.`P8'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 5 \(2\)) #endif #if `BEPATH' == 3 #call ACCU2(AB `P6'.`P8' `P6'.`P6' `P8'.`P8' `P7'.`P7',Benz scalar 0 \(3\)) id `P6'.`P8' = `P6'.`P6'/2+`P8'.`P8'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P6' `P2'.`P2' `P6'.`P6' `P1'.`P1',Benz scalar 1 \(3\)) id `P2'.`P6' = `P2'.`P2'/2+`P6'.`P6'/2-`P1'.`P1'/2; #call ACCU2(AB `P2'.`P8' `P3'.`P3' `P1'.`P1' `P7'.`P7' `P6'.`P6',Benz scalar 2 \(3\)) id `P2'.`P8' = `P3'.`P3'/2-`P1'.`P1'/2-`P7'.`P7'/2+`P6'.`P6'/2; #call ACCU2(AB `Q'.`P8' `P3'.`P3' `P4'.`P4' `P1'.`P1' `P5'.`P5',Benz scalar 3 \(3\)) id `Q'.`P8' = `P3'.`P3'/2-`P4'.`P4'/2-`P1'.`P1'/2+`P5'.`P5'/2; #call ACCU2(AB `Q'.`P6' `Q'.`P2' `Q'.`Q' `P1'.`P1' `P5'.`P5',Benz scalar 4 \(3\)) id `Q'.`P6' = `Q'.`P2'-`Q'.`Q'/2-`P1'.`P1'/2+`P5'.`P5'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 5 \(3\)) #endif #if `BEPATH' == 4 #call ACCU2(AB `P6'.`P8' `P6'.`P6' `P8'.`P8' `P7'.`P7',Benz scalar 0 \(4\)) id `P6'.`P8' = `P6'.`P6'/2+`P8'.`P8'/2-`P7'.`P7'/2; #call ACCU2(AB `P4'.`P8' `P4'.`P4' `P8'.`P8' `P5'.`P5',Benz scalar 1 \(4\)) id `P4'.`P8' = `P4'.`P4'/2+`P8'.`P8'/2-`P5'.`P5'/2; #call ACCU2(AB `Q'.`P4' `P3'.`P3' `Q'.`Q' `P4'.`P4',Benz scalar 2 \(4\)) id `Q'.`P4' = `P3'.`P3'/2-`Q'.`Q'/2-`P4'.`P4'/2; #call ACCU2(AB `Q'.`P8' `P3'.`P3' `P4'.`P4' `P1'.`P1' `P5'.`P5',Benz scalar 3 \(4\)) id `Q'.`P8' = `P3'.`P3'/2-`P4'.`P4'/2-`P1'.`P1'/2+`P5'.`P5'/2; #call ACCU2(AB `Q'.`P6' `Q'.`P2' `Q'.`Q' `P1'.`P1' `P5'.`P5',Benz scalar 4 \(4\)) id `Q'.`P6' = `Q'.`P2'-`Q'.`Q'/2-`P1'.`P1'/2+`P5'.`P5'/2; #call ACCU2(AB `P4'.`P6' `Q'.`P2' `Q'.`Q' `P2'.`P2' `P8'.`P8' `P7'.`P7' `P5'.`P5',Benz scalar 5 \(4\)) id `P4'.`P6' = -`Q'.`P2'+`Q'.`Q'/2+`P2'.`P2'/2+`P8'.`P8'/2 -`P7'.`P7'/2-`P5'.`P5'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 6 \(4\)) #endif #if `BEPATH' == 5 #call ACCU2(AB `P1'.`P6' `P2'.`P2' `P1'.`P1' `P6'.`P6',Benz scalar 0 \(5\)) id `P1'.`P6' = `P2'.`P2'/2-`P1'.`P1'/2-`P6'.`P6'/2; #call ACCU2(AB `P6'.`P7' `P6'.`P6' `P7'.`P7' `P8'.`P8',Benz scalar 1 \(5\)) id `P6'.`P7' = `P6'.`P6'/2+`P7'.`P7'/2-`P8'.`P8'/2; #call ACCU2(AB `Q'.`P1' `P1'.`P1' `Q'.`Q' `P5'.`P5',Benz scalar 2 \(5\)) id `Q'.`P1' = `P1'.`P1'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `P1'.`P7' `P2'.`P2' `P6'.`P6' `P3'.`P3' `P8'.`P8',Benz scalar 3 \(5\)) id `P1'.`P7' = `P2'.`P2'/2-`P6'.`P6'/2-`P3'.`P3'/2+`P8'.`P8'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU2(AB `Q'.`P6' `Q'.`P2' `Q'.`Q' `P1'.`P1' `P5'.`P5',Benz scalar 4 \(5\)) id `Q'.`P6' = `Q'.`P2'-`Q'.`Q'/2-`P1'.`P1'/2+`P5'.`P5'/2; #call ACCU2(AB `Q'.`P7' `Q'.`P2' `Q'.`Q' `P3'.`P3' `P4'.`P4',Benz scalar 5 \(5\)) id `Q'.`P7' = `Q'.`P2'-`Q'.`Q'/2-`P3'.`P3'/2+`P4'.`P4'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 6 \(5\)) #endif #if `BEPATH' == 6 #call ACCU2(AB `P5'.`P8' `P4'.`P4' `P5'.`P5' `P8'.`P8',Benz scalar 0 \(6\)) id `P5'.`P8' = `P4'.`P4'/2-`P5'.`P5'/2-`P8'.`P8'/2; #call ACCU2(AB `P6'.`P8' `P6'.`P6' `P8'.`P8' `P7'.`P7',Benz scalar 1 \(6\)) id `P6'.`P8' = `P6'.`P6'/2+`P8'.`P8'/2-`P7'.`P7'/2; #call ACCU2(AB `Q'.`P5' `P1'.`P1' `Q'.`Q' `P5'.`P5',Benz scalar 2 \(6\)) id `Q'.`P5' = `P1'.`P1'/2-`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `P5'.`P6' `P2'.`P2' `P1'.`P1' `P6'.`P6' `Q'.`P6',Benz scalar 3 \(6\)) id `P5'.`P6' = `P2'.`P2'/2-`P1'.`P1'/2-`P6'.`P6'/2-`Q'.`P6'; #call ACCU2(AB `Q'.`P8' `P3'.`P3' `P4'.`P4' `P1'.`P1' `P5'.`P5',Benz scalar 4 \(6\)) id `Q'.`P8' = `P3'.`P3'/2-`P4'.`P4'/2-`P1'.`P1'/2+`P5'.`P5'/2; #call ACCU2(AB `Q'.`P6' `Q'.`P2' `Q'.`Q' `P1'.`P1' `P5'.`P5',Benz scalar 5 \(6\)) id `Q'.`P6' = `Q'.`P2'-`Q'.`Q'/2-`P1'.`P1'/2+`P5'.`P5'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 6 \(6\)) #endif #if `BEPATH' == 7 #call ACCU2(AB `P4'.`P5' `P4'.`P4' `P5'.`P5' `P8'.`P8',Benz scalar 0 \(7\)) id `P4'.`P5' = `P4'.`P4'/2+`P5'.`P5'/2-`P8'.`P8'/2; #call ACCU2(AB `Q'.`P4' `P3'.`P3' `Q'.`Q' `P4'.`P4',Benz scalar 1 \(7\)) id `Q'.`P4' = `P3'.`P3'/2-`Q'.`Q'/2-`P4'.`P4'/2; #call ACCU2(AB `Q'.`P5' `P1'.`P1' `Q'.`Q' `P5'.`P5',Benz scalar 2 \(7\)) id `Q'.`P5' = `P1'.`P1'/2-`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `P2'.`P4' `P2'.`P2' `P3'.`P3' `P7'.`P7' `Q'.`P2',Benz scalar 3 \(7\)) id `P2'.`P4' = `P2'.`P2'/2+`P3'.`P3'/2-`P7'.`P7'/2-`Q'.`P2'; #call ACCU2(AB `P2'.`P5' `P2'.`P2' `P1'.`P1' `P6'.`P6' `Q'.`P2',Benz scalar 4 \(7\)) id `P2'.`P5' = `P2'.`P2'/2+`P1'.`P1'/2-`P6'.`P6'/2-`Q'.`P2'; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 5 \(7\)) #endif #if `BEPATH' == 8 if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU2(AB `P2'.`P6' `P2'.`P2' `P1'.`P1' `P6'.`P6',Benz scalar 0 \(8\)) id `P2'.`P6' = `P2'.`P2'/2+`P6'.`P6'/2-`P1'.`P1'/2; #call ACCU2(AB `P2'.`P7' `P2'.`P2' `P7'.`P7' `P3'.`P3',Benz scalar 1 \(8\)) id `P2'.`P7' = `P2'.`P2'/2+`P7'.`P7'/2-`P3'.`P3'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU2(AB `P6'.`P7' `P6'.`P6' `P7'.`P7' `P8'.`P8',Benz scalar 2 \(8\)) id `P6'.`P7' = `P6'.`P6'/2+`P7'.`P7'/2-`P8'.`P8'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU2(AB `Q'.`P6' `Q'.`P2' `Q'.`Q' `P1'.`P1' `P5'.`P5',Benz scalar 3 \(8\)) id `Q'.`P6' = `Q'.`P2'-`Q'.`Q'/2-`P1'.`P1'/2+`P5'.`P5'/2; #call ACCU2(AB `Q'.`P7' `Q'.`P2' `Q'.`Q' `P3'.`P3' `P4'.`P4',Benz scalar 4 \(8\)) id `Q'.`P7' = `Q'.`P2'-`Q'.`Q'/2-`P3'.`P3'/2+`P4'.`P4'/2; if ( count(`P6'.`P6',1) < count(`P7'.`P7',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P6'.`P6',1) == count(`P7'.`P7',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P5'.`P5',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P5',`P5',`P4',`P6',`P7',`P7',`P6',`P8',-`P8'); endif; endif; #call ACCU(Benz scalar 5 \(8\)) #endif #endif * #endprocedure *--#] benzred : *--#[ dotwo : #procedure dotwo() #ifdef `OLDTWO' if ( count(p1.p1,1,p3.p3,1) > count(p4.p4,1,p6.p6,1) ); multiply replace_(p1,p6,p6,p1,p3,p4,p4,p3,mnce1,mnce6,mnce6,mnce1,mnce3,mnce4,mnce4,mnce3); id Q.mncq1?{p1,p3,p4,p6,p7} = -Q.mncq1; endif; if ( count(p1.p1,1,p6.p6,1) > count(p3.p3,1,p4.p4,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,mnce1,mnce3,mnce3,mnce1,mnce4,mnce6,mnce6,mnce4); id p7.mncq1?{Q,p1,p3,p4,p6} = -p7.mncq1; endif; #call ACCU(Presymmetrize) id p7.Q = Q.p1-Q.p3; id p1.p4 = p1.p3-p1.Q; id p3.p6 = p1.p3-p3.Q; id p1.p7 = p1.p1/2+p7.p7/2-p3.p3/2; id p3.p7 = p1.p1/2-p3.p3/2-p7.p7/2; id p4.p7 = p6.p6/2-p4.p4/2-p7.p7/2; id p6.p7 = p6.p6/2+p7.p7/2-p4.p4/2; #call ACCU2(AB p1.Q Q.Q p6.Q p1.p6 p1.p1,Rewrite vectors\(2\)) id p6.Q = p1.Q-Q.Q; id p1.p6 = p1.p1-p1.Q; #call ACCU2(AB p3.Q Q.Q p4.Q p3.p4 p3.p3,Scalars\(2\) 1) id p4.Q = p3.Q-Q.Q; id p3.p4 = p3.p3-p3.Q; #call ACCU2(AB p1.Q p1.p1 Q.Q p6.p6,Scalars\(2\) 2) id p1.Q = p1.p1/2+Q.Q/2-p6.p6/2; #call ACCU2(AB p3.Q p3.p3 Q.Q p4.p4,Scalars\(2\) 3) id p3.Q = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU2(AB p1.p3 p1.p1 p3.p3 p7.p7,Scalars\(2\) 4) id p1.p3 = p1.p1/2+p3.p3/2-p7.p7/2; #call ACCU2(AB p4.p6 p4.p4 p6.p6 p7.p7,Scalars\(2\) 5) id p4.p6 = p4.p4/2+p6.p6/2-p7.p7/2; #call ACCU(Scalars\(2\) 6) *id p1.p6 = p1.p1/2+p6.p6/2-Q.Q/2; *id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; *#call ACCU(Scalars\(2\) 7) #else if ( count(Q.p6,1,p4.p6,1,Q.p4,1,p4.p7,1,p6.p7,1) > count(Q.p1,1,Q.p3,1,p1.p3,1,p1.p7,1,p3.p7,1) ); multiply replace_(p1,p6,p6,p1,p3,p4,p4,p3,mnce1,mnce6,mnce6,mnce1,mnce3,mnce4,mnce4,mnce3); id Q = -Q; endif; if ( count(Q.p3,1,p3.p4,1,Q.p4,1,p3.p7,1,p4.p7,1) > count(Q.p1,1,Q.p6,1,p1.p6,1,p1.p7,1,p6.p7,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,mnce1,mnce3,mnce3,mnce1,mnce4,mnce6,mnce6,mnce4); id p7 = -p7; endif; #call ACCU(Presymmetrize) id p7.mncq1?{Q,p1,p3,p4,p6,p7} = p1.mncq1-p3.mncq1; #call ACCU(Eliminate p7) id p6.mncq1?{Q,p1,p3,p4} = p1.mncq1-Q.mncq1; #call ACCU(Eliminate p6) id p4.mncq1?{Q,p1,p3} = p3.mncq1-Q.mncq1; #call ACCU2(AB p1.Q p1.p1 Q.Q p6.p6,Eliminate p4) id p1.Q = p1.p1/2+Q.Q/2-p6.p6/2; #call ACCU2(AB p3.Q p3.p3 Q.Q p4.p4,Eliminate Q.p1) id p3.Q = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU2(AB p1.p3 p1.p1 p3.p3 p7.p7,Eliminate Q.p3) id p1.p3 = p1.p1/2+p3.p3/2-p7.p7/2; #call ACCU(Eliminate p1.p3) #endif * * Now relabel the lines so that we get a uniform orientation. * This can be done easily because we have only squares of momenta. * if ( count(mnce7,1,mnceq,1) > 0 ); label 2; if ( ( ( count(p1.p1,1) > count(p3.p3,1) ) && ( count(p6.p6,1) > count(p3.p3,1) ) ) || ( ( count(p1.p1,1) > count(p4.p4,1) ) && ( count(p6.p6,1) > count(p4.p4,1) ) ) ); multiply replace_(p1,p3,p3,p1,mnce1,mnce3,mnce3,mnce1,p6,p4,p4,p6,mnce6,mnce4,mnce4,mnce6); endif; if ( ( count(p1.p1,1) > count(p6.p6,1) ) || ( ( count(p1.p1,1) == count(p6.p6,1) ) && ( count(p3.p3,1) > count(p4.p4,1) ) ) ); multiply replace_(p1,p6,p6,p1,mnce1,mnce6,mnce6,mnce1,p3,p4,p4,p3,mnce3,mnce4,mnce4,mnce3); endif; else; if ( ( count(mnce3,1) > 0 ) || ( count(mnce4,1) > 0 ) ); multiply replace_(p1,p3,p3,p1,mnce1,mnce3,mnce3,mnce1,p6,p4,p4,p6,mnce6,mnce4,mnce4,mnce6); endif; if ( count(mnce6,1) > 0 ); multiply replace_(p1,p6,p6,p1,mnce1,mnce6,mnce6,mnce1,p3,p4,p4,p3,mnce3,mnce4,mnce4,mnce3); endif; if ( count(mnce1,1) == 0 ) goto 2; endif; #call ACCU(Use symmetry\(2\)) multiply acc(1/ep); #call newtwo(p1,mnce1,p3,mnce3,p4,mnce4,p6,mnce6,p7,mnce7,Q,mnceq,0,mncint1*mncint3) multiply ep; if ( count(mnce7,1) ); if ( count(p1.p1,1) < count(p6.p6,1) ) multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,-p3,p3,-p1,p6,-p4,p4,-p6,Q,-Q); if ( count(p1.p1,1) < count(p6.p6,1) ); multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); endif; elseif ( count(p1.p1,1) < count(p4.p4,1) ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p7,-p7,Q,-Q); endif; endif; #call ACCU(Two loop reduction) if ( count(mncint3,1) ); if ( count(mnce7,1) ); if ( count(p1.p1,1) < count(p6.p6,1) ) multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,-p3,p3,-p1,p6,-p4,p4,-p6,Q,-Q); if ( count(p1.p1,1) < count(p6.p6,1) ); multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); endif; elseif ( count(p1.p1,1) < count(p4.p4,1) ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p7,-p7,Q,-Q); endif; id p1.p1 = Q.Q+p6.p6+2*Q.p6; id p1 = Q+p6; if ( count(p6.p6,1) >= 0 ) discard; * Integrate over (6,7)->4 multiply replace_(p6,-mncp9,p7,-p8,p4,-p1,p3,-p2,mnce7,mnce8); multiply mncnaar(p1,mnce1); elseif ( count(mnce1,1) ); if ( count(p7.p7,1) >= 0 ); id p7.p7 = p6.p6+p4.p4-2*p4.p6; id p7 = p6-p4; if ( count(p6.p6,1) >= 0 ) discard; if ( count(p3.p3,1) >= 0 ) discard; if ( count(p4.p4,1) >= 0 ) discard; * Integrate over (6,1)->Q multiply replace_(p6,-mncp9,p1,-p8,mnce1,mnce8,p3,p1,p4,p2); multiply mncnaar(Q,mnceq); elseif ( count(p3.p3,1) >= 0 ); id p3.p3 = Q.Q+p4.p4+2*Q.p4; id p3 = p4+Q; if ( count(p4.p4,1) >= 0 ) discard; * if ( count(p7.p7,1) >= 0 ) discard; * Integrate over (4,7)->6 multiply replace_(p4,-mncp9,p7,p8,p6,-p1,p1,-p2,mnce1,mnce2); multiply mncnaar(p1,mnce1); elseif ( count(p4.p4,1) >= 0 ); id p4.p4 = p3.p3+Q.Q-2*Q.p3; id p4 = p3-Q; if ( count(p3.p3,1) >= 0 ) discard; if ( count(p6.p6,1) >= 0 ) discard; * if ( count(p7.p7,1) >= 0 ) discard; * Integrate over (3,7)->1 * id p7 = -p7; multiply replace_(p3,mncp9,p7,-p8,p6,p2); multiply mncnaar(p1,mnce1); else; id p6.p6 = p4.p4+p7.p7+2*p4.p7; id p6 = p4+p7; if ( count(p4.p4,1) >= 0 ) discard; if ( count(p7.p7,1) >= 0 ) discard; * Integrate over (7,1)->3 multiply replace_(p1,-p8,p7,-mncp9,p3,p1,p4,p2,mnce1,mnce8); multiply mncnaar(p1,mnce1); endif; else; * Here we have no internal fractional power. * 1: order so that p1.p1 has the highest power (or p7.p7). if ( count(p1.p1,1) < count(p6.p6,1) ) multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,-p3,p3,-p1,p6,-p4,p4,-p6,Q,-Q); if ( count(p1.p1,1) < count(p6.p6,1) ) multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); elseif ( count(p1.p1,1) < count(p4.p4,1) ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p7,-p7,Q,-Q); endif; if ( count(p7.p7,1) >= 0 ); id p7.p7 = p1.p1+p3.p3-2*p1.p3; if ( count(p1.p1,1) >= 0 ) discard; if ( count(p3.p3,1) >= 0 ) discard; if ( count(p1.p1,1) < count(p3.p3,1) ) multiply replace_(p1,-p3,p3,-p1,p6,-p4,p4,-p6,Q,-Q); * Integrate over (1,6)->Q multiply replace_(p1,mncp9,p6,p8,p3,p1,p4,p2); multiply mncnaar(Q,mnceq); else; * p1.p1 is missing or positive if ( count(p7.p7,1) >= 0 ) discard; if ( count(p3.p3,1) >= 0 ) discard; id p1.p1 = Q.Q+p6.p6+2*Q.p6; if ( count(p6.p6,1) >= 0 ) discard; * Integrate over (6,7)->4 multiply replace_(p6,-mncp9,p7,-p8,p4,-p1,p3,-p2); multiply mncnaar(p1,mnce1); endif; endif; ToTensor,nosquare,mncFQ,mncp9; endif; #call ACCU2(B mncnaar p8 mncp9 mnce8 mnce9 mncint3 mncFQ,Prepare second loop) Keep brackets; if ( count(mncint3,1) ); if ( count(mncFQ,1) == 0 ); id mncint3/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mnce9^mncy1?*mnce8^mncy2? = mncq1.mncq1^2/mncq1.mncq1^mncx1/mncq1.mncq1^mncx2*mnce3^mncy1*mnce3^mncy2*mnce3*mncG(mncx1,mncy1,mncx2,mncy2,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncint3/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mnce9^mncy1?*mnce8^mncy2?*mncFQ(mnci1?) = mncq1.mncq1^2/mncq1.mncq1^mncx1/mncq1.mncq1^mncx2*mnce3^mncy1*mnce3^mncy2*mnce3*mncG(mncx1,mncy1,mncx2,mncy2,1,0)*mncq1(mnci1); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncint3/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mnce9^mncy1?*mnce8^mncy2?*mncFQ(mnci1?,mnci2?) = mncq1.mncq1^2/mncq1.mncq1^mncx1/mncq1.mncq1^mncx2*mnce3^mncy1*mnce3^mncy2*mnce3*( +mncG(mncx1,mncy1,mncx2,mncy2,2,0)*mncq1(mnci1)*mncq1(mnci2)+mncG(mncx1,mncy1,mncx2,mncy2,2,1)*mncq1.mncq1*d_(mnci1,mnci2)/2); else; id mncint3/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mnce9^mncy1?*mnce8^mncy2?*mncFQ(?a) = mncq1.mncq1^2/mncq1.mncq1^mncx1/mncq1.mncq1^mncx2*mnce3^mncy1*mnce3^mncy2*mnce3 *sum_(mncj,0,integer_(nargs_(?a)/2),mncG(mncx1,mncy1,mncx2,mncy2,nargs_(?a),mncj) *mncy^mncj*mncq1.mncq1^mncj/2^mncj)*mncFQ(?a); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncj?*mncFQ(?a) = distrib_(1,2*mncj,mncdel,mncFQ,?a); tovector,mncFQ,mncq1; id mncnaar(mncq2?,mnce4?) = replace_(mncq1,mncq2,mnce3,mnce4); id mncdel(?a) = dd_(?a); else; id mncnaar(mncq2?,mnce4?) = replace_(mncq1,mncq2,mnce3,mnce4); endif; else; multiply ep; endif; #call ACCU(Second loop) if ( count(mncint1,1) ); #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint1) endif; #call ACCU(Third loop) multiply 1/Q.Q/mnceq^3; #call simplify #endprocedure *--#] dotwo : *--#[ dovert1 : #procedure dovert1(P1,P2,P3) * * P3 = P1+P2 * id g_(mnci1?,`P1',`P2',`P3') = g_(mnci1,`P1')*`P3'.`P3'-g_(mnci1,`P3')*`P1'.`P1'; id g_(mnci1?,`P1',`P3',`P2') = g_(mnci1,`P1')*`P2'.`P2'+g_(mnci1,`P2')*`P1'.`P1'; id g_(mnci1?,`P2',`P1',`P3') = g_(mnci1,`P2')*`P3'.`P3'-g_(mnci1,`P3')*`P2'.`P2'; id g_(mnci1?,`P3',`P2',`P1') = g_(mnci1,`P1')*`P3'.`P3'-g_(mnci1,`P3')*`P1'.`P1'; id g_(mnci1?,`P2',`P3',`P1') = g_(mnci1,`P1')*`P2'.`P2'+g_(mnci1,`P2')*`P1'.`P1'; id g_(mnci1?,`P3',`P1',`P2') = g_(mnci1,`P2')*`P3'.`P3'-g_(mnci1,`P3')*`P2'.`P2'; * id g_(mnci1?,[P+`P1'],`P2',[P+`P3']) = g_(mnci1,[P+`P1'])*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*[P+`P1'].[P+`P1']; id g_(mnci1?,[P+`P1'],[P+`P3'],`P2') = g_(mnci1,[P+`P1'])*`P2'.`P2'+g_(mnci1,`P2')*[P+`P1'].[P+`P1']; id g_(mnci1?,`P2',[P+`P1'],[P+`P3']) = g_(mnci1,`P2')*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*`P2'.`P2'; id g_(mnci1?,[P+`P3'],`P2',[P+`P1']) = g_(mnci1,[P+`P1'])*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*[P+`P1'].[P+`P1']; id g_(mnci1?,`P2',[P+`P3'],[P+`P1']) = g_(mnci1,[P+`P1'])*`P2'.`P2'+g_(mnci1,`P2')*[P+`P1'].[P+`P1']; id g_(mnci1?,[P+`P3'],[P+`P1'],`P2') = g_(mnci1,`P2')*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*`P2'.`P2'; * id g_(mnci1?,`P1',[P+`P2'],[P+`P3']) = g_(mnci1,`P1')*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*`P1'.`P1'; id g_(mnci1?,`P1',[P+`P3'],[P+`P2']) = g_(mnci1,`P1')*[P+`P2'].[P+`P2']+g_(mnci1,[P+`P2'])*`P1'.`P1'; id g_(mnci1?,[P+`P2'],`P1',[P+`P3']) = g_(mnci1,[P+`P2'])*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*[P+`P2'].[P+`P2']; id g_(mnci1?,[P+`P3'],[P+`P2'],`P1') = g_(mnci1,`P1')*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*`P1'.`P1'; id g_(mnci1?,[P+`P2'],[P+`P3'],`P1') = g_(mnci1,`P1')*[P+`P2'].[P+`P2']+g_(mnci1,[P+`P2'])*`P1'.`P1'; id g_(mnci1?,[P+`P3'],`P1',[P+`P2']) = g_(mnci1,[P+`P2'])*[P+`P3'].[P+`P3']-g_(mnci1,[P+`P3'])*[P+`P2'].[P+`P2']; * id g_(mnci1?,[P-`P3'],`P2',[P-`P1']) = g_(mnci1,[P-`P3'])*[P-`P1'].[P-`P1']-g_(mnci1,[P-`P1'])*[P-`P3'].[P-`P3']; id g_(mnci1?,[P-`P3'],[P-`P1'],`P2') = g_(mnci1,[P-`P3'])*`P2'.`P2'+g_(mnci1,`P2')*[P-`P3'].[P-`P3']; id g_(mnci1?,`P2',[P-`P3'],[P-`P1']) = g_(mnci1,`P2')*[P-`P1'].[P-`P1']-g_(mnci1,[P-`P1'])*`P2'.`P2'; id g_(mnci1?,[P-`P1'],`P2',[P-`P3']) = g_(mnci1,[P-`P3'])*[P-`P1'].[P-`P1']-g_(mnci1,[P-`P1'])*[P-`P3'].[P-`P3']; id g_(mnci1?,`P2',[P-`P1'],[P-`P3']) = g_(mnci1,[P-`P3'])*`P2'.`P2'+g_(mnci1,`P2')*[P-`P3'].[P-`P3']; id g_(mnci1?,[P-`P1'],[P-`P3'],`P2') = g_(mnci1,`P2')*[P-`P1'].[P-`P1']-g_(mnci1,[P-`P1'])*`P2'.`P2'; * id g_(mnci1?,`P1',[P-`P3'],[P-`P2']) = g_(mnci1,`P1')*[P-`P2'].[P-`P2']-g_(mnci1,[P-`P2'])*`P1'.`P1'; id g_(mnci1?,`P1',[P-`P2'],[P-`P3']) = g_(mnci1,`P1')*[P-`P3'].[P-`P3']+g_(mnci1,[P-`P3'])*`P1'.`P1'; id g_(mnci1?,[P-`P3'],`P1',[P-`P2']) = g_(mnci1,[P-`P3'])*[P-`P2'].[P-`P2']-g_(mnci1,[P-`P2'])*[P-`P3'].[P-`P3']; id g_(mnci1?,[P-`P2'],[P-`P3'],`P1') = g_(mnci1,`P1')*[P-`P2'].[P-`P2']-g_(mnci1,[P-`P2'])*`P1'.`P1'; id g_(mnci1?,[P-`P3'],[P-`P2'],`P1') = g_(mnci1,`P1')*[P-`P3'].[P-`P3']+g_(mnci1,[P-`P3'])*`P1'.`P1'; id g_(mnci1?,[P-`P2'],`P1',[P-`P3']) = g_(mnci1,[P-`P3'])*[P-`P2'].[P-`P2']-g_(mnci1,[P-`P2'])*[P-`P3'].[P-`P3']; * id g_(mnci1?,`P3',[P-`P2'],[P+`P1']) = g_(mnci1,`P3')*[P+`P1'].[P+`P1']-g_(mnci1,[P+`P1'])*`P3'.`P3'; id g_(mnci1?,`P3',[P+`P1'],[P-`P2']) = g_(mnci1,`P3')*[P-`P2'].[P-`P2']+g_(mnci1,[P-`P2'])*`P3'.`P3'; id g_(mnci1?,[P-`P2'],`P3',[P+`P1']) = g_(mnci1,[P-`P2'])*[P+`P1'].[P+`P1']-g_(mnci1,[P+`P1'])*[P-`P2'].[P-`P2']; id g_(mnci1?,[P+`P1'],[P-`P2'],`P3') = g_(mnci1,`P3')*[P+`P1'].[P+`P1']-g_(mnci1,[P+`P1'])*`P3'.`P3'; id g_(mnci1?,[P-`P2'],[P+`P1'],`P3') = g_(mnci1,`P3')*[P-`P2'].[P-`P2']+g_(mnci1,[P-`P2'])*`P3'.`P3'; id g_(mnci1?,[P+`P1'],`P3',[P-`P2']) = g_(mnci1,[P-`P2'])*[P+`P1'].[P+`P1']-g_(mnci1,[P+`P1'])*[P-`P2'].[P-`P2']; * id g_(mnci1?,[P-`P1'],`P3',[P+`P2']) = g_(mnci1,[P-`P1'])*[P+`P2'].[P+`P2']-g_(mnci1,[P+`P2'])*[P-`P1'].[P-`P1']; id g_(mnci1?,[P-`P1'],[P+`P2'],`P3') = g_(mnci1,[P-`P1'])*`P3'.`P3'+g_(mnci1,`P3')*[P-`P1'].[P-`P1']; id g_(mnci1?,`P3',[P-`P1'],[P+`P2']) = g_(mnci1,`P3')*[P+`P2'].[P+`P2']-g_(mnci1,[P+`P2'])*`P3'.`P3'; id g_(mnci1?,[P+`P2'],`P3',[P-`P1']) = g_(mnci1,[P-`P1'])*[P+`P2'].[P+`P2']-g_(mnci1,[P+`P2'])*[P-`P1'].[P-`P1']; id g_(mnci1?,`P3',[P+`P2'],[P-`P1']) = g_(mnci1,[P-`P1'])*`P3'.`P3'+g_(mnci1,`P3')*[P-`P1'].[P-`P1']; id g_(mnci1?,[P+`P2'],[P-`P1'],`P3') = g_(mnci1,`P3')*[P+`P2'].[P+`P2']-g_(mnci1,[P+`P2'])*`P3'.`P3'; * #endprocedure *--#] dovert1 : *--#[ dovert2 : #procedure dovert2(P1,P2,P3) * * P1 + P2 + P3 = 0 * id g_(mnci1?,`P3',`P2',`P1') = -g_(mnci1,`P3')*`P1'.`P1'-g_(mnci1,`P1')*`P3'.`P3'; id g_(mnci1?,`P3',`P1',`P2') = -g_(mnci1,`P3')*`P2'.`P2'-g_(mnci1,`P2')*`P3'.`P3'; id g_(mnci1?,`P2',`P3',`P1') = -g_(mnci1,`P2')*`P1'.`P1'-g_(mnci1,`P1')*`P2'.`P2'; id g_(mnci1?,`P1',`P2',`P3') = -g_(mnci1,`P3')*`P1'.`P1'-g_(mnci1,`P1')*`P3'.`P3'; id g_(mnci1?,`P2',`P1',`P3') = -g_(mnci1,`P3')*`P2'.`P2'-g_(mnci1,`P2')*`P3'.`P3'; id g_(mnci1?,`P1',`P3',`P2') = -g_(mnci1,`P2')*`P1'.`P1'-g_(mnci1,`P1')*`P2'.`P2'; * #endprocedure *--#] dovert2 : *--#[ expandP : * #procedure expandP(topo,power) * * Expands the denominators in P. * id 1/P.Q = 1/Q.Q/mncproexp; #do mnci = 1,8 id 1/P.p`mnci' = 1/P.p`mnci'/mncproexp; #enddo id P = mncproexp*P; if ( count(mncproexp,1) > `power' ) discard; id mncepexp(mncp?mncpp18[mncn],mncx?) = mncee18[mncn]^mncx/mnceq^mncx; id mncepexp(-mncp?mncpp18[mncn],mncx?) = mncee18[mncn]^mncx/mnceq^mncx; id mncepexp(-mncp?[mncPp],mncx?) = mncepexp(mncp,mncx); id mncepexp([P+Q],mncx?) = mncepexp( mncproexp*2*P.Q/Q.Q,mncx); id mncepexp([P-Q],mncx?) = mncepexp(-mncproexp*2*P.Q/Q.Q,mncx); id mncepexp(mncp?[mncpp18][D],mncx?) = mncee18[D]^mncx/mnceq^mncx *mncepexp( 2*mncproexp*P.mncpp18[D]/mncpp18[D].mncpp18[D],mncx); id mncepexp(mncp?[-mncpp18][D],mncx?) = mncee18[D]^mncx/mnceq^mncx *mncepexp(-2*mncproexp*P.mncpp18[D]/mncpp18[D].mncpp18[D],mncx); #do mnci = 1,8 if ( count([P+p`mnci'].[P+p`mnci'],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P+p`mnci'].[P+p`mnci'] = ( sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.p`mnci'^mncj/ p`mnci'.p`mnci'^mncj*sign_(mncj)))*mncproexp^mncx/p`mnci'.p`mnci'; endrepeat; endif; if ( count([P-p`mnci'].[P-p`mnci'],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P-p`mnci'].[P-p`mnci'] = ( sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.p`mnci'^mncj/ p`mnci'.p`mnci'^mncj))*mncproexp^mncx/p`mnci'.p`mnci'; endrepeat; endif; #enddo if ( count([P+Q].[P+Q],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P+Q].[P+Q] = (sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.Q^mncj/ Q.Q^mncj*sign_(mncj)))*mncproexp^mncx/Q.Q; endrepeat; endif; if ( count([P-Q].[P-Q],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P-Q].[P-Q] = (sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.Q^mncj/Q.Q^mncj)) *mncproexp^mncx/Q.Q; endrepeat; endif; repeat; id,once,mncproexp^mncx?*mncepexp(y?,D?) = sump_(mncj,0,`power'-mncx, y*acc((-D*ep-mncj+1)/mncj))*mncproexp^mncx; if ( count(P.P,1) > 0 ) discard; if ( count(mncproexp,1) > `power' ) discard; endrepeat; if ( count(mncproexp,1) != `power' ) discard; id mncproexp^`power' = 1; #call ACCU(Expand in P) #endprocedure * *--#] expandP : *--#[ finish : #procedure finish(LOOPS,SCHEME) * id ep = 0; * * Substitute the integrals. * id mncexp20*mncexp10 = 1 + ep * ( 3 ) + ep^2 * ( 13 ) + ep^3 * ( 55 - 22*z3 ) + ep^4 * ( 229 - 66*z3 - 33*z4 ) + ep^5 * ( 943 - 286*z3 - 99*z4 - 234*z5 ) + ep^6 * ( 3853 - 1210*z3 + 242*z3^2 - 429*z4 - 702*z5 - 530*z6 ); id mncexp11 = 1 + ep * ( 2 ) + ep^2 * ( 8 ) + ep^3 * ( 32 - 22*z3 ) + ep^4 * ( 128 - 44*z3 - 33*z4 ) + ep^5 * ( 512 - 176*z3 - 66*z4 - 234*z5 ) + ep^6 * ( 2048 - 704*z3 + 242*z3^2 - 264*z4 - 468*z5 - 530*z6 ); id mncexp20 = 1 + ep * ( 2 ) + ep^2 * ( 8 ) + ep^3 * ( 32 - 16*z3 ) + ep^4 * ( 128 - 32*z3 - 24*z4 ) + ep^5 * ( 512 - 128*z3 - 48*z4 - 192*z5 ) + ep^6 * ( 2048 - 512*z3 + 128*z3^2 - 192*z4 - 384*z5 - 440*z6 ); id mncexp10 = 1 + ep * ( 1 ) + ep^2 * ( 3 ) + ep^3 * ( 9 - 6*z3 ) + ep^4 * ( 27 - 6*z3 - 9*z4 ) + ep^5 * ( 81 - 18*z3 - 9*z4 - 42*z5 ) + ep^6 * ( 243 - 54*z3 + 18*z3^2 - 27*z4 - 42*z5 - 90*z6 ); * * Note that in Gorishny,Larin,Surguladze and Tkachov Comp.Phys.Comm. * 55(1989)381 the factor (1-2*ep) is erroneously absent in the * following integral: * id mncG311 = (1-2*ep)*(6*z3+9*z4*ep+102*z5*ep^2); *id mncG311 = (1-2*ep)*(6*z3+9*z4*ep+102*z5*ep^2+240*z6*ep^3-186*ep^3*z3^2); * id mncF321 = 20*z5; *id mncF321 = (20*z5+50*z6*ep+68*z3^2*ep)*(1+2*ep); *id mncF321 = (20*z5+50*z6*ep+68*z3^2*ep+450*z7*ep^2+204*z3*z4*ep^2)*(1+2*ep+4*ep^2); * * Now follow some convenient integrals. * * * The three loop fermion propagator * id mncfermi3 =ep^3*( +cf*ca*nf*(+260075/1296-1/6*ep^-3*mncxi+1/6*ep^-3-13/12*ep^-2*mncxi +227/36*ep^-2+2*ep^-1*z3*mncxi-6*ep^-1*z3-155/24*ep^-1*mncxi +8267/216*ep^-1+61/6*z3*mncxi-137/6*z3+3*z4*mncxi-9*z4-4483/144*mncxi) +cf*ca^2*(-2008997/2592+55/24*ep^-3*mncxi-5/8*ep^-3*mncxi^2+1/12*ep^-3*mncxi^3 -7/4*ep^-3+623/48*ep^-2*mncxi-49/16*ep^-2*mncxi^2+3/8*ep^-2*mncxi^3 -1841/72*ep^-2-18*ep^-1*z3*mncxi+11/8*ep^-1*z3*mncxi^2+83/2*ep^-1*z3 +6869/96*ep^-1*mncxi-497/32*ep^-1*mncxi^2+89/48*ep^-1*mncxi^3 -66629/432*ep^-1-2917/24*z3*mncxi+23*z3*mncxi^2-29/12*z3*mncxi^3+1015/4*z3 -27*z4*mncxi+33/16*z4*mncxi^2+249/4*z4+5*z5*mncxi-5/4*z5*mncxi^2-45*z5 +189061/576*mncxi-4403/64*mncxi^2+49/6*mncxi^3) +cf*nf^2*(-1108/81-4/9*ep^-2-68/27*ep^-1) +cf^2*ca*(-1199/16+9/4*ep^-3*mncxi-3/2*ep^-3*mncxi^2+1/4*ep^-3*mncxi^3-ep^-3 +49/4*ep^-2*mncxi-47/8*ep^-2*mncxi^2+7/8*ep^-2*mncxi^3-43/12*ep^-2 -9*ep^-1*z3*mncxi+3*ep^-1*z3*mncxi^2+2*ep^-1*z3+365/8*ep^-1*mncxi -81/4*ep^-1*mncxi^2+11/4*ep^-1*mncxi^3-93/8*ep^-1-101/4*z3*mncxi +3/2*z3*mncxi^2+3/4*z3*mncxi^3+23*z3-27/2*z4*mncxi+9/2*z4*mncxi^2+3*z4 +20*z5*mncxi+2147/16*mncxi-217/4*mncxi^2+27/4*mncxi^3) +cf^2*nf*(+163/8-1/2*ep^-2*mncxi-1/6*ep^-2-9/4*ep^-1*mncxi+11/12*ep^-1 -16*z3-67/8*mncxi) +cf^3*(+79/48+1/2*ep^-3*mncxi-1/2*ep^-3*mncxi^2+1/6*ep^-3*mncxi^3-1/6*ep^-3 +3/4*ep^-2*mncxi-3/2*ep^-2*mncxi^2+1/2*ep^-2*mncxi^3+1/4*ep^-2+13/8*ep^-1*mncxi -3*ep^-1*mncxi^2+ep^-1*mncxi^3-1/8*ep^-1-5/2*z3*mncxi-7/2*z3*mncxi^2 +7/6*z3*mncxi^3+29/6*z3+103/16*mncxi-3*mncxi^2+mncxi^3)) +2*mncfermi2*mncfermi1-mncfermi1^3; * * The two loop fermion propagator * id mncfermi2 = +cf*ca*(-1+5/4*mncxi-1/4*mncxi^2-25/4*ep+15/4*ep*mncxi-5/8*ep*mncxi^2 -175/8*ep^2+55/4*ep^2*mncxi-17/8*ep^2*mncxi^2+6*ep^2*z3-3*ep^2*z3*mncxi -1165/16*ep^3+175/4*ep^3*mncxi-53/8*ep^3*mncxi^2 +50/3*ep^3*z3-49/3*ep^3*z3*mncxi+8/3*ep^3*z3*mncxi^2 +9*ep^3*z4-9/2*ep^3*z4*mncxi) +cf*nf*(+1/2*ep+7/4*ep^2+53/8*ep^3) +cf^2*(+1/2-mncxi+1/2*mncxi^2+7/4*ep-2*ep*mncxi+ep*mncxi^2+29/8*ep^2-6*ep^2*mncxi +3*ep^2*mncxi^2+79/16*ep^3-18*ep^3*mncxi+9*ep^3*mncxi^2+2/3*ep^3*z3 +32/3*ep^3*z3*mncxi-16/3*ep^3*z3*mncxi^2); * * The one loop fermion propagator in QCD (times ep) * id mncfermi1 = cf*(mncxi-1)*(1+ep+2*ep^2-7/3*ep^3*z3+4*ep^3); * * The two loop ghost propagator * id mncghost2 = +ca*nf*(-1/4-7/8*ep-53/16*ep^2-351/32*ep^3+8/3*ep^3*z3) +ca^2*(+5/4+7/16*mncxi-1/32*mncxi^2+83/16*ep+7/32*ep*mncxi +599/32*ep^2-9/64*ep^2*mncxi+3/8*ep^2*mncxi^2-3/4*ep^2*z3-3/16*ep^2*z3*mncxi^2 +3881/64*ep^3-383/128*ep^3*mncxi+17/8*ep^3*mncxi^2 -40/3*ep^3*z3-85/24*ep^3*z3*mncxi-29/48*ep^3*z3*mncxi^2 -9/8*ep^3*z4-9/32*ep^3*z4*mncxi^2); * * The one loop ghost propagator (times ep) * id mncghost1 = ca*(1/2+1/4*mncxi+ep+2*ep^2-7/12*ep^3*z3*mncxi-7/6*ep^3*z3+4*ep^3); * * The three loop gluon propagator * id mncgluon3 = ep^3*( + cf*ca*nf*(-416699/648-1/2*ep^-2*mncxi-131/18*ep^-2+4*ep^-1*z3 *mncxi+68*ep^-1*z3-49/12*ep^-1*mncxi-9551/108*ep^-1+26/3*z3*mncxi+ 358*z3+6*z4*mncxi+102*z4+40*z5-1309/72*mncxi) + cf*nf^2*(11536/81+16/9*ep^-2-16*ep^-1*z3+566/27*ep^-1-256/ 3*z3-24*z4) + cf^2*nf*(143/9+1/3*ep^-1+148/3*z3-80*z5) + ca*nf^2*(475477/1944+2/9*ep^-3*mncxi+31/9*ep^-3+14/27*ep^-2*mncxi +1021/54*ep^-2+8*ep^-1*z3+22/27*ep^-1*mncxi+8003/108*ep^-1-26/ 3*z3*mncxi-5/3*z3+12*z4+586/243*mncxi) + ca^2*nf*(-3265189/2592-73/36*ep^-3*mncxi-155/12*ep^-3-947/216 *ep^-2*mncxi-1/24*ep^-2*mncxi^2-16451/216*ep^-2+2/3*ep^-1*z3*mncxi-89/ 3*ep^-1*z3-2299/432*ep^-1*mncxi-121/144*ep^-1*mncxi^2-144949/432* ep^-1+2735/36*z3*mncxi+13/12*z3*mncxi^2+1913/36*z3+z4*mncxi-89/2*z4 +80/3*z5+14435/7776*mncxi-5503/864*mncxi^2) + ca^3*(99584761/46656+665/144*ep^-3*mncxi+3325/216*ep^-3+5455/ 864*ep^-2*mncxi+37/24*ep^-2*mncxi^2-47/96*ep^-2*mncxi^3+1/16*ep^-2*mncxi^4 +14017/144*ep^-2-379/24*ep^-1*z3*mncxi-1/16*ep^-1*z3*mncxi^2-77/6* ep^-1*z3-1519/192*ep^-1*mncxi+281/18*ep^-1*mncxi^2-757/192*ep^-1*mncxi^3 +15/32*ep^-1*mncxi^4+1266119/2592*ep^-1-23483/144*z3*mncxi-247/24* z3*mncxi^2+59/32*z3*mncxi^3-13/96*z3*mncxi^4-73711/216*z3-379/16*z4*mncxi -3/32*z4*mncxi^2-77/4*z4+505/24*z5*mncxi-55/24*z5*mncxi^2-15/16*z5* mncxi^3+35/192*z5*mncxi^4-655/12*z5-4628509/31104*mncxi+178133/1728* mncxi^2-8873/384*mncxi^3+493/192*mncxi^4) + nf^3*(-11656/729-8/27*ep^-3-40/27*ep^-2-424/81*ep^-1+56/ 27*z3) ); * * The two loop gluon propagator * id mncgluon2 = +nf^2*(+4/9+40/27*ep+4*ep^2+2432/243*ep^3-56/27*ep^3*z3) +cf*nf*(-ep-55/6*ep^2+8*z3*ep^2-1711/36*ep^3+76/3*ep^3*z3+12*ep^3*z4) +ca*nf*(-55/18-1/3*mncxi-1199/108*ep-2/9*ep*mncxi-2371/72*ep^2 +5/27*ep^2*mncxi-4*ep^2*z3-337315/3888*ep^3+37/81*ep^3*mncxi +286/27*ep^3*z3+50/9*ep^3*z3*mncxi-6*ep^3*z4) +ca^2*(+175/36+35/24*mncxi+4229/216*ep-97/144*ep*mncxi+5/8*ep*mncxi^2 -1/8*ep*mncxi^3+9821/144*ep^2-6121/864*ep^2*mncxi+27/8*ep^2*mncxi^2 -9/16*ep^2*mncxi^3-ep^2*z3-2*ep^2*z3*mncxi+1659373/7776*ep^3 -165073/5184*ep^3*mncxi+113/8*ep^3*mncxi^2-33/16*ep^3*mncxi^3 -1184/27*ep^3*z3-134/9*ep^3*z3*mncxi-3/2*ep^3*z3*mncxi^2 -3/2*ep^3*z4-3*ep^3*z4*mncxi); * * The one loop gluon propagator * id mncgluon1 = +ca*(5/3+mncxi/2-ep*mncxi+ep*mncxi^2/4+31/9*ep-2*ep^2*mncxi+ep^2*mncxi^2/2+188/27*ep^2 -7/6*ep^3*z3*mncxi-35/9*ep^3*z3-4*ep^3*mncxi+ep^3*mncxi^2+1132/81*ep^3) +nf*(-2/3-10/9*ep-56/27*ep^2+14/9*ep^3*z3-328/81*ep^3); id ep = 0; * .sort: Sub integrals; * * The next factor is the conversion to MS-bar. Because there are three * loops we need the factor (1/(1-2*ep)-7/3*ep^3*z3+...)^3 * We have multiplied it out here. * Note also that somehow the original Mincer program has a different * normalization for mncG311, using effectively only two powers. * For the comparison we have corrected that in subint.prc * This may have to be changed as it isn't clear to me why this has * been done! (But the factor 1-2*ep was needed to get the answer to * come out right) * #if `SCHEME' == 0 * * This is MS-bar * #message Answer in MS-bar #if `LOOPS' == 0 #else #if `LOOPS' == 1 multiply,1+2*ep+4*ep^2+8*ep^3-7/3*ep^3*z3; #else #if `LOOPS' == 2 multiply,1+4*ep+12*ep^2+32*ep^3-14/3*ep^3*z3; #else #if `LOOPS' == 3 multiply,1+6*ep+24*ep^2+80*ep^3-7*ep^3*z3; #else #message Illegal number of loops specified: 'LOOPS' #message Answer will be in the G-scheme anyway #endif #endif #endif #endif #else #if ( `SCHEME' != 1 ) #message Invalid value `SCHEME' for output corrected to G-scheme #else #message Answer in the G-scheme #endif #endif id ep = 0; #endprocedure *--#] finish : *--#[ gtreat : #procedure gtreat(POWER) Multiply d_(MU,NU)/Q.Q; sum mu,mu1,nu,nu1,MU,NU,ga1,ga2,ro,ro1,si,si1,ka,ka1,la,la1; id mncVv(mnci1?,p1?,mnci2?,p2?) = p1(11)*p2(mnci2)-p1(mnci2)*p2(mnci1); *print +f +s; .sort id Glonel(mu?,ro?,Q?,p1?,p2?) = (-1)*nf/2 *mncSS(mu,p1,ro,-p2) +1/2*ca *mncV3G(mu,Q,ga4,-p2,ga2,-p1)*mncV3G(ro,-Q,ga3,p1,ga5,p2) *mncDg(ga4,ga5,p2)*mncDg(ga2,ga3,p1) +(-1)*ca *mncVgh(p1,ro)*(-mncVgh(p2,mu))*mncDs(p1)*mncDs(p2); .sort repeat; id mncS(mnci1?index_,?a) = g_(1,mnci1)*mncS(?a); id mncS(mncp?,?a) = g_(1,mncp) *mncS(?a)*mncpropxp(mncp); endrepeat; id mncS = 1; repeat; id mncSS(mnci1?index_,?a) = g_(2,mnci1)*mncSS(?a); id mncSS(mncp?,?a) = g_(2,mncp) *mncSS(?a)*mncpropxp(mncp); endrepeat; id mncSS = 1; repeat; id mncSSS(mnci1?index_,?a) = g_(3,mnci1)*mncSSS(?a); id mncSSS(mncp?,?a) = g_(3,mncp) *mncSSS(?a)*mncpropxp(mncp); endrepeat; id mncSSS = 1; id mncVgh(mncp?,mu?) = mncp(mu); id mncDs(mncp?) = mncpropxp(mncp); id mncDL(mnci1?,mnci2?,mncp?) = (d_(mnci1,mnci2)-mncp(mnci1)*mncp(mnci2)*mncpropxp(mncp))*mncpropxp(mncp); #call vertsub #call ACCU(Vertex substitutions) id mncpropxp(mncp?) = 1/mncp.mncp; *#call reduceto(`TOPO') *id g_(1,P,Q,[P+Q]) = [P+Q].[P+Q]*g_(1,P); #call sym1(`TOPO') id P.P = 0; id D = acc(4-2*ep); #call ACCU(Vertex identities) *tracen,3; *tracen,2; *tracen,1; *id P.P = 0; *id D = acc(4-2*ep); *id [D-4] = acc(-2*ep); *id [1-ep/2] = acc(1-ep/2); *#call ACCU(Traces) #do mnci = 1,8 id [P+p`mnci'] = P+p`mnci'; id [P-p`mnci'] = P-p`mnci'; #enddo id [P+Q] = P+Q; id [P-Q] = P-Q; id P.P = 0; #call ACCU(Introduce P) #call momsubs(`TOPO') #call ACCU(moms) id P = mncproexp*P; if ( count(mncproexp,1) > `POWER' ) discard; #do mnci = 1,8 repeat id,once,mncproexp^mncx?/[P+p`mnci'].[P+p`mnci'] = sump_(mncj,0,`POWER'-mncx,-2*mncproexp*P.p`mnci'/p`mnci'.p`mnci')*mncproexp^mncx/p`mnci'.p`mnci'; repeat id,once,mncproexp^mncx?/[P-p`mnci'].[P-p`mnci'] = sump_(mncj,0,`POWER'-mncx, 2*mncproexp*P.p`mnci'/p`mnci'.p`mnci')*mncproexp^mncx/p`mnci'.p`mnci'; #enddo repeat id,once,mncproexp^mncx?/[P-Q].[P-Q] = sump_(mncj,0,`POWER'-mncx, 2*mncproexp*P.Q/Q.Q)*mncproexp^mncx/Q.Q; repeat id,once,mncproexp^mncx?/[P+Q].[P+Q] = sump_(mncj,0,`POWER'-mncx,-2*mncproexp*P.Q/Q.Q)*mncproexp^mncx/Q.Q; if ( count(mncproexp,1) != `POWER' ) discard; id mncproexp^`POWER' = 1; #call ACCU(Expand in P) #call momsubs(`TOPO') #call sym2(`TOPO') #call ACCU(moms) #call harmo(P,Q,mncFFPP) #call ACCU(Harmonics) #endprocedure *--#] gtreat : *--#[ harmo : #procedure harmo(P,Q,TT) * * Routine to generate the harmonic projection for * P(mnci1)*P(mnci2)*...*P(in) = TT(mnci1,mnci2,...,in) at P->Q * The object mnchfac is a table to give better speed. * id `P'.`P' = 0; id `Q'.`P' = `Q'.`Q'; ToTensor,nosquare,`TT',`P'; * * Next generate the splits between indices that connect to a Q and * the indices that go to d_. * id `TT'(?a) = sum_(mncj,0,nargs_(?a),2,`Q'.`Q'^(mncj/2)* acc(mnchfac(nargs_(?a),mncj))*distrib_(1,mncj,mncdd,`TT',?a)); * * The indices in TT contract with Q and the indices in mncdd go to d_'mncs. * We used mncdd as an intemediary to have the mnchfac worked out before * the dd_ is expanded. At that moment there are fewer terms. * tovector,`TT',`Q'; id mncdd(?a) = dd_(?a); id D = acc(4-2*ep); * #endprocedure * * Table is good up to D30 or P28. * We have only terms up to ep^3 as the integrals at this point can have * divergences up to ep^-3 only. * CTable,relax,mnchfac(0:30,0:30); Fill mnchfac(0,0) = 1; Fill mnchfac(1,0) = 1; Fill mnchfac(2,0) = 4/3 + 2/9*ep + 4/27*ep^2 + 8/81*ep^3; Fill mnchfac(2,2) = - 1/3 - 2/9*ep - 4/27*ep^2 - 8/81*ep^3; Fill mnchfac(3,0) = 2 + 2/3*ep + 4/9*ep^2 + 8/27*ep^3; Fill mnchfac(3,2) = - 1/3 - 2/9*ep - 4/27*ep^2 - 8/81*ep^3; Fill mnchfac(4,0) = 16/5 + 116/75*ep + 1196/1125*ep^2 + 12176/16875*ep^3; Fill mnchfac(4,2) = - 2/5 - 22/75*ep - 232/1125*ep^2 - 2392/16875*ep^3; Fill mnchfac(4,4) = 1/15 + 16/225*ep + 196/3375*ep^2 + 2176/50625*ep^3; Fill mnchfac(5,0) = 16/3 + 148/45*ep + 1588/675*ep^2 + 16528/10125*ep^3; Fill mnchfac(5,2) = - 8/15 - 98/225*ep - 1088/3375*ep^2 - 11528/50625*ep^3; Fill mnchfac(5,4) = 1/15 + 16/225*ep + 196/3375*ep^2 + 2176/50625*ep^3; Fill mnchfac(6,0) = 64/7 + 1648/245*ep + 129016/25725*ep^2 + 9613672/2701125*ep^3; Fill mnchfac(6,2) = - 16/21 - 1516/2205*ep - 123292/231525*ep^2 - 9367864/24310125*ep^3; Fill mnchfac(6,4) = 8/105 + 926/11025*ep + 81092/1157625*ep^2 + 6386864/121550625*ep^3; Fill mnchfac(6,6) = - 1/105 - 142/11025*ep - 13864/1157625*ep^2 - 1162288/121550625*ep^3; Fill mnchfac(7,0) = 16 + 472/35*ep + 38464/3675*ep^2 + 2929288/385875*ep^3; Fill mnchfac(7,2) = - 8/7 - 276/245*ep - 23372/25725*ep^2 - 1815224/2701125*ep^3; Fill mnchfac(7,4) = 2/21 + 242/2205*ep + 21764/231525*ep^2 + 1742288/24310125*ep^3; Fill mnchfac(7,6) = - 1/105 - 142/11025*ep - 13864/1157625*ep^2 - 1162288/121550625*ep^3; Fill mnchfac(8,0) = 256/9 + 75808/2835*ep + 19246768/893025*ep^2 + 4489358368/281302875*ep^3; Fill mnchfac(8,2) = - 16/9 - 5368/2835*ep - 1414288/893025*ep^2 - 336272488/281302875*ep^3; Fill mnchfac(8,4) = 8/63 + 3044/19845*ep + 844124/6251175*ep^2 + 206121824/1969120125*ep^3; Fill mnchfac(8,6) = - 2/189 - 866/59535*ep - 256496/18753525*ep^2 - 64996496/5907360375* ep^3; Fill mnchfac(8,8) = 1/945 + 496/297675*ep + 159496/93767625*ep^2 + 42546496/29536801875*ep^3; Fill mnchfac(9,0) = 256/5 + 82976/1575*ep + 21820976/496125*ep^2 + 5190442976/156279375*ep^3; Fill mnchfac(9,2) = - 128/45 - 45968/14175*ep - 12519368/4465125*ep^2 - 3033399368/ 1406514375*ep^3; Fill mnchfac(9,4) = 8/45 + 3188/14175*ep + 907988/4465125*ep^2 + 225339488/1406514375*ep^3; Fill mnchfac(9,6) = - 4/315 - 1774/99225*ep - 533824/31255875*ep^2 - 136691824/9845600625* ep^3; Fill mnchfac(9,8) = 1/945 + 496/297675*ep + 159496/93767625*ep^2 + 42546496/29536801875*ep^3; Fill mnchfac(10,0) = 1024/11 + 3941248/38115*ep + 11779286528/132068475*ep^2 + 31395360315808/ 457617265875*ep^3; Fill mnchfac(10,2) = - 256/55 - 1074016/190575*ep - 3316968176/660342375*ep^2 - 8998169551936/2288086329375*ep^3; Fill mnchfac(10,4) = 128/495 + 586288/1715175*ep + 1884204968/5943081375*ep^2 + 5224503688648/ 20592776964375*ep^3; Fill mnchfac(10,6) = - 8/495 - 40108/1715175*ep - 135134588/5943081375*ep^2 - 385061648968/ 20592776964375*ep^3; Fill mnchfac(10,8) = 4/3465 + 22034/12006225*ep + 78474124/41601569625*ep^2 + 231375515864/ 144149438750625*ep^3; Fill mnchfac(10,10) = - 1/10395 - 6086/36018675*ep - 23133196/124804708875*ep^2 - 71203299656/ 432448316251875*ep^3; Fill mnchfac(11,0) = 512/3 + 2105024/10395*ep + 6484548064/36018675*ep^2 + 17587269036704/ 124804708875*ep^3; Fill mnchfac(11,2) = - 256/33 - 1133152/114345*ep - 3599216912/396205425*ep^2 - 9927387845632/1372851797625*ep^3; Fill mnchfac(11,4) = 64/165 + 305464/571725*ep + 1005647504/1981027125*ep^2 + 2830303821544/ 6864258988125*ep^3; Fill mnchfac(11,6) = - 32/1485 - 165052/5145525*ep - 566368772/17829244125*ep^2 - 1633203887992/61778330893125*ep^3; Fill mnchfac(11,8) = 2/1485 + 11182/5145525*ep + 40241252/17829244125*ep^2 + 119504735272/ 61778330893125*ep^3; Fill mnchfac(11,10) = - 1/10395 - 6086/36018675*ep - 23133196/124804708875*ep^2 - 71203299656/ 432448316251875*ep^3; Fill mnchfac(12,0) = 4096/13 + 231932416/585585*ep + 9552620306048/26377676325*ep^2 + 342403963966857664/1188182430059625*ep^3; Fill mnchfac(12,2) = - 512/39 - 30913472/1756755*ep - 1310118983776/79133028975*ep^2 - 47718354631206368/3564547290178875*ep^3; Fill mnchfac(12,4) = 256/429 + 16505056/19324305*ep + 722647696208/870463318725*ep^2 + 26818419631574944/39210020191967625*ep^3; Fill mnchfac(12,6) = - 64/2145 - 4414552/96621525*ep - 200547273536/4352316593625*ep^2 - 7607970101536648/196050100959838125*ep^3; Fill mnchfac(12,8) = 32/19305 + 2367436/869593725*ep + 112122653948/39170849342625*ep^2 + 4365158933778064/1764450908638543125*ep^3; Fill mnchfac(12,10) = - 2/19305 - 159226/869593725*ep - 7904207768/39170849342625*ep^2 - 317328063224824/1764450908638543125*ep^3; Fill mnchfac(12,12) = 1/135135 + 86048/6087156075*ep + 4505822764/274195945398375*ep^2 + 187659001098752/12351156360469801875*ep^3; Fill mnchfac(13,0)= 4096/7+244097536/315315*ep+10319742128768/14203364175*ep^2+ 375711675205023424/639790539262875*ep^3; Fill mnchfac(13,2)= -2048/91-129145088/4099095*ep-5607358794304/184643734275*ep^2- 207285335824775072/8317277010417375*ep^3; Fill mnchfac(13,4)= 256/273+17104096/12297285*ep+765124349648/553931202825*ep^2+ 28782752505588064/24951831031252125*ep^3; Fill mnchfac(13,6)= -128/3003-9076208/135270135*ep-419729246584/6093243231075*ep^2- 16110167517555512/274470141343773375*ep^3; Fill mnchfac(13,8)= 32/15015+2413196/676350675*ep+115802553028/30466216155375*ep^2+ 4549174479503504/1372350706718866875*ep^3; Fill mnchfac(13,10)= -16/135135-1286678/6087156075*ep-64341099904/274195945398375*ep^2- 2596614444771272/12351156360469801875*ep^3; Fill mnchfac(13,12)= 1/135135+86048/6087156075*ep+4505822764/274195945398375*ep^2+ 187659001098752/12351156360469801875*ep^3; Fill mnchfac(14,0)= 16384/15+1022076928/675675*ep+8855205451264/6087156075*ep^2+ 1635953439324307456/1370979726991875*ep^3; Fill mnchfac(14,2)= -4096/105-268698112/4729725*ep-2386708597888/42610092525*ep^2- 447384534399600064/9596858088943125*ep^3; Fill mnchfac(14,4)= 2048/1365+141445376/61486425*ep+1291375944512/553931202825*ep^2+ 246065355438470432/124759155156260625*ep^3; Fill mnchfac(14,6)= -256/4095-18641632/184459275*ep-175417198288/1661793608475*ep^2- 34050530970176704/374277465468781875*ep^3; Fill mnchfac(14,8)= 128/45045+9844976/2029052025*ep+95771634488/18279729693225*ep^2+ 18986189701230152/4117052120156600625*ep^3; Fill mnchfac(14,10)= -32/225225-2605388/10145260125*ep-131450513356/456993242330625*ep^2- 1067733252543928/4117052120156600625*ep^3; Fill mnchfac(14,12)= 16/2027025+1382774/91307341125*ep+72646040548/4112939180975625*ep^2+ 606585312860512/37053469081409405625*ep^3; Fill mnchfac(14,14)= -1/2027025-92054/91307341125*ep-5058699088/4112939180975625*ep^2- 43608309564256/37053469081409405625*ep^3; Fill mnchfac(15,0)= 2048+133140992/45045*ep+5900508278272/2029052025*ep^2+ 221097615608542592/91398648466125*ep^3; Fill mnchfac(15,2)= -1024/15-69645568/675675*ep-631879955968/6087156075*ep^2- 120036485343130816/1370979726991875*ep^3; Fill mnchfac(15,4)= 256/105+18235072/4729725*ep+169704257824/42610092525*ep^2+ 32739238583526304/9596858088943125*ep^3; Fill mnchfac(15,6)= -128/1365-9561056/61486425*ep-18295588144/110786240565*ep^2- 17954474614737152/124759155156260625*ep^3; Fill mnchfac(15,8)= 16/4095+1255192/184459275*ep+12377077984/1661793608475*ep^2+ 2476611609254344/374277465468781875*ep^3; Fill mnchfac(15,10)= -8/45045-660356/2029052025*ep-6729370556/18279729693225*ep^2- 1376089666761272/4117052120156600625*ep^3; Fill mnchfac(15,12)= 2/225225+174098/10145260125*ep+9195937636/456993242330625*ep^2+ 77089103554336/4117052120156600625*ep^3; Fill mnchfac(15,14)= -1/2027025-92054/91307341125*ep-5058699088/4112939180975625*ep^2- 43608309564256/37053469081409405625*ep^3; Fill mnchfac(16,0)= 65536/17+75196264448/13018005*ep+57875871822457856/9968732598825*ep^2+ 37362483254848926620672/7633706518539226125*ep^3; Fill mnchfac(16,2)= -2048/17-2447901184/13018005*ep-1925778310087168/9968732598825*ep^2- 1259745953440522719616/7633706518539226125*ep^3; Fill mnchfac(16,4)= 1024/255+1276226816/195270075*ep+41121672409088/5981239559295*ep^2+ 682355539174170147008/114505597778088391875*ep^3; Fill mnchfac(16,6)= -256/1785-333059264/1366890525*ep-55045592329888/209343384575325*ep^2- 185643166225862781152/801539184446618743125*ep^3; Fill mnchfac(16,8)= 128/23205+174069472/17769576825*ep+29573508614576/2721463999479225*ep^2 +101531720737639386976/10420009397806043660625*ep^3; Fill mnchfac(16,10)= -16/69615-22779704/53308730475*ep-3987420244048/8164391998437675*ep^2- 13963726285198013672/31260028193418130981875*ep^3; Fill mnchfac(16,12)= 8/765765+11946772/586396035225*ep+432009005716/17961662396562885*ep^2+ 7733720815921990336/343860310127599440800625*ep^3; Fill mnchfac(16,14)= -2/3828825-3139846/2931980176125*ep-2940494702944/2245207799570360625* ep^2-86344119864019552/68772062025519888160125*ep^3; Fill mnchfac(16,16)= 1/34459425+1655008/26387821585125*ep+1611063707152/20206870196133245625 *ep^2+243275770764654464/3094742791148394967205625*ep^3; Fill mnchfac(17,0)= 65536/9+77820325888/6891885*ep+61109998518578176/5277564317025*ep^2+ 39955008832559536602112/4041374039226649125*ep^3; Fill mnchfac(17,2)= -32768/153-40386197504/117162045*ep-32374195525856768/89718593389425* ep^2-21435800053741986415616/68703358666853035125*ep^3; Fill mnchfac(17,4)= 1024/153+1311077632/117162045*ep+1074442195362304/89718593389425*ep^2+ 721291890912662995648/68703358666853035125*ep^3; Fill mnchfac(17,6)= -512/2295-681676928/1757430675*ep-114404277306496/269155780168275*ep^2- 389848209260201134304/1030550380002795526875*ep^3; Fill mnchfac(17,8)= 128/16065+177420512/12302014725*ep+30541961017648/1884090461177925*ep^2 +105814896878864290976/7213852660019568688125*ep^3; Fill mnchfac(17,10)= -64/208845-92480176/159926191425*ep-3272097892456/4898635199062605*ep^2 -57726021598310162488/93780084580254392945625*ep^3; Fill mnchfac(17,12)= 8/626535+12070532/479778574275*ep+2199114365068/73479527985939075*ep^2+ 7917421371358060736/281340253740763178836875*ep^3; Fill mnchfac(17,14)= -4/6891885-6313726/5277564317025*ep-1187463189632/808274807845329825* ep^2-4372036935410188768/3094742791148394967205625*ep^3; Fill mnchfac(17,16)= 1/34459425+1655008/26387821585125*ep+1611063707152/20206870196133245625 *ep^2+243275770764654464/3094742791148394967205625*ep^3; Fill mnchfac(18,0)= 262144/19+2034644402176/92147055*ep+30936861817158135808/ 1340696801869425*ep^2+389006823534136572381927424/ 19506515043187264467375*ep^3; Fill mnchfac(18,2)= -65536/171-1578956541952/2487970485*ep-24478928777902468096/ 36198813650474475*ep^2-311541619373746828516953088/ 526675906166056140619125*ep^3; Fill mnchfac(18,4)= 32768/2907+817522927616/42295498245*ep+12939145474166025728/ 615379832058066075*ep^2+166844842036665778207913984/ 8953490404822954390525125*ep^3; Fill mnchfac(18,6)= -1024/2907-26478761728/42295498245*ep-428426650475075584/ 615379832058066075*ep^2-5603489347772047996313152/ 8953490404822954390525125*ep^3; Fill mnchfac(18,8)= 512/43605+13736004992/634432473675*ep+45507364852724608/ 1846139496174198225*ep^2+3022448339780186174642336/ 134302356072344315857876875*ep^3; Fill mnchfac(18,10)= -128/305235-3567025568/4441027315725*ep-12118249261002736/ 12922976473219387575*ep^2-818581689145647773134784/ 940116492506410211005138125*ep^3; Fill mnchfac(18,12)= 64/3968055+1855141264/57733355104425*ep+6474377595893864/ 167998694151852038475*ep^2+445521299740006052164792/ 12221514402583332743066795625*ep^3; Fill mnchfac(18,14)= -8/11904165-241592348/173200065313275*ep-867881471536036/ 503996082455556115425*ep^2-60951525736652864663624/ 36664543207749998229200386875*ep^3; Fill mnchfac(18,16)= 4/130945815+126086914/1905200718446025*ep+467295389736836/ 5543956907011117269675*ep^2+33566185881196766955112/ 403309975285249980521204255625*ep^3; Fill mnchfac(18,18)= -1/654729075-32976682/9526003592230125*ep-632098776065332/ 138598922675277931741875*ep^2-1862244159376232552168/ 403309975285249980521204255625*ep^3; Fill mnchfac(19,0)= 131072/5+1047433306112/24249225*ep+16213367928007141376/352814947860375 *ep^2+206247925186001974627463168/5133293432417701175625*ep^3; Fill mnchfac(19,2)= -65536/95-540445044736/460735275*ep-8520537863685833728/ 6703484009347125*ep^2-109648692270186369778453504/ 97532575215936322336875*ep^3; Fill mnchfac(19,4)= 16384/855+418577093632/12439852425*ep+6728742401875323136/ 180994068252372375*ep^2+87675412151643615089592448/ 2633379530830280703095625*ep^3; Fill mnchfac(19,6)= -8192/14535-216299710976/211477491225*ep-3549492390075026048/ 3076899160290330375*ep^2-46875556885329468963107264/ 44767452024114771952625625*ep^3; Fill mnchfac(19,8)= 256/14535+6992158528/211477491225*ep+117279928141637344/ 3076899160290330375*ep^2+1571509178872435748461792/ 44767452024114771952625625*ep^3; Fill mnchfac(19,10)= -128/218025-3620235296/3172162368375*ep-62151480080644496/ 46153487404354955625*ep^2-169207919683712107074304/ 134302356072344315857876875*ep^3; Fill mnchfac(19,12)= 32/1526175+938314904/22205136578625*ep+16513016129930384/ 323074411830484689375*ep^2+45734218580042122048168/ 940116492506410211005138125*ep^3; Fill mnchfac(19,14)= -16/19840275-487064572/288666775522125*ep-8801628298624732/ 4199967353796300961875*ep^2-24837256966756922410232/ 12221514402583332743066795625*ep^3; Fill mnchfac(19,16)= 2/59520825+63307994/866000326566375*ep+1176962026868324/ 12599902061388902885625*ep^2+3390061290904475641768/ 36664543207749998229200386875*ep^3; Fill mnchfac(19,18)= -1/654729075-32976682/9526003592230125*ep-632098776065332/ 138598922675277931741875*ep^2-1862244159376232552168/ 403309975285249980521204255625*ep^3; Fill mnchfac(20,0)= 1048576/21+1721904332800/20369349*ep+27108206457847021568/ 296364556202715*ep^2+348687951609134651084066816/4311966483230868987525 *ep^3; Fill mnchfac(20,2)= -131072/105-1107974152192/509233725*ep-17748654471475030016/ 7409113905067875*ep^2-230841703227490779469733888/ 107799162080771724688125*ep^3; Fill mnchfac(20,4)= 65536/1995+570715467776/9675440775*ep+9311361165919003648/ 140773164196289625*ep^2+122551166096965355563377664/ 2048184079534662769074375*ep^3; Fill mnchfac(20,6)= -16384/17955-441279910912/261236900925*ep-7340210736028754176/ 3800875433299819875*ep^2-97846521962236578888650368/ 55300970147435894765008125*ep^3; Fill mnchfac(20,8)= 8192/305235+227651119616/4441027315725*ep+3864941716993328768/ 64614882366096937875*ep^2+52231090674315614837061824/ 940116492506410211005138125*ep^3; Fill mnchfac(20,10)= -256/305235-7346890048/4441027315725*ep-127460293274449504/ 64614882366096937875*ep^2-1748127083454042192669472/ 940116492506410211005138125*ep^3; Fill mnchfac(20,12)= 128/4578525+3797601056/66615409735875*ep+67413701935912016/ 969223235491454068125*ep^2+187890548556019147716448/ 2820349477519230633015414375*ep^3; Fill mnchfac(20,14)= -32/32049675-982656344/466307868151125*ep-17874653546120864/ 6784562648440178476875*ep^2-50687892815892781571944/ 19742446342634614431107900625*ep^3; Fill mnchfac(20,16)= 16/416645775+509235292/6062002285964625*ep+9507260365690372/ 88199314429722320199375*ep^2+5494408412188431592816/ 51330360490849997520880541625*ep^3; Fill mnchfac(20,18)= -2/1249937325-66079334/18186006857893875*ep-1268526177612104/ 264597943289166960598125*ep^2-3741613024610828471704/ 769955407362749962813208124375*ep^3; Fill mnchfac(20,20)= 1/13749310575+34362352/200046075436832625*ep+679713656361172/ 2910577376180836566579375*ep^2+2050615923818229593216/ 8469509480990249590945289368125*ep^3; Fill mnchfac(21,0)= 1048576/11+588644679680/3556553*ep+28250985333859155968/155238577058565 *ep^2+367273591924227707607535616/2258649110263788517275*ep^3; Fill mnchfac(21,2)= -524288/231-907183357952/224062839*ep-14754021048736251904/ 3260010118229865*ep^2-193858898135415034891675648/ 47431631315539558862775*ep^3; Fill mnchfac(21,4)= 65536/1155+582881570816/5601570975*ep+9645295946232275968/ 81500252955746625*ep^2+128178539882387627673601024/ 1185790782888488971569375*ep^3; Fill mnchfac(21,6)= -32768/21945-299804981248/106429848525*ep-5052228134581512704/ 1548504806159185875*ep^2-67958089418671625912579072/ 22530024874881290459818125*ep^3; Fill mnchfac(21,8)= 8192/197505+231475390976/2873605910175*ep+3976274395527467648/ 41809629766298018625*ep^2+54182619479966537990320064/ 608310671621794842415089375*ep^3; Fill mnchfac(21,10)= -4096/3357585-119243277568/48851300472975*ep-2090192153086694464/ 710763706027066316625*ep^2-28880211145163281885646752/ 10341281417570512321056519375*ep^3; Fill mnchfac(21,12)= 128/3357585+3842748704/48851300472975*ep+68812892706774992/ 710763706027066316625*ep^2+965081322716881776628256/ 10341281417570512321056519375*ep^3; Fill mnchfac(21,14)= -64/50363775-1983452368/732769507094625*ep-36330333663324088/ 10661455590405994749375*ep^2-20711198350860867625096/ 6204768850542307392633911625*ep^3; Fill mnchfac(21,16)= 16/352546425+512491132/5129386549662375*ep+9615191105989852/ 74630189132841963245625*ep^2+27887520217551628264496/ 217166909768980758742186906875*ep^3; Fill mnchfac(21,18)= -8/4583103525-265199126/66682025145610875*ep-5104405088818496/ 970192458726945522193125*ep^2-15086325039451857458392/ 2823169826996749863648429789375*ep^3; Fill mnchfac(21,20)= 1/13749310575+34362352/200046075436832625*ep+679713656361172/ 2910577376180836566579375*ep^2+2050615923818229593216/ 8469509480990249590945289368125*ep^3; Fill mnchfac(22,0)= 4194304/23+55449783894016/171037867*ep+62148447012132082024448/ 171707978824687305*ep^2+18773640843278935056606227120128/ 57460238696848076587523025*ep^3; Fill mnchfac(22,2)= -1048576/253-14216885108736/1881416537*ep-16185865646494692933632/ 1888787767071560355*ep^2-4939611430400022842765148762112/ 632062625665328842462753275*ep^3; Fill mnchfac(22,4)= 524288/5313+21882303447040/118529241831*ep+8441631814548135510016/ 39664543108502767455*ep^2+2604324848699357943102458894336/ 13273315138971905691717818775*ep^3; Fill mnchfac(22,6)= -65536/26565-14041955012608/2963231045775*ep-5510969387405605061632/ 991613577712569186375*ep^2-1719912378720983085985487541248/ 331832878474297642292945469375*ep^3; Fill mnchfac(22,8)= 32768/504735+7213354010624/56301389869725*ep+2882530576483548740096/ 18840657976538814541125*ep^2+910725032979212811114814879744/ 6304824691011655203565963918125*ep^3; Fill mnchfac(22,10)= -8192/4542615-5562313573888/1520137526482575*ep-2265307307282547469952/ 508697765366547992610375*ep^2-725158267118879226334680363328/ 170230266657314690496281025789375*ep^3; Fill mnchfac(22,12)= 4096/77224455+2861785174784/25842337950203775*ep+1188986936108863222336/ 8647862011231315874376375*ep^2+385983943086118989229844859104/ 2893914533174349738436777438419375*ep^3; Fill mnchfac(22,14)= -128/77224455-92107901152/25842337950203775*ep-39082274505059099408/ 8647862011231315874376375*ep^2-12879402295078230664046341312/ 2893914533174349738436777438419375*ep^3; Fill mnchfac(22,16)= 64/1158366825+47481744944/387635069253056625*ep+20600421127746044632/ 129717930168469738115645625*ep^2+1379856370959773100966653608/ 8681743599523049215310332315258125*ep^3; Fill mnchfac(22,18)= -16/8108567775-12252881156/2713445484771396375*ep-5442983541528756628/ 908025511179288166809519375*ep^2-370984610303709300320350024/ 60772205196661344507172326206806875*ep^3; Fill mnchfac(22,20)= 8/105411381075+6332372458/35274791302028152875*ep+2884496441406398444/ 11804331645330746168523751875*ep^2+40068509905531577410044976/158007733\ 511319495718648048137697875*ep^3; Fill mnchfac(22,22)= -1/316234143225-819433166/105824373906084458625*ep-383413267272815608/ 35412994935992238505571255625*ep^2-27181237845756473555515984/237011600\ 2669792435779720722065468125*ep^3; Fill mnchfac(23,0)= 1048576/3+42519666950144/66927861*ep+16117764640820675428352/ 22396692890176605*ep^2+4916822256033218930723353403392/ 7494813743067140424459525*ep^3; Fill mnchfac(23,2)= -524288/69-21768376582144/1539340803*ep-8375602077385422217216/ 515123936474061915*ep^2-2580272243587601374400838496256/ 172380716090544229762569075*ep^3; Fill mnchfac(23,4)= 131072/759+5575008821248/16932748833*ep+2178701295587778279424/ 5666363301214681065*ep^2+678208019413177329505688858624/ 1896187876995986527388259825*ep^3; Fill mnchfac(23,6)= -65536/15939-2857126383616/355587725493*ep-1134879542427718740992/ 118993629325508302365*ep^2-357188547865480560572893852672/ 39819945416915717075153456325*ep^3; Fill mnchfac(23,8)= 8192/79695+1831393409536/8889693137325*ep+739942524904759583744/ 2974840733137707559125*ep^2+235623535029629047272867730816/ 995498635422892926878836408125*ep^3; Fill mnchfac(23,10)= -4096/1514205-939743767808/168904169609175*ep-386522588838556133632/ 56521973929616443623375*ep^2-124619433330379533202860160448/ 18914474073034965610697891754375*ep^3; Fill mnchfac(23,12)= 1024/13627845+723845084096/4560412579447725*ep+303348998066114433184/ 1526093296099643977831125*ep^2+99104158213634143122765270176/ 510690799971944071488843077368125*ep^3; Fill mnchfac(23,14)= -512/231673365-372001090528/77527013850611325*ep-158997215879735569712/ 25943586033693947623129125*ep^2-52681886037342346539747501568/ 8681743599523049215310332315258125*ep^3; Fill mnchfac(23,16)= 16/231673365+11959673384/77527013850611325*ep+5218799045569783936/ 25943586033693947623129125*ep^2+1755459894013456818451059704/ 8681743599523049215310332315258125*ep^3; Fill mnchfac(23,18)= -8/3475100475-6158310988/1162905207759169875*ep-2746787050051437524/ 389153790505409214346936875*ep^2-187801761526841858742203048/ 26045230798569147645930996945774375*ep^3; Fill mnchfac(23,20)= 2/24325703325+1587383362/8140336454314189125*ep+724639681443448196/ 2724076533537864500428558125*ep^2+50414624944191277558592816/1823166155\ 89984033521516978620420625*ep^3; Fill mnchfac(23,22)= -1/316234143225-819433166/105824373906084458625*ep-383413267272815608/ 35412994935992238505571255625*ep^2-27181237845756473555515984/237011600\ 2669792435779720722065468125*ep^3; Fill mnchfac(24,0)= 16777216/25+17366559184912384/13943304375*ep+33374413283574558039605248/ 23329888427267296875*ep^2+51388229764415700241549844693549056/ 39035488245141356377393359375*ep^3; Fill mnchfac(24,2)= -1048576/75-1109777639604224/41829913125*ep-2163270667311263626313728/ 69989665281801890625*ep^2-3362580067075132823134658137071616/ 117106464735424069132180078125*ep^3; Fill mnchfac(24,4)= 524288/1725+567602397478912/962088001875*ep+1122927088396648522686464/ 1609762301481443484375*ep^2+1762980368412942069384954078507008/ 2693448688914753590040141796875*ep^3; Fill mnchfac(24,6)= -131072/18975-145223466262528/10582968020625*ep- 291776653876385611913216/17707385316295878328125*ep^2- 462935986800603525774110865661952/29627935578062289490441559765625*ep^3; Fill mnchfac(24,8)= 65536/398475+74352282456064/222242328433125*ep+151812421253969222622208/ 371855091642213444890625*ep^2+243563803671443546017933042994176/ 622186647139308079299272755078125*ep^3; Fill mnchfac(24,10)= -8192/1992375-9522482405888/1111211642165625*ep-19773201880291424884736/ 1859275458211067224453125*ep^2-32099698092641797157463570411392/ 3110933235696540396496363775390625*ep^3; Fill mnchfac(24,12)= 4096/37855125+4881476518144/21113021201146875*ep+ 10316478284726114560768/35326233706010277264609375*ep^2+ 16958348815596777287143833570496/59107731478234267533430911732421875* ep^3; Fill mnchfac(24,14)= -1024/340696125-3756293679808/570051572430965625*ep- 8086526354207597490976/953808310062277486144453125*ep^2- 13470447600318753590385639736672/1595908749912325223402634616775390625* ep^3; Fill mnchfac(24,16)= 512/5791834125+1928539582304/9690876731326415625*ep+ 4233076455188269586288/16214741271058717264455703125*ep^2+ 7151857259858219788871659235936/27130448748509528797844788485181640625* ep^3; Fill mnchfac(24,18)= -16/5791834125-61940058472/9690876731326415625*ep-138761007386736375184/ 16214741271058717264455703125*ep^2-238006441580881033030299665848/ 27130448748509528797844788485181640625*ep^3; Fill mnchfac(24,20)= 8/86877511875+31862400716/145363150969896234375*ep+72934640903779435052/ 243221119065880758966835546875*ep^2+127138819971262290521514472544/ 406956731227642931967671827277724609375*ep^3; Fill mnchfac(24,22)= -2/608142583125-8204628254/1017542056789273640625*ep- 19214228474766974288/1702547833461165312767848828125*ep^2- 34081075015282440599196185936/2848697118593500523773702790944072265625* ep^3; Fill mnchfac(24,24)= 1/7905853580625+4231021552/13228046738260557328125*ep+ 10151678126460910744/22133121834995149065982034765625*ep^2+ 18347133858726828484613167168/37033062541715506809058136282272939453125 *ep^3; Fill mnchfac(25,0)= 16777216/13+17712055548116992/7250518275*ep+34491779685453570345140224/ 12131541982178994375*ep^2+53593899818198107634118071655497728/ 20298453887473505316244546875*ep^3; Fill mnchfac(25,2)= -8388608/325-9043171637460992/181262956875*ep- 17851129977077916838068224/303288549554474859375*ep^2- 27991687854897857821366825432137728/507461347186837632906113671875*ep^3; Fill mnchfac(25,4)= 524288/975+577382072614912/543788870625*ep+1155948693463060153278464/ 909865648663424578125*ep^2+1830069213305311216515905477931008/ 1522384041560512898718341015625*ep^3; Fill mnchfac(25,6)= -262144/22425-295047825145856/12507144024375*ep- 599438390024697636524032/20926909919258765296875*ep^2- 958642355832695553893071148591104/35014832955891796670521843359375*ep^3; Fill mnchfac(25,8)= 65536/246675+75423389732864/137578584268125*ep+155595877215481169271808/ 230196009111846418265625*ep^2+251494338097322514320018965605376/ 385163162514809763375740276953125*ep^3; Fill mnchfac(25,10)= -32768/5180175-38581969528832/2889150269630625*ep- 80871996576469041288704/4834116191348774783578125*ep^2- 132190728269687918905454294924288/8088426412811005030890545816015625* ep^3; Fill mnchfac(25,12)= 4096/25900875+4936969740544/14445751348153125*ep+ 10522025602754048781568/24170580956743873917890625*ep^2+ 17404111867435445105731789948096/40442132064055025154452729080078125* ep^3; Fill mnchfac(25,14)= -2048/492116625-2528602527872/274469275614909375*ep- 5483689062573953129984/459241038178133604439921875*ep^2- 9184965906542946023002847716448/768400509217045477934601852521484375* ep^3; Fill mnchfac(25,16)= 512/4429049625+1944045041504/7410670441602553125*ep+ 4293476208479796712688/12399508030809607319877890625*ep^2+ 7287826067251574594606357176736/20746813748860227904234250018080078125* ep^3; Fill mnchfac(25,18)= -256/75293843625-997218891952/125981397507243403125*ep- 2244887703338629936744/210791636523763324437924140625*ep^2- 3864862345639988856622062742168/352695833730623874371982250307361328125 *ep^3; Fill mnchfac(25,20)= 8/75293843625+31999688636/125981397507243403125*ep+73499101218509509892/ 210791636523763324437924140625*ep^2+128463100848089237871361181024/ 352695833730623874371982250307361328125*ep^3; Fill mnchfac(25,22)= -4/1129407654375-16446030058/1889720962608651046875*ep- 38584046632127498176/3161874547856449866568862109375*ep^2- 68535463273732197822682393072/5290437505959358115579733754610419921875* ep^3; Fill mnchfac(25,24)= 1/7905853580625+4231021552/13228046738260557328125*ep+ 10151678126460910744/22133121834995149065982034765625*ep^2+ 18347133858726828484613167168/37033062541715506809058136282272939453125 *ep^3; Fill mnchfac(26,0)= 67108864/27+649630401232371712/135528918525*ep+ 3843556378482312345660424192/680299546539114376875*ep^2+180743658470891\ 38731789559108881743872/3414824511684965855894371078125*ep^3; Fill mnchfac(26,2)= -16777216/351-165646628713136128/1761875940825*ep- 992869021182976308479131648/8843894105008486899375*ep^2-471027588439038\ 1684697921828195565568/44392718651904556126626824015625*ep^3; Fill mnchfac(26,4)= 8388608/8775+84507609127190528/44046898520625*ep+ 513402251142808971175067648/221097352625212172484375*ep^2+2458220685699\ 909872266034716730605568/1109817966297613903165670600390625*ep^3; Fill mnchfac(26,6)= -524288/26325-5391380177911808/132140695561875*ep- 33215245518755050561200128/663292057875636517453125*ep^2-16058574702861\ 9713632277089045557248/3329453898892841709497011801171875*ep^3; Fill mnchfac(26,8)= 262144/605475+2752901188501504/3039235997923125*ep+ 17208424242282188730609664/15255717331139639901421875*ep^2+ 84048492076428854588327707688372224/76577439674535359318431271426953125 *ep^3; Fill mnchfac(26,10)= -65536/6660225-703178198142976/33431595977154375*ep- 4462545422059900213974016/167812890642536038915640625*ep^2- 22030311495404297744336665105478656/842351836419888952502743985696484375 *ep^3; Fill mnchfac(26,12)= 32768/139864725+359421571033088/702063515520241875*ep+ 2317184557267464892932608/3524070703493256817228453125*ep^2+ 11569027911845518265656094947708928/17689388564817668002557623699626171\ 875*ep^3; Fill mnchfac(26,14)= -4096/699323625-45955708324096/3510317577601209375*ep- 301182009379201761761536/17620353517466284086142265625*ep^2- 1521718992703559452465003855542976/884469428240883400127881184981308593\ 75*ep^3; Fill mnchfac(26,16)= 2048/13287148875+23518913080448/66696033974422978125*ep+ 156804441053492876519168/334786716831859397636703046875*ep^2+ 802285493068927876775258663585888/1680491913657678460242974251464486328\ 125*ep^3; Fill mnchfac(26,18)= -512/119584339875-6022507706912/600264305769806803125*ep- 40880583424538365276592/3013080451486734578730327421875*ep^2- 211971581621550334612143732270272/1512442722291910614218676826318037695\ 3125*ep^3; Fill mnchfac(26,20)= 256/2032933777875+3086842967056/10204493198086715653125*ep+ 21351743757980733581896/51222367675274487838415566171875*ep^2+ 112290319656400544561279958507736/2571152627896248044171750604740664082\ 03125*ep^3; Fill mnchfac(26,22)= -8/2032933777875-98973637508/10204493198086715653125*ep- 698292432376584535628/51222367675274487838415566171875*ep^2- 3728143827628698030611531508248/257115262789624804417175060474066408203\ 125*ep^3; Fill mnchfac(26,24)= 4/30494006668125+50825375974/153067397971300734796875*ep+ 366154384680595325884/768335515129117317576233492578125*ep^2+ 1986601562626566082145836024744/385672894184437206625762590711099612304\ 6875*ep^3; Fill mnchfac(26,26)= -1/213458046676875-13064886106/1071471785799105143578125*ep- 96222908034165970396/5378348605903821223033634448046875*ep^2- 531150355374104609737853307736/2699710259291060446380338134977697286132\ 8125*ep^3; Fill mnchfac(27,0)= 33554432/7+47229678395588608/5019589575*ep+1979928360456130264959287296/ 176373956510140764375*ep^2+9389791444050161230739377115371995136/ 885324873399805962639281390625*ep^3; Fill mnchfac(27,2)= -16777216/189-24060419824943104/135528918525*ep- 1021275810882281951318376448/4762096825773800638125*ep^2-48847618484511\ 68542593702628956602368/23903771581794760991260597546875*ep^3; Fill mnchfac(27,4)= 4194304/2457+6130784542130176/1761875940825*ep+ 263604266382867966991040512/61907258735059408295625*ep^2+12720822016305\ 21635868028390794452992/310749030563331892886387768109375*ep^3; Fill mnchfac(27,6)= -2097152/61425-446506522247168/6292414074375*ep- 136195040980547108025024512/1547681468376485207390625*ep^2-663386829130\ 166899583566670579412992/7768725764083297322159694202734375*ep^3; Fill mnchfac(27,8)= 131072/184275+199262839463936/132140695561875*ep+ 8803920215517798507333632/4643044405129455622171875*ep^2+ 43303012909508135166238019420966912/23306177292249891966479082608203125 *ep^3; Fill mnchfac(27,10)= -65536/4238325-101674673287168/3039235997923125*ep- 4557288625607446919689216/106790021317977479309953125*ep^2- 22646102910204729261398916270201856/536042077721747515229018899988671875 *ep^3; Fill mnchfac(27,12)= 16384/46621575+25952700500992/33431595977154375*ep+ 1180772307953913413672704/1174690234497752272409484375*ep^2+ 5930934471526371104064463952116864/5896462854939222667519207899875390625 *ep^3; Fill mnchfac(27,14)= -8192/979053075-92792569743872/4914444608641693125*ep- 612566183297137674042752/24668494924452797720599171875*ep^2- 3111887751366797523268648454320832/123825719953723676017903365897383203\ 125*ep^3; Fill mnchfac(27,16)= 1024/4895265375+11856074204224/24572223043208465625*ep+ 79546404235939669823584/123342474622263988602995859375*ep^2+ 408950483992422620757351273566944/6191285997686183800895168294869160156\ 25*ep^3; Fill mnchfac(27,18)= -512/93010042125-6063301831712/466872237820960846875*ep- 41375059310840359101392/2343507017823015783456921328125*ep^2- 215406074437353465696286355267072/1176344339560374922170081976025140429\ 6875*ep^3; Fill mnchfac(27,20)= 128/837090379125+1551520317128/4201850140388647621875*ep+ 10776431228224334372048/21091563160407142051112291953125*ep^2+ 56856699823166106122696383938968/10587099056043374299530737784226263867\ 1875*ep^3; Fill mnchfac(27,22)= -64/14230536445125-794657436964/71431452386607009571875*ep- 5622854095658091541924/358556573726921414868908963203125*ep^2- 30088609899836665359479802901384/17998068395273736309202254233184648574\ 21875*ep^3; Fill mnchfac(27,24)= 2/14230536445125+25460493602/71431452386607009571875*ep+ 183701767255499948132/358556573726921414868908963203125*ep^2+ 997900776608944786299770585912/1799806839527373630920225423318464857421\ 875*ep^3; Fill mnchfac(27,26)= -1/213458046676875-13064886106/1071471785799105143578125*ep- 96222908034165970396/5378348605903821223033634448046875*ep^2- 531150355374104609737853307736/2699710259291060446380338134977697286132\ 8125*ep^3; Fill mnchfac(28,0)= 268435456/29+78000310823201800192/4221474832575*ep+ 13705259305863474244225322713088/614512060760831871763125*ep^2+ 1900396737535984816840884348536253822533632/ 89453351683298308723067654463234375*ep^3; Fill mnchfac(28,2)= -33554432/203-1417783381204140032/4221474832575*ep- 1764753420662213284351303745536/4301584425325823102341875*ep^2- 246724299274542653053615298304309506146304/6261734617830881610614735812\ 42640625*ep^3; Fill mnchfac(28,4)= 16777216/5481+721813528789385216/113979820479525*ep+ 909617864250871366671252717568/116142779483797223763230625*ep^2+ 128266273419130427778935858604212079460352/1690668346814338034865978669\ 3551296875*ep^3; Fill mnchfac(28,6)= -4194304/71253-26258298598326272/211676809461975*ep- 234608164454328735642686881792/1509856133289363908921998125*ep^2- 33380086208576460347295268416750675058688/21978688508586394453257722701\ 6166859375*ep^3; Fill mnchfac(28,8)= 2097152/1781325+93648493249429504/37043441655845625*ep+ 121121107470650236830707105792/37746403332234097723049953125*ep^2+ 17395297872399901608477004384985194098688/54946721271465986133144306754\ 04171484375*ep^3; Fill mnchfac(28,10)= -131072/5343975-852371667361792/15875760709648125*ep- 7823395382930901194566387712/113239209996702293169149859375*ep^2- 1134657649660520077732580028467088621568/164840163814397958399432920262\ 12514453125*ep^3; Fill mnchfac(28,12)= 65536/122911425+3042555188867072/2555997474253348125*ep+ 4046493030439453208866272256/2604501829924152742890446765625*ep^2+ 592939272338791215948109044484611728384/3791323767731153043186957166028\ 87832421875*ep^3; Fill mnchfac(28,14)= -16384/1352025675-776125730413568/28115972216786829375*ep- 1047571167743066070097694464/28649520129165680171794914421875*ep^2- 155166315451404006305025424054237421696/4170456144504268347505652882631\ 766156640625*ep^3; Fill mnchfac(28,16)= 8192/28392539175+2773225478169088/4133047915867663918125*ep+ 543009067551576672294069632/601639922712479283607693202859375*ep^2+ 81347195677309554873120073670653344448/87579579034589635297618710535267\ 089289453125*ep^3; Fill mnchfac(28,18)= -1024/141962695875-354106271372096/20665239579338319590625*ep- 70453462258868250376632544/3008199613562396418038466014296875*ep^2- 10681188283445737339429109293960454816/43789789517294817648809355267633\ 5446447265625*ep^3; Fill mnchfac(28,20)= 512/2697291221625+180975812844448/392639552007428072221875*ep+ 36613273487379026559129872/57155792657685531942730854271640625*ep^2+ 5621105961260356986446440771733187808/832006000828601535327377750085037\ 3482498046875*ep^3; Fill mnchfac(28,22)= -128/24275620994625-46279104127912/3533755968066852649996875*ep- 9527582880178278290327168/514402133919169787484577688444765625*ep^2- 1482327163387780881921592259551637752/748805400745741381794639975076533\ 61342482421875*ep^3; Fill mnchfac(28,24)= 64/412685556908625+23687573137556/60073851457136495049946875*ep+ 4966624084805107263915484/8744836276625886387237820703561015625*ep^2+ 783691935805179696109766787296812976/1272969181267760349050887957630107\ 142822201171875*ep^3; Fill mnchfac(28,26)= -2/412685556908625-758432672758/60073851457136495049946875*ep- 162107227736906342974712/8744836276625886387237820703561015625*ep^2- 25965225541476206236959582507462568/12729691812677603490508879576301071\ 42822201171875*ep^3; Fill mnchfac(28,28)= 1/6190283353629375+388920876224/901107771857047425749203125*ep+ 84827912008321292632636/131172544149388295808567310553415234375*ep^2+ 13805828622791011074395112263112704/19094537719016405235763319364451607\ 142333017578125*ep^3; Fill mnchfac(29,0)= 268435456/15+79257917585266573312/2183521465125*ep+ 14082891378046516465513244131328/317851065910775106084375*ep^2+ 1968269941312660162454311760742311570440192/ 46268975008602573477448786791328125*ep^3; Fill mnchfac(29,2)= -134217728/435-40302676700882272256/63322122488625*ep- 7243748584835602279875151396864/9217680911412478076446875*ep^2- 1020495615536691873520063422624401007312896/134180027524947463084601481\ 6948515625*ep^3; Fill mnchfac(29,4)= 16777216/3045+732150999339237376/63322122488625*ep+ 932113030150616026686788599808/64523766379887346535128125*ep^2+ 132407877678411666109085172454083248422912/9392601926746322415922103718\ 639609375*ep^3; Fill mnchfac(29,6)= -8388608/82215-372536418763276288/1709697307192875*ep- 480115993762648425853104226304/1742141692256958356448459375*ep^2- 68792441501256607010885907383211104813056/25360025202215070522989680040\ 3269453125*ep^3; Fill mnchfac(29,8)= 2097152/1068795+94811458686287872/22226064993507375*ep+ 123744793277249931884093259776/22647841999340458633829971875*ep^2+ 17890929381258590269640353169567465304064/32968032762879591679886584052\ 42502890625*ep^3; Fill mnchfac(29,10)= -1048576/26719875-48277953420787712/555651624837684375*ep- 63840160993574737232086245376/566196049983511465845749296875*ep^2- 9317188322273311630692688173220436056064/824200819071989791997164601310\ 62572265625*ep^3; Fill mnchfac(29,12)= 65536/80159625+3074157510520832/1666954874513053125*ep+ 4120530679820038543209051136/1698588149950534397537247890625*ep^2+ 607316678995118540338298005147498824704/2472602457215969375991493803931\ 87716796875*ep^3; Fill mnchfac(29,14)= -32768/1843671375-1566705931810816/38339962113800221875*ep- 2129675636204318022550880768/39067527448862291143356701484375*ep^2- 317137158237866136784951153195206065152/5686985651596729564780435749043\ 317486328125*ep^3; Fill mnchfac(29,16)= 8192/20280385125+399419949551104/421739583251802440625*ep+ 550918891578679085471019392/429742801937485202576923716328125*ep^2+ 82929572060390529289934380309550385088/62556842167564025212584793239476\ 492349609375*ep^3; Fill mnchfac(29,18)= -4096/425888087625-1426362534289664/61995718738014958771875*ep- 285346725823217559206696896/9024598840687189254115398042890625*ep^2- 43442756509046482665985073453396493344/13136936855188445294642806580290\ 06339341796875*ep^3; Fill mnchfac(29,20)= 512/2129440438125+182021860086688/309978593690074793859375*ep+ 36993169523306404038399632/45122994203435946270576990214453125*ep^2+ 5699595829354635323848872785757564448/656846842759422264732140329014503\ 1696708984375*ep^3; Fill mnchfac(29,22)= -256/40459368324375-92972268622544/5889593280111421083328125*ep- 19208889829017034792830616/857336889865282979140962814074609375*ep^2- 2996966417354089544553996419174488424/124800900124290230299106662512755\ 602237470703125*ep^3; Fill mnchfac(29,24)= 64/364134314919375+23760642614036/53006339521002789749953125*ep+ 4994377543079856463428004/7716032008787546812268665326671484375*ep^2+ 789631717561682112027013979882638256/1123208101118612072691959962614800\ 420137236328125*ep^3; Fill mnchfac(29,26)= -32/6190283353629375-12154331843818/901107771857047425749203125*ep- 2601264240070237729885952/131172544149388295808567310553415234375*ep^2- 417090040367725115703183962138163928/1909453771901640523576331936445160\ 7142333017578125*ep^3; Fill mnchfac(29,28)= 1/6190283353629375+388920876224/901107771857047425749203125*ep+ 84827912008321292632636/131172544149388295808567310553415234375*ep^2+ 13805828622791011074395112263112704/19094537719016405235763319364451607\ 142333017578125*ep^3; Fill mnchfac(30,0)= 1073741824/31+9979074250129694261248/139890941865675*ep+ 55561575535333391193766474444439552/631273406969860079023974375*ep^2+ 242579953380780498786203325032020785111727341568/2848691337927977150697\ 798735087609421875*ep^3; Fill mnchfac(30,2)= -268435456/465-2535146722500146102272/2098364127985125*ep- 14271731585745417099392829681041408/9469101104547901185359615625*ep^2- 62791747456575801927692462892683153545910812672/42730370068919657260466\ 981026314141328125*ep^3; Fill mnchfac(30,4)= 134217728/13485+1288458616405791604736/60852559711568625*ep+ 7336359329473321050467830573563904/274603932031889134375428853125*ep^2+ 32537464625356927413998478954159333709511131136/12391807319986700605535\ 42449763110098515625*ep^3; Fill mnchfac(30,6)= -16777216/94395-23394460241631379456/60852559711568625*ep- 943437441003849812089947793522688/1922227524223223940628001971875*ep^2- 4219231871042162864050436205165916811992072192/867426512399069042387479\ 7148341770689609375*ep^3; Fill mnchfac(30,8)= 8388608/2548665+11897518612719075328/1643019112212352875*ep+ 485638058126995029210380974751744/51900143154027046396956053240625*ep^2 +2190782441324191059393974498566489182422941696/23420515834774864144461\ 9523005227808619453125*ep^3; Fill mnchfac(30,10)= -2097152/33132645-3026377627039301632/21359248458760587375*ep- 125086362815637269475044303323136/674701861002351603160428692128125* ep^2-569405844957389010843482851516773535543988224/30446670585207323387\ 80053799067961512052890625*ep^3; Fill mnchfac(30,12)= 1048576/828316125+1540227759926607872/533981211469014684375*ep+ 64489307064807723157632960372736/16867546525058790079010717303203125* ep^2+296343528808450223189375221763085687456180224/76116676463018308469\ 501344976699037801322265625*ep^3; Fill mnchfac(30,14)= -65536/2484948375-98024583068782592/1601943634407044053125*ep- 4159599512464964778362237572096/50602639575176370237032151909609375* ep^2-19303581160182341180962373722201988251710464/228350029389054925408\ 504034930097113403966796875*ep^3; Fill mnchfac(30,16)= 32768/57153812625+49930734007453696/36844703591362013221875*ep+ 2148374793902090112834545013248/1163860710229056515451739493921015625* ep^2+10073302744746764976823981444043721952940032/525205067594826328439\ 5592803392233608291236328125*ep^3; Fill mnchfac(30,18)= -8192/628691938875-12722730966413824/405291739504982145440625*ep- 555361387223274046608681264512/12802467812519621669969134433131171875* ep^2-2632240682571576364976485157432666176575808/5777255743543089612835\ 1520837314569691203599609375*ep^3; Fill mnchfac(30,20)= 4096/13202530716375+45409732419133184/59577885707232375379771875*ep+ 287438620244480061132327211456/268851824062912055069351823095754609375* ep^2+1377886945455635176939362480484709707140704/1213223706144048818695\ 381937583605963515275591796875*ep^3; Fill mnchfac(30,22)= -512/66012653581875-5791739394706528/297889428536161876898859375*ep- 37236620883731024772630291152/1344259120314560275346759115478773046875* ep^2-180637587484083746197841950938659651013568/60661185307202440934769\ 09687918029817576377958984375*ep^3; Fill mnchfac(30,24)= 256/1254240418055625+2956671193308464/5659899142187075661078328125*ep+ 19320537127806141023822664376/25540923285976645231588423194096687890625 *ep^2+94907534210903578211849391543155806490984/11525625208368463777606\ 1284070442566533951181220703125*ep^3; Fill mnchfac(30,26)= -64/11288163762500625-755212637537516/50939092279683680949704953125*ep- 5019466552872653062484062444/229868309573789807084295808746870191015625 *ep^2-24985266892769995625068909234641658719896/10373062687531617399845\ 51556633983098805560630986328125*ep^3; Fill mnchfac(30,28)= 32/191898783962510625+386100645409558/865964568754622576144984203125*ep +2612222807634216617065555172/39077612627544267204330287486967932472656\ 25*ep^2+13186042002216019682283767030369636429248/176342065688037495797\ 37376462777712679694530726767578125*ep^3; Fill mnchfac(30,30)= -1/191898783962510625-12347683358294/865964568754622576144984203125*ep- 85114480994316988246696096/3907761262754426720433028748696793247265625* ep^2-436069346667442343847318558027528918464/17634206568803749579737376\ 462777712679694530726767578125*ep^3; *--#] harmo : *--#[ harmo1 : #procedure harmo1(P,Q,TT) * * Routine to generate the harmonic projection for * P(mnci1)*P(mnci2)*...*P(in) = TT(mnci1,mnci2,...,in) at P->Q * The object mnchfac1 is a table to give better speed. * It has been generated with the program hfac1.frm * id `P'.`P' = 0; id `Q'.`P' = `Q'.`Q'; id 1/`Q'.`P' = 1/`Q'.`Q'; ToTensor,nosquare,`TT',`P'; * * Next generate the splits between indices that connect to a Q and * the indices that go to d_. * id `TT'(?a) = sum_(mncj,0,nargs_(?a),2,`Q'.`Q'^(mncj/2)* acc(mnchfac1(nargs_(?a),mncj))*distrib_(1,mncj,mncdd,`TT',?a)); * * The indices in TT contract with Q and the indices in mncdd go to * d_'mncs. We do not expand the mncdd directly to make the multiplication * of the acc'mncs much faster. * tovector,`TT',`Q'; id mncdd(?a) = dd_(?a); id D = acc(4-2*ep); * #endprocedure #procedure harmo1x(P,Q,TT) * * Routine to generate the harmonic projection for * P(mnci1)*P(mnci2)*...*P(in) = TT(mnci1,mnci2,...,in) at P->Q * The object mnchfac1 is a table to give better speed. * It has been generated with the program hfac1.frm * id `P' = mncx*`P'; id `P'.`P' = 0; id `Q'.`P' = `Q'.`Q'; id 1/`Q'.`P' = 1/`Q'.`Q'/mncx; ToTensor,nosquare,`TT',`P'; * * Next generate the splits between indices that connect to a Q and * the indices that go to d_. * id `TT'(?a) = sum_(mncj,0,nargs_(?a),2,`Q'.`Q'^(mncj/2)* acc(mnchfac1(nargs_(?a),mncj))*distrib_(1,mncj,mncdd,`TT',?a)); * * The indices in TT contract with Q and the indices in mncdd go to * d_'mncs. We do not expand the mncdd directly to make the multiplication * of the acc'mncs much faster. * tovector,`TT',`Q'; id mncdd(?a) = dd_(?a); id D = acc(4-2*ep); id mncx^n? = (`P'.`Q'/`Q'.`Q')^n; * #endprocedure CTable,relax,mnchfac1(0:30,0:30); Fill mnchfac1(0,0)= 1; Fill mnchfac1(1,0)= 1; Fill mnchfac1(2,0)= 4/3+2/9*ep+4/27*ep^2+8/81*ep^3+16/243*ep^4+32/729*ep^5+64/2187*ep^6; Fill mnchfac1(2,2)= -1/3-2/9*ep-4/27*ep^2-8/81*ep^3-16/243*ep^4-32/729*ep^5-64/2187*ep^6; Fill mnchfac1(3,0)= 2+2/3*ep+4/9*ep^2+8/27*ep^3+16/81*ep^4+32/243*ep^5+64/729*ep^6; Fill mnchfac1(3,2)= -1/3-2/9*ep-4/27*ep^2-8/81*ep^3-16/243*ep^4-32/729*ep^5-64/2187*ep^6; Fill mnchfac1(4,0)= 16/5+116/75*ep+1196/1125*ep^2+12176/16875*ep^3+123056/253125*ep^4+ 1238336/3796875*ep^5+12430016/56953125*ep^6; Fill mnchfac1(4,2)= -2/5-22/75*ep-232/1125*ep^2-2392/16875*ep^3-24352/253125*ep^4-246112/ 3796875*ep^5-2476672/56953125*ep^6; Fill mnchfac1(4,4)= 1/15+16/225*ep+196/3375*ep^2+2176/50625*ep^3+23056/759375*ep^4+238336/ 11390625*ep^5+2430016/170859375*ep^6; Fill mnchfac1(5,0)= 16/3+148/45*ep+1588/675*ep^2+16528/10125*ep^3+169168/151875*ep^4+ 1715008/2278125*ep^5+17290048/34171875*ep^6; Fill mnchfac1(5,2)= -8/15-98/225*ep-1088/3375*ep^2-11528/50625*ep^3-119168/759375*ep^4- 1215008/11390625*ep^5-12290048/170859375*ep^6; Fill mnchfac1(5,4)= 1/15+16/225*ep+196/3375*ep^2+2176/50625*ep^3+23056/759375*ep^4+238336/ 11390625*ep^5+2430016/170859375*ep^6; Fill mnchfac1(6,0)= 64/7+1648/245*ep+129016/25725*ep^2+9613672/2701125*ep^3+697694224/ 283618125*ep^4+49885657408/29779903125*ep^5+3536215611136/3126889828125 *ep^6; Fill mnchfac1(6,2)= -16/21-1516/2205*ep-123292/231525*ep^2-9367864/24310125*ep^3-687208288/ 2552563125*ep^4-49440388096/268019128125*ep^5-3517368500032/ 28142008453125*ep^6; Fill mnchfac1(6,4)= 8/105+926/11025*ep+81092/1157625*ep^2+6386864/121550625*ep^3+477728288/ 12762815625*ep^4+34752488096/1340095640625*ep^5+2488486500032/ 140710042265625*ep^6; Fill mnchfac1(6,6)= -1/105-142/11025*ep-13864/1157625*ep^2-1162288/121550625*ep^3-90226096/ 12762815625*ep^4-6712496032/1340095640625*ep^5-487263833344/ 140710042265625*ep^6; Fill mnchfac1(7,0)= 16+472/35*ep+38464/3675*ep^2+2929288/385875*ep^3+215266096/40516875* ep^4+15505796032/4254271875*ep^5+1104009833344/446698546875*ep^6; Fill mnchfac1(7,2)= -8/7-276/245*ep-23372/25725*ep^2-1815224/2701125*ep^3-134861408/ 283618125*ep^4-9775819136/29779903125*ep^5-698642203712/3126889828125* ep^6; Fill mnchfac1(7,4)= 2/21+242/2205*ep+21764/231525*ep^2+1742288/24310125*ep^3+131636096/ 2552563125*ep^4+9635496032/268019128125*ep^5+692602833344/ 28142008453125*ep^6; Fill mnchfac1(7,6)= -1/105-142/11025*ep-13864/1157625*ep^2-1162288/121550625*ep^3-90226096/ 12762815625*ep^4-6712496032/1340095640625*ep^5-487263833344/ 140710042265625*ep^6; Fill mnchfac1(8,0)= 256/9+75808/2835*ep+19246768/893025*ep^2+4489358368/281302875*ep^3+ 1001728100368/88610405625*ep^4+218025485306368/27912277771875*ep^5+ 46771949116202368/8792367498140625*ep^6; Fill mnchfac1(8,2)= -16/9-5368/2835*ep-1414288/893025*ep^2-336272488/281302875*ep^3- 75848735488/88610405625*ep^4-16613136791488/27912277771875*ep^5- 3577389080927488/8792367498140625*ep^6; Fill mnchfac1(8,4)= 8/63+3044/19845*ep+844124/6251175*ep^2+206121824/1969120125*ep^3+ 47199849824/620272839375*ep^4+10430561637824/195385944403125*ep^5+ 2258069814165824/61546572486984375*ep^6; Fill mnchfac1(8,6)= -2/189-866/59535*ep-256496/18753525*ep^2-64996496/5907360375*ep^3- 15212278496/1860818518125*ep^4-3406285030496/586157833209375*ep^5- 743347417642496/184639717460953125*ep^6; Fill mnchfac1(8,8)= 1/945+496/297675*ep+159496/93767625*ep^2+42546496/29536801875*ep^3+ 10286568496/9304092590625*ep^4+2351196330496/2930789166046875*ep^5+ 519799077642496/923198587304765625*ep^6; Fill mnchfac1(9,0)= 256/5+82976/1575*ep+21820976/496125*ep^2+5190442976/156279375*ep^3+ 1171598464976/49228003125*ep^4+256775705086976/15506820984375*ep^5+ 55317926550958976/4884648610078125*ep^6; Fill mnchfac1(9,2)= -128/45-45968/14175*ep-12519368/4465125*ep^2-3033399368/1406514375*ep^3 -691968210368/443052028125*ep^4-152606739906368/139561388859375*ep^5- 33000199172202368/43961837490703125*ep^6; Fill mnchfac1(9,4)= 8/45+3188/14175*ep+907988/4465125*ep^2+225339488/1406514375*ep^3+ 52120755488/443052028125*ep^4+11590175991488/139561388859375*ep^5+ 2518875627927488/43961837490703125*ep^6; Fill mnchfac1(9,6)= -4/315-1774/99225*ep-533824/31255875*ep^2-136691824/9845600625*ep^3- 32211509824/3101364196875*ep^4-7244605937824/976929722015625*ep^5- 1585445081165824/307732862434921875*ep^6; Fill mnchfac1(9,8)= 1/945+496/297675*ep+159496/93767625*ep^2+42546496/29536801875*ep^3+ 10286568496/9304092590625*ep^4+2351196330496/2930789166046875*ep^5+ 519799077642496/923198587304765625*ep^6; Fill mnchfac1(10,0)= 1024/11+3941248/38115*ep+11779286528/132068475*ep^2+31395360315808/ 457617265875*ep^3+78817416774749888/1585643826256875*ep^4+ 191296333735703644768/5494255857980071875*ep^5+455196393432838909648448/ 19037596547900949046875*ep^6; Fill mnchfac1(10,2)= -256/55-1074016/190575*ep-3316968176/660342375*ep^2-8998169551936/ 2288086329375*ep^3-22822219943433296/7928219131284375*ep^4- 55731982644325548256/27471279289900359375*ep^5-133110230344468529882816/ 95187982739504745234375*ep^6; Fill mnchfac1(10,4)= 128/495+586288/1715175*ep+1884204968/5943081375*ep^2+5224503688648/ 20592776964375*ep^3+13422543891846128/71353972181559375*ep^4+ 33033670720523533408/247241513609103234375*ep^5+79273078399635825303488/ 856691844655542707109375*ep^6; Fill mnchfac1(10,6)= -8/495-40108/1715175*ep-135134588/5943081375*ep^2-385061648968/ 20592776964375*ep^3-1005688819949648/71353972181559375*ep^4- 2500193390173412128/247241513609103234375*ep^5-6037463662096098209408/ 856691844655542707109375*ep^6; Fill mnchfac1(10,8)= 4/3465+22034/12006225*ep+78474124/41601569625*ep^2+231375515864/ 144149438750625*ep^3+617375290327504/499477805270915625*ep^4+ 1555697463798820544/1730690595263722640625*ep^5+3788802075628465273984/ 5996842912588798949765625*ep^6; Fill mnchfac1(10,10)= -1/10395-6086/36018675*ep-23133196/124804708875*ep^2-71203299656/ 432448316251875*ep^3-195463728133216/1498433415812746875*ep^4- 501804668946637376/5192071785791167921875*ep^5-1236992715223799403136/ 17990528737766396849296875*ep^6; Fill mnchfac1(11,0)= 512/3+2105024/10395*ep+6484548064/36018675*ep^2+17587269036704/ 124804708875*ep^3+44620587006331744/432448316251875*ep^4+ 109002812721985297184/1498433415812746875*ep^5+260418148499992639897024/ 5192071785791167921875*ep^6; Fill mnchfac1(11,2)= -256/33-1133152/114345*ep-3599216912/396205425*ep^2-9927387845632/ 1372851797625*ep^3-25437420674539952/4756931478770625*ep^4- 62514193873472733472/16482767573940215625*ep^5-149901045320140230992192/ 57112789643702847140625*ep^6; Fill mnchfac1(11,4)= 64/165+305464/571725*ep+1005647504/1981027125*ep^2+2830303821544/ 6864258988125*ep^3+7340055442799984/23784657393853125*ep^4+ 18171877679298377824/82413837869701078125*ep^5+43771816945911945664064/ 285563948218514235703125*ep^6; Fill mnchfac1(11,6)= -32/1485-165052/5145525*ep-566368772/17829244125*ep^2-1633203887992/ 61778330893125*ep^3-4298811218276912/214061916544678125*ep^4- 10740981158685800032/741724540827309703125*ep^5-26021186219050005844352/ 2570075533966628121328125*ep^6; Fill mnchfac1(11,8)= 2/1485+11182/5145525*ep+40241252/17829244125*ep^2+119504735272/ 61778330893125*ep^3+320436189606992/214061916544678125*ep^4+ 810100247041390912/741724540827309703125*ep^5+1977198808190427804032/ 2570075533966628121328125*ep^6; Fill mnchfac1(11,10)= -1/10395-6086/36018675*ep-23133196/124804708875*ep^2-71203299656/ 432448316251875*ep^3-195463728133216/1498433415812746875*ep^4- 501804668946637376/5192071785791167921875*ep^5-1236992715223799403136/ 17990528737766396849296875*ep^6; Fill mnchfac1(12,0)= 4096/13+231932416/585585*ep+9552620306048/26377676325*ep^2+ 342403963966857664/1188182430059625*ep^3+11407792075081681333952/ 53521677562035808125*ep^4+364561360009988883783267136/ 2410883965781902976990625*ep^5+11366945928654188627099169856448/ 108598268238645819598542703125*ep^6; Fill mnchfac1(12,2)= -512/39-30913472/1756755*ep-1310118983776/79133028975*ep^2- 47718354631206368/3564547290178875*ep^3-1605096783082101070624/ 160565032686107424375*ep^4-51595302050743047366763232/ 7232651897345708930971875*ep^5-1614544106154750292440383714176/ 325794804715937458795628109375*ep^6; Fill mnchfac1(12,4)= 256/429+16505056/19324305*ep+722647696208/870463318725*ep^2+ 26818419631574944/39210020191967625*ep^3+912369819932349930992/ 1766215359547181668125*ep^4+29533805437994496650793856/ 79559170870802798240690625*ep^5+928212986345962610005192697408/ 3583742851875312046751909203125*ep^6; Fill mnchfac1(12,6)= -64/2145-4414552/96621525*ep-200547273536/4352316593625*ep^2- 7607970101536648/196050100959838125*ep^3-262362556305459313664/ 8831076797735908340625*ep^4-8565263494376565641097952/ 397795854354013991203453125*ep^5-270635475996909892431623899136/ 17918714259376560233759546015625*ep^6; Fill mnchfac1(12,8)= 32/19305+2367436/869593725*ep+112122653948/39170849342625*ep^2+ 4365158933778064/1764450908638543125*ep^3+153028898616288867152/ 79479691179623175065625*ep^4+5048541384762808600644736/ 3580162689186125920831078125*ep^5+160585687629192803262038853248/ 161268428334389042103835914140625*ep^6; Fill mnchfac1(12,10)= -2/19305-159226/869593725*ep-7904207768/39170849342625*ep^2- 317328063224824/1764450908638543125*ep^3-11351061489513328832/ 79479691179623175065625*ep^4-379447407147066524694976/ 3580162689186125920831078125*ep^5-12173131533692001654488077568/ 161268428334389042103835914140625*ep^6; Fill mnchfac1(12,12)= 1/135135+86048/6087156075*ep+4505822764/274195945398375*ep^2+ 187659001098752/12351156360469801875*ep^3+6883116416827133536/ 556357838257362225459375*ep^4+234016557715815866651648/ 25061138824302881445817546875*ep^5+7592462315747275929147393664/ 1128878998340723294726851398984375*ep^6; Fill mnchfac1(13,0)= 4096/7+244097536/315315*ep+10319742128768/14203364175*ep^2+ 375711675205023424/639790539262875*ep^3+12639066969880845261632/ 28819364841096204375*ep^4+406365756421014097219725376/ 1298168289267178526071875*ep^5+12718704458788802860399082024768/ 58475990590040056706907609375*ep^6; Fill mnchfac1(13,2)= -2048/91-129145088/4099095*ep-5607358794304/184643734275*ep^2- 207285335824775072/8317277010417375*ep^3-7037777173573268255296/ 374651742934250656875*ep^4-227568776116938423114463328/ 16876187760473320838934375*ep^5-7147878038639593066291156443904/ 760187877670520737189798921875*ep^6; Fill mnchfac1(13,4)= 256/273+17104096/12297285*ep+765124349648/553931202825*ep^2+ 28782752505588064/24951831031252125*ep^3+987765403914509727152/ 1123955228802751970625*ep^4+32153921399561393777604736/ 50628563281419962516803125*ep^5+1014182537283552715179078333248/ 2280563633011562211569396765625*ep^6; Fill mnchfac1(13,6)= -128/3003-9076208/135270135*ep-419729246584/6093243231075*ep^2- 16110167517555512/274470141343773375*ep^3-559853837941644685216/ 12363507516830271676875*ep^4-18369562166151731874761888/ 556914196095619587684834375*ep^5-582314625712167699616689097984/ 25086199963127184327263364421875*ep^6; Fill mnchfac1(13,8)= 32/15015+2413196/676350675*ep+115802553028/30466216155375*ep^2+ 4549174479503504/1372350706718866875*ep^3+160455215928334705072/ 61817537584151358384375*ep^4+5315161061687116647687296/ 2784570980478097938424171875*ep^5+169520799430411541843679699328/ 125430999815635921636316822109375*ep^6; Fill mnchfac1(13,10)= -16/135135-1286678/6087156075*ep-64341099904/274195945398375*ep^2- 2596614444771272/12351156360469801875*ep^3-93223663260247568896/ 556357838257362225459375*ep^4-3124164965461097406168128/ 25061138824302881445817546875*ep^5-100396845367338563439711330304/ 1128878998340723294726851398984375*ep^6; Fill mnchfac1(13,12)= 1/135135+86048/6087156075*ep+4505822764/274195945398375*ep^2+ 187659001098752/12351156360469801875*ep^3+6883116416827133536/ 556357838257362225459375*ep^4+234016557715815866651648/ 25061138824302881445817546875*ep^5+7592462315747275929147393664/ 1128878998340723294726851398984375*ep^6; Fill mnchfac1(14,0)= 16384/15+1022076928/675675*ep+8855205451264/6087156075*ep^2+ 1635953439324307456/1370979726991875*ep^3+55546394976216520160384/ 61755781802349009375*ep^4+1796409882008846330444963968/ 2781789191286811127296875*ep^5+11286825660272378214206183220352/ 25061138824302881445817546875*ep^6; Fill mnchfac1(14,2)= -4096/105-268698112/4729725*ep-2386708597888/42610092525*ep^2- 447384534399600064/9596858088943125*ep^3-15326058483484843246016/ 432290472616443065625*ep^4-498414063672824065755297472/ 19472524339007677891078125*ep^5-628487173008311367973015945664/ 35085594354024034024144565625*ep^6; Fill mnchfac1(14,4)= 2048/1365+141445376/61486425*ep+1291375944512/553931202825*ep^2+ 246065355438470432/124759155156260625*ep^3+8515645698336721669888/ 5619776144013759853125*ep^4+278713744181148773463810656/ 253142816407099812584015625*ep^5+1764366557238314519942960648768/ 2280563633011562211569396765625*ep^6; Fill mnchfac1(14,6)= -256/4095-18641632/184459275*ep-175417198288/1661793608475*ep^2- 34050530970176704/374277465468781875*ep^3-1192272892921391011376/ 16859328432041279559375*ep^4-39314712394447268191928992/ 759428449221299437752046875*ep^5-50012267996984120317592154368/ 1368338179806937326941638059375*ep^6; Fill mnchfac1(14,8)= 128/45045+9844976/2029052025*ep+95771634488/18279729693225*ep^2+ 18986189701230152/4117052120156600625*ep^3+673884893287232978128/ 185452612752454075153125*ep^4+22416914835234853141398656/ 8353712941434293815272515625*ep^5+143390123242517645516785885184/ 75258599889381552981790093265625*ep^6; Fill mnchfac1(14,10)= -32/225225-2605388/10145260125*ep-131450513356/456993242330625*ep^2- 1067733252543928/4117052120156600625*ep^3-192519245502228862912/ 927263063762270375765625*ep^4-6471431650173503198336768/ 41768564707171469076362578125*ep^5-208388217921353602052890327936/ 1881464997234538824544752331640625*ep^6; Fill mnchfac1(14,12)= 16/2027025+1382774/91307341125*ep+72646040548/4112939180975625*ep^2+ 606585312860512/37053469081409405625*ep^3+111439420205448744256/ 8345367573860433381890625*ep^4+3793470123215022564169664/ 375917082364543221687263203125*ep^5+123180426927367988960114332288/ 16933184975110849420902770984765625*ep^6; Fill mnchfac1(14,14)= -1/2027025-92054/91307341125*ep-5058699088/4112939180975625*ep^2- 43608309564256/37053469081409405625*ep^3-8192673953041741216/ 8345367573860433381890625*ep^4-283221757477784564394944/ 375917082364543221687263203125*ep^5-9293492191158850022903427328/ 16933184975110849420902770984765625*ep^6; Fill mnchfac1(15,0)= 2048+133140992/45045*ep+5900508278272/2029052025*ep^2+ 221097615608542592/91398648466125*ep^3+7574121111626553240832/ 4117052120156600625*ep^4+246347542921060776392076032/ 185452612752454075153125*ep^5+7767029312071063526660719270912/ 8353712941434293815272515625*ep^6; Fill mnchfac1(15,2)= -1024/15-69645568/675675*ep-631879955968/6087156075*ep^2- 120036485343130816/1370979726991875*ep^3-4147530121298698460864/ 61755781802349009375*ep^4-135628804414790379674012608/ 2781789191286811127296875*ep^5-858161591138629454698283899456/ 25061138824302881445817546875*ep^6; Fill mnchfac1(15,4)= 256/105+18235072/4729725*ep+169704257824/42610092525*ep^2+ 32739238583526304/9596858088943125*ep^3+1142221030467170498336/ 432290472616443065625*ep^4+37582297269225715996899232/ 19472524339007677891078125*ep^5+238724606077404111918575630656/ 175427971770120170120722828125*ep^6; Fill mnchfac1(15,6)= -128/1365-9561056/61486425*ep-18295588144/110786240565*ep^2- 17954474614737152/124759155156260625*ep^3-633322769773649480848/ 5619776144013759853125*ep^4-20985612031878553449587936/ 253142816407099812584015625*ep^5-133905332176793893499852254976/ 2280563633011562211569396765625*ep^6; Fill mnchfac1(15,8)= 16/4095+1255192/184459275*ep+12377077984/1661793608475*ep^2+ 2476611609254344/374277465468781875*ep^3+88461927049944678896/ 16859328432041279559375*ep^4+2955265462648549019604352/ 759428449221299437752046875*ep^5+18956832068182634863949499136/ 6841690899034686634708190296875*ep^6; Fill mnchfac1(15,10)= -8/45045-660356/2029052025*ep-6729370556/18279729693225*ep^2- 1376089666761272/4117052120156600625*ep^3-49866050710359748288/ 185452612752454075153125*ep^4-1681834208983197679041536/ 8353712941434293815272515625*ep^5-10855838251248556331109767552/ 75258599889381552981790093265625*ep^6; Fill mnchfac1(15,12)= 2/225225+174098/10145260125*ep+9195937636/456993242330625*ep^2+ 77089103554336/4117052120156600625*ep^3+14202752012392469632/ 927263063762270375765625*ep^4+484434848685621299217728/ 41768564707171469076362578125*ep^5+15751934589965076556213465216/ 1881464997234538824544752331640625*ep^6; Fill mnchfac1(15,14)= -1/2027025-92054/91307341125*ep-5058699088/4112939180975625*ep^2- 43608309564256/37053469081409405625*ep^3-8192673953041741216/ 8345367573860433381890625*ep^4-283221757477784564394944/ 375917082364543221687263203125*ep^5-9293492191158850022903427328/ 16933184975110849420902770984765625*ep^6; Fill mnchfac1(16,0)= 65536/17+75196264448/13018005*ep+57875871822457856/9968732598825*ep^2+ 37362483254848926620672/7633706518539226125*ep^3+ 21945499113835013680434024704/5845625272169190493610625*ep^4+ 12201132004815697250304907827488768/4476375236542640158339740253125* ep^5+6562774638413504361334915855526075204096/3427851483011074840851031\ 194934265625*ep^6; Fill mnchfac1(16,2)= -2048/17-2447901184/13018005*ep-1925778310087168/9968732598825*ep^2- 1259745953440522719616/7633706518539226125*ep^3- 746088682309618045037734912/5845625272169190493610625*ep^4- 416993412638542080463173436789504/4476375236542640158339740253125*ep^5- 225044142489744084807083745911634508288/3427851483011074840851031194934\ 265625*ep^6; Fill mnchfac1(16,4)= 1024/255+1276226816/195270075*ep+41121672409088/5981239559295*ep^2+ 682355539174170147008/114505597778088391875*ep^3+ 407879273785189582693772864/87684379082537857404159375*ep^4+ 229319351125278753617686516874816/67145628548139602375096103796875*ep^5 +24845810687833729610895677465758697152/1028355444903322452255309358480\ 2796875*ep^6; Fill mnchfac1(16,6)= -256/1785-333059264/1366890525*ep-55045592329888/209343384575325*ep^2- 185643166225862781152/801539184446618743125*ep^3- 112124035530936525145504736/613790653577765001829115625*ep^4- 63462742214773088988567874516064/470019399836977216625672726578125*ep^5 -6905703340416942609714357629708156416/71984881143232571657871655093619\ 578125*ep^6; Fill mnchfac1(16,8)= 128/23205+174069472/17769576825*ep+29573508614576/2721463999479225*ep^2 +101531720737639386976/10420009397806043660625*ep^3+ 62042743775518910662573648/7979278496510945023778503125*ep^4+ 35385998929483485926862837993472/6110252197880703816133745445515625* ep^5+773946824719343250512309981851034368/18716069097240468631046630324\ 3410903125*ep^6; Fill mnchfac1(16,10)= -16/69615-22779704/53308730475*ep-3987420244048/8164391998437675*ep^2- 13963726285198013672/31260028193418130981875*ep^3- 8646420710171918577783296/23937835489532835071335509375*ep^4- 4975010395779169010000873554304/18330756593642111448401236336546875* ep^5-547211579378320120852582387612089856/28074103645860702946569945486\ 51163546875*ep^6; Fill mnchfac1(16,12)= 8/765765+11946772/586396035225*ep+432009005716/17961662396562885*ep^2+ 7733720815921990336/343860310127599440800625*ep^3+ 4861593329686368646132288/263316190384861185784690603125*ep^4+ 2825945017535701058300936006272/201638322530063225932413599702015625* ep^5+312951422168309626261015125821369984/30881514010446773241226940035\ 162799015625*ep^6; Fill mnchfac1(16,14)= -2/3828825-3139846/2931980176125*ep-2940494702944/2245207799570360625* ep^2-86344119864019552/68772062025519888160125*ep^3- 1380696594790769492126272/1316580951924305928923453015625*ep^4- 812215167174920624589041469376/1008191612650316129662067998510078125* ep^5-453385872459557342035111641356383744/77203785026116933103067350087\ 9069975390625*ep^6; Fill mnchfac1(16,16)= 1/34459425+1655008/26387821585125*ep+1611063707152/20206870196133245625 *ep^2+243275770764654464/3094742791148394967205625*ep^3+ 793843892172937871410336/11849228567318753360311077140625*ep^4+ 473651791152994731083469173248/9073724513852845166958611986590703125* ep^5+266993598880031227711792795283997952/69483406523505239792760615079\ 11629778515625*ep^6; Fill mnchfac1(17,0)= 65536/9+77820325888/6891885*ep+61109998518578176/5277564317025*ep^2+ 39955008832559536602112/4041374039226649125*ep^3+ 23662077982138671952596553984/3094742791148394967205625*ep^4+ 13225884902343267962156434980425728/2369845713463750672062215428125* ep^5+7138499064172458233255011552746366716416/1814744902770569033391722\ 397318140625*ep^6; Fill mnchfac1(17,2)= -32768/153-40386197504/117162045*ep-32374195525856768/89718593389425* ep^2-21435800053741986415616/68703358666853035125*ep^3- 12796614604490143754389699712/52610627449522714442495625*ep^4- 7189365956030892506494701513739904/40287377128883761425057662278125* ep^5-3893094521575640669582559606059597333888/3085066334709967356765928\ 0754408390625*ep^6; Fill mnchfac1(17,4)= 1024/153+1311077632/117162045*ep+1074442195362304/89718593389425*ep^2+ 721291890912662995648/68703358666853035125*ep^3+ 434415461693112953503577536/52610627449522714442495625*ep^4+ 245458945877429555880438613045312/40287377128883761425057662278125*ep^5 +133406945654853136165628992346777625664/308506633470996735676592807544\ 08390625*ep^6; Fill mnchfac1(17,6)= -512/2295-681676928/1757430675*ep-114404277306496/269155780168275*ep^2- 389848209260201134304/1030550380002795526875*ep^3- 237109871777499004859142272/789159411742840716637434375*ep^4- 134834169002827879637283378650528/604310656933256421375864934171875* ep^5-14717378397837986833235489987375383552/925519900412990207029778422\ 63225171875*ep^6; Fill mnchfac1(17,8)= 128/16065+177420512/12302014725*ep+30541961017648/1884090461177925*ep^2 +105814896878864290976/7213852660019568688125*ep^3+ 65065278266406430770445328/5524115882199885016462040625*ep^4+ 37267450308683735656387277990912/4230174598532794949631054539203125* ep^5+4087031872111342434521921124425427712/6478639302890931449208448958\ 42576203125*ep^6; Fill mnchfac1(17,10)= -64/208845-92480176/159926191425*ep-3272097892456/4898635199062605*ep^2 -57726021598310162488/93780084580254392945625*ep^3- 35932990435451675506578304/71813506468598505214006528125*ep^4- 20750357955942148773908633992576/54992269780926334345203709009640625* ep^5-2287975903134625671966378179279251712/8422231093758210883970983645\ 953490640625*ep^6; Fill mnchfac1(17,12)= 8/626535+12070532/479778574275*ep+2199114365068/73479527985939075*ep^2+ 7917421371358060736/281340253740763178836875*ep^3+ 4996864152467959886614208/215440519405795515642019584375*ep^4+ 2912663384302320871953006664832/164976809342779003035611127028921875* ep^5+323170582499832654704315508221491072/25266693281274632651912950937\ 860471921875*ep^6; Fill mnchfac1(17,14)= -4/6891885-6313726/5277564317025*ep-1187463189632/808274807845329825* ep^2-4372036935410188768/3094742791148394967205625*ep^3- 2802791427492560234391424/2369845713463750672062215428125*ep^4- 1651448017376055016693662314176/1814744902770569033391722397318140625* ep^5-184578401995843141349583614511017984/27793362609402095917104246031\ 6465191140625*ep^6; Fill mnchfac1(17,16)= 1/34459425+1655008/26387821585125*ep+1611063707152/20206870196133245625 *ep^2+243275770764654464/3094742791148394967205625*ep^3+ 793843892172937871410336/11849228567318753360311077140625*ep^4+ 473651791152994731083469173248/9073724513852845166958611986590703125* ep^5+266993598880031227711792795283997952/69483406523505239792760615079\ 11629778515625*ep^6; Fill mnchfac1(18,0)= 262144/19+2034644402176/92147055*ep+30936861817158135808/ 1340696801869425*ep^2+389006823534136572381927424/ 19506515043187264467375*ep^3+4411972764703764644295250155246592/ 283810723348879615922328920625*ep^4+47098469043699353462338273266177106\ 095616/4129314052739841182648481912145659375*ep^5+484620769213642826023\ 838328042569508681648268288/60079599336330165181385480277630196174640625 *ep^6; Fill mnchfac1(18,2)= -65536/171-1578956541952/2487970485*ep-24478928777902468096/ 36198813650474475*ep^2-311541619373746828516953088/ 526675906166056140619125*ep^3-3560801001029768347812904674613504/ 7662889530419749629902880856875*ep^4-3820207393791438457555348439490798\ 4456192/111491479423975711931509011627932803125*ep^5-394344599789802850\ 928182944119464217157059616256/1622149182080914459897407967496015296715\ 296875*ep^6; Fill mnchfac1(18,4)= 32768/2907+817522927616/42295498245*ep+12939145474166025728/ 615379832058066075*ep^2+166844842036665778207913984/ 8953490404822954390525125*ep^3+1923195492796174763514586560083072/ 130269122017135743708348974566875*ep^4+20747013447444262440004518677833\ 889814656/1895355150207587102835653197674857653125*ep^5+214928735088963\ 834694681539392749632345852219008/2757653609537554581825593544743226004\ 4160046875*ep^6; Fill mnchfac1(18,6)= -1024/2907-26478761728/42295498245*ep-428426650475075584/ 615379832058066075*ep^2-5603489347772047996313152/ 8953490404822954390525125*ep^3-65195369424101497881333209751616/ 130269122017135743708348974566875*ep^4-70762931456225161293619642005377\ 6450368/1895355150207587102835653197674857653125*ep^5-73600028139832129\ 29285150767301371157483193024/27576536095375545818255935447432260044160\ 046875*ep^6; Fill mnchfac1(18,8)= 512/43605+13736004992/634432473675*ep+45507364852724608/ 1846139496174198225*ep^2+3022448339780186174642336/ 134302356072344315857876875*ep^3+35529365905738996344298256883392/ 1954036830257036155625234618503125*ep^4+3882770407993495550131808459578\ 15080032/28430327253113806542534797965122864796875*ep^5+811323619995742\ 150633831079124708302821031104/8272960828612663745476780634229678013248\ 0140625*ep^6; Fill mnchfac1(18,10)= -128/305235-3567025568/4441027315725*ep-12118249261002736/ 12922976473219387575*ep^2-818581689145647773134784/ 940116492506410211005138125*ep^3-9733054543333586398424321329808/ 13678257811799253089376642329521875*ep^4-107184361466633176751823683492\ 260058528/199012290771796645797743585755860053578125*ep^5-4502184562439\ 1195352582539661377015000066368/115821451600577292436674928879215492185\ 472196875*ep^6; Fill mnchfac1(18,12)= 64/3968055+1855141264/57733355104425*ep+6474377595893864/ 167998694151852038475*ep^2+445521299740006052164792/ 12221514402583332743066795625*ep^3+5365152482729309272764735047344/ 177817351553390290161896350283784375*ep^4+59596832566224817667443769387\ 442197344/2587159780033356395370666614826180696515625*ep^5+125894709465\ 769185343319295049358211511449536/7528394354037524008383870377149006992\ 055692796875*ep^6; Fill mnchfac1(18,14)= -8/11904165-241592348/173200065313275*ep-867881471536036/ 503996082455556115425*ep^2-60951525736652864663624/ 36664543207749998229200386875*ep^3-744545423425232962201730265488/ 533452054660170870485689050851353125*ep^4-83523365455460394473227838032\ 86687008/7761479340100069186111999844478542089546875*ep^5-3552443112981\ 566950416994040378464513309376/4517036612422514405030322226289404195233\ 415678125*ep^6; Fill mnchfac1(18,16)= 4/130945815+126086914/1905200718446025*ep+467295389736836/ 5543956907011117269675*ep^2+33566185881196766955112/ 403309975285249980521204255625*ep^3+416670202284887226800887448464/ 5867972601261879575342579559364884375*ep^4+4727291699282205785242523716\ 414949344/85376272741100761047231998289263962985015625*ep^5+10131651346\ 706934247853186597315422737887168/2484370136832382922766677224459172307\ 37837862296875*ep^6; Fill mnchfac1(18,18)= -1/654729075-32976682/9526003592230125*ep-632098776065332/ 138598922675277931741875*ep^2-1862244159376232552168/ 403309975285249980521204255625*ep^3-117714943858916843543175683056/ 29339863006309397876712897796824421875*ep^4-135309269439038601403272679\ 0280955232/426881363705503805236159991446319814925078125*ep^5- 14633251134911390307284448204707320220500672/62109253420809573069166930\ 61147930768445946557421875*ep^6; Fill mnchfac1(19,0)= 131072/5+1047433306112/24249225*ep+16213367928007141376/352814947860375 *ep^2+206247925186001974627463168/5133293432417701175625*ep^3+ 2357123617857184999963740483106304/74687032460231477874297084375*ep^4+ 25289472617501961380594504604509557663232/10866615928262739954338110295\ 12015625*ep^5+261072211731185835277436236662544995221740660736/ 15810420877981622416154073757271104256484375*ep^6; Fill mnchfac1(19,2)= -65536/95-540445044736/460735275*ep-8520537863685833728/ 6703484009347125*ep^2-109648692270186369778453504/ 97532575215936322336875*ep^3-1262526939764871765435267689043712/ 1419053616744398079611644603125*ep^4-1361153525078002771775579006415533\ 6951296/20646570263699205913242409560728296875*ep^5-1409593431569064855\ 64005380909750409211379511808/30039799668165082590692740138815098087320\ 3125*ep^6; Fill mnchfac1(19,4)= 16384/855+418577093632/12439852425*ep+6728742401875323136/ 180994068252372375*ep^2+87675412151643615089592448/ 2633379530830280703095625*ep^3+1017763898031418495480481514444544/ 38314447652098748149514404284375*ep^4+110313176300930515938524318598533\ 85962752/557457397119878559657545058139664015625*ep^5+11463620414296630\ 3474201910247871247682621796096/811074591040457229948703983748007648357\ 6484375*ep^6; Fill mnchfac1(19,6)= -8192/14535-216299710976/211477491225*ep-3549492390075026048/ 3076899160290330375*ep^2-46875556885329468963107264/ 44767452024114771952625625*ep^3-549000628753802900399660924652992/ 651345610085678718541744872834375*ep^4-59855237481686117782477677305955\ 79449536/9476775751037935514178265988374288265625*ep^5-6244084249897199\ 8970573198375004503491093531328/137882680476877729091279677237161300220\ 800234375*ep^6; Fill mnchfac1(19,8)= 256/14535+6992158528/211477491225*ep+117279928141637344/ 3076899160290330375*ep^2+1571509178872435748461792/ 44767452024114771952625625*ep^3+18585315136107950916082906324576/ 651345610085678718541744872834375*ep^4+20394809794644614279723213586055\ 8099808/9476775751037935514178265988374288265625*ep^5+21367357024213278\ 60345620378208137308639797184/13788268047687772909127967723716130022080\ 0234375*ep^6; Fill mnchfac1(19,10)= -128/218025-3620235296/3172162368375*ep-62151480080644496/ 46153487404354955625*ep^2-169207919683712107074304/ 134302356072344315857876875*ep^3-10113289751292428201975231045168/ 9770184151285180778126173092515625*ep^4-1117836265199944366892577808119\ 29609696/142151636265569032712673989825614323984375*ep^5-11767945036426\ 36413933852869500435205907118016/20682402071531659363691951585574195033\ 12003515625*ep^6; Fill mnchfac1(19,12)= 32/1526175+938314904/22205136578625*ep+16513016129930384/ 323074411830484689375*ep^2+45734218580042122048168/ 940116492506410211005138125*ep^3+2765969442797383177713126333392/ 68391289058996265446883211647609375*ep^4+308204472883493966332107560277\ 75871904/995061453858983228988717928779300267890625*ep^5+32622885280619\ 4434808019078603864945792691264/144776814500721615545843661099019365231\ 84024609375*ep^6; Fill mnchfac1(19,14)= -16/19840275-487064572/288666775522125*ep-8801628298624732/ 4199967353796300961875*ep^2-24837256966756922410232/ 12221514402583332743066795625*ep^3-1521973390453239157741161182896/ 889086757766951450809481751418921875*ep^4-17113608652903011315753496903\ 979224672/12935798900166781976853333074130903482578125*ep^5-18226789163\ 9383003153544274269381501253124672/188209858850938100209596759428725174\ 801392319921875*ep^6; Fill mnchfac1(19,16)= 2/59520825+63307994/866000326566375*ep+1176962026868324/ 12599902061388902885625*ep^2+3390061290904475641768/ 36664543207749998229200386875*ep^3+210798263558388165553708055312/ 2667260273300854352428445254256765625*ep^4+2394785807744709177661642923\ 876059744/38807396700500345930559999222392710447734375*ep^5+25687071448\ 863285164627141940209109898925504/5646295765528143006287902782861755244\ 04176959765625*ep^6; Fill mnchfac1(19,18)= -1/654729075-32976682/9526003592230125*ep-632098776065332/ 138598922675277931741875*ep^2-1862244159376232552168/ 403309975285249980521204255625*ep^3-117714943858916843543175683056/ 29339863006309397876712897796824421875*ep^4-135309269439038601403272679\ 0280955232/426881363705503805236159991446319814925078125*ep^5- 14633251134911390307284448204707320220500672/62109253420809573069166930\ 61147930768445946557421875*ep^6; Fill mnchfac1(20,0)= 1048576/21+1721904332800/20369349*ep+27108206457847021568/ 296364556202715*ep^2+348687951609134651084066816/4311966483230868987525 *ep^3+573499901426290890388104664567808/8962443895227777344915650125* ep^4+1731292929627261545714560281195489901568/ 36511829518962806246576050591603725*ep^5+448254550256421612121106702037\ 098017287971345408/13280753537504562829569421956107727575446875*ep^6; Fill mnchfac1(20,2)= -131072/105-1107974152192/509233725*ep-17748654471475030016/ 7409113905067875*ep^2-230841703227490779469733888/ 107799162080771724688125*ep^3-382427720109774592621652377098752/ 224061097380694433622891253125*ep^4-28998902949973540898900819950130551\ 450112/22819893449351753904110031619752328125*ep^5-30125512158187567169\ 4816135842842396449617355776/332018838437614070739235548902693189386171\ 875*ep^6; Fill mnchfac1(20,4)= 65536/1995+570715467776/9675440775*ep+9311361165919003648/ 140773164196289625*ep^2+122551166096965355563377664/ 2048184079534662769074375*ep^3+204620344870064821382681888102656/ 4257160850233194238834933809375*ep^4+1559628916371274676507317574736578\ 8327936/433577975537683324178090600775294234375*ep^5+162570653162388327\ 373964328347602761123750588928/6308357930314667344045475429151170598337\ 265625*ep^6; Fill mnchfac1(20,6)= -16384/17955-441279910912/261236900925*ep-7340210736028754176/ 3800875433299819875*ep^2-97846521962236578888650368/ 55300970147435894765008125*ep^3-164763841159832979392731095695872/ 114943342956296244448543212853125*ep^4-12629475812552671945738311741463\ 678642432/11706605339517449752808446220932944328125*ep^5-13213648989214\ 6164409253116678665223267080545536/170325664118496018289227836587081606\ 155106171875*ep^6; Fill mnchfac1(20,8)= 8192/305235+227651119616/4441027315725*ep+3864941716993328768/ 64614882366096937875*ep^2+52231090674315614837061824/ 940116492506410211005138125*ep^3+88767954881211688344418911759296/ 1954036830257036155625234618503125*ep^4+6846545392450351979565244404798\ 105267776/199012290771796645797743585755860053578125*ep^5+7192789505292\ 8678198097370589401094017492701248/289553629001443231091687322198038730\ 4636804921875*ep^6; Fill mnchfac1(20,10)= -256/305235-7346890048/4441027315725*ep-127460293274449504/ 64614882366096937875*ep^2-1748127083454042192669472/ 940116492506410211005138125*ep^3-3001091770262530508742744798688/ 1954036830257036155625234618503125*ep^4-2330577577795439073475790501569\ 44106528/199012290771796645797743585755860053578125*ep^5-24596768456437\ 08466439940240639110048732450944/28955362900144323109168732219803873046\ 36804921875*ep^6; Fill mnchfac1(20,12)= 128/4578525+3797601056/66615409735875*ep+67413701935912016/ 969223235491454068125*ep^2+187890548556019147716448/ 2820349477519230633015414375*ep^3+1630723033340074780579497649424/ 29310552453855542334378519277546875*ep^4+127601134419252826637696928367\ 071088256/2985184361576949686966153786337900803671875*ep^5+135360756757\ 3362478220910372230834600770809536/434330443502164846637530983297058095\ 69552073828125*ep^6; Fill mnchfac1(20,14)= -32/32049675-982656344/466307868151125*ep-17874653546120864/ 6784562648440178476875*ep^2-50687892815892781571944/ 19742446342634614431107900625*ep^3-3117152904988373930917104545792/ 1436217070238921574384547444599796875*ep^4-5019970364886376676866380040\ 534781792/2985184361576949686966153786337900803671875*ep^5-374921009154\ 779173796853136419239763392735744/3040313104515153926462716883079406669\ 86864516796875*ep^6; Fill mnchfac1(20,16)= 16/416645775+509235292/6062002285964625*ep+9507260365690372/ 88199314429722320199375*ep^2+5494408412188431592816/ 51330360490849997520880541625*ep^3+1712309313066167757871594850896/ 18670821913105980466999116779797359375*ep^4+278375775696277257040048996\ 3002897856/38807396700500345930559999222392710447734375*ep^5+2092694789\ 17017238626932202758621079557989312/39524070358697001044015319480032286\ 70829238718359375*ep^6; Fill mnchfac1(20,18)= -2/1249937325-66079334/18186006857893875*ep-1268526177612104/ 264597943289166960598125*ep^2-3741613024610828471704/ 769955407362749962813208124375*ep^3-236721468157450598995638463712/ 56012465739317941400997350339392078125*ep^4-388971949218063392738847039\ 126838112/116422190101501037791679997667178131343203125*ep^5-2945997877\ 4974242474542209177157310265510784/118572211076091003132045958440096860\ 12487716155078125*ep^6; Fill mnchfac1(20,20)= 1/13749310575+34362352/200046075436832625*ep+679713656361172/ 2910577376180836566579375*ep^2+2050615923818229593216/ 8469509480990249590945289368125*ep^3+131922328694702874545333756656/ 616137123132497355410970853733312859375*ep^4+21941335822753927802913705\ 9552353536/1280644091116511415708479974338959444775234375*ep^5+ 16761492691577470766990888649876688290104512/13042943218370010344525055\ 4284106546137364877705859375*ep^6; Fill mnchfac1(21,0)= 1048576/11+588644679680/3556553*ep+28250985333859155968/155238577058565 *ep^2+367273591924227707607535616/2258649110263788517275*ep^3+ 4258703363965218552169776465760256/32862294282501850264690717125*ep^4+ 1845354426808603360009855613902819638272/ 19125244033742422319635074119411475*ep^5+684696581906496366680491306490\ 60337281477817344/993797883758844837586827493314183696121875*ep^6; Fill mnchfac1(21,2)= -524288/231-907183357952/224062839*ep-14754021048736251904/ 3260010118229865*ep^2-193858898135415034891675648/ 47431631315539558862775*ep^3-323380558810322793112008904351744/ 98586882847505550794072151375*ep^4-492705518427019838933670119970220587\ 1616/2008150623542954343561682782538204875*ep^5-25671198506024294284355\ 2424150189569510477717504/146088288912550191125263641517185003329915625 *ep^6; Fill mnchfac1(21,4)= 65536/1155+582881570816/5601570975*ep+9645295946232275968/ 81500252955746625*ep^2+128178539882387627673601024/ 1185790782888488971569375*ep^3+30776262294051978642555924291328/ 352096010169662681407400540625*ep^4+16494109199114769376621035028407759\ 333376/251018827942869292945210347817275609375*ep^5+1724440716169689545\ 80324061637970715378675112448/36522072228137547781315910379296250832478\ 90625*ep^6; Fill mnchfac1(21,6)= -32768/21945-299804981248/106429848525*ep-5052228134581512704/ 1548504806159185875*ep^2-67958089418671625912579072/ 22530024874881290459818125*ep^3-115151193221137507765652322601088/ 46828769352565136627184271903125*ep^4-886430587389627523374967076992023\ 4732928/4769357730914516565958996608528236578125*ep^5-93010010996008658\ 494534347456113326239598166144/6939193723346134078450022972066287658170\ 9921875*ep^6; Fill mnchfac1(21,8)= 8192/197505+231475390976/2873605910175*ep+3976274395527467648/ 41809629766298018625*ep^2+54182619479966537990320064/ 608310671621794842415089375*ep^3+92619997443753566882326475541056/ 1264376772519258688933975341384375*ep^4+7172287475508574279151405830838\ 990908736/128772658734691947280892908430262387609375*ep^5+7555492200561\ 6140775045935560695882323661748928/187358230530345620118150620245789766\ 7706167890625*ep^6; Fill mnchfac1(21,10)= -4096/3357585-119243277568/48851300472975*ep-2090192153086694464/ 710763706027066316625*ep^2-28880211145163281885646752/ 10341281417570512321056519375*ep^3-49841037737540172100911837903808/ 21494405132827397711877580803534375*ep^4-388474064722432424752968422262\ 3640625248/2189135198489763103775179443314460589359375*ep^5-41102235709\ 438244416392485670701497109152501504/3185089919015875542008560544178426\ 0351004854140625*ep^6; Fill mnchfac1(21,12)= 128/3357585+3842748704/48851300472975*ep+68812892706774992/ 710763706027066316625*ep^2+965081322716881776628256/ 10341281417570512321056519375*ep^3+240414689495033378639166358832/ 3070629304689628244553940114790625*ep^4+1321105311649341266706314670897\ 25545344/2189135198489763103775179443314460589359375*ep^5+1404579040735\ 745128555314302367128657309554112/3185089919015875542008560544178426035\ 1004854140625*ep^6; Fill mnchfac1(21,14)= -64/50363775-1983452368/732769507094625*ep-36330333663324088/ 10661455590405994749375*ep^2-20711198350860867625096/ 6204768850542307392633911625*ep^3-913198628779710271342249191712/ 322416076992410965678163712053015625*ep^4-72255686107778850880600724288\ 512651168/32837027977346446556627691649716908840390625*ep^5-77237529596\ 6148708487462555120968656395550848/477763487852381331301284081626763905\ 265072812109375*ep^6; Fill mnchfac1(21,16)= 16/352546425+512491132/5129386549662375*ep+9615191105989852/ 74630189132841963245625*ep^2+27887520217551628264496/ 217166909768980758742186906875*ep^3+1743008475888948342613676731696/ 15798387772628137318230021890597765625*ep^4+283933534900478457251175730\ 7105008576/32837027977346446556627691649716908840390625*ep^5+2137493285\ 10078341274475564205857199574793792/33443444149666693191089885713873473\ 36855509684765625*ep^6; Fill mnchfac1(21,18)= -8/4583103525-265199126/66682025145610875*ep-5104405088818496/ 970192458726945522193125*ep^2-15086325039451857458392/ 2823169826996749863648429789375*ep^3-955926935707120779347563538048/ 205379041044165785136990284577770953125*ep^4-22464372180256075600883769\ 2833329824/60983051957929115033737141635188544989296875*ep^5-1191942506\ 35957202917982026082827929833609216/43476477394566701148416851428035515\ 379121625901953125*ep^6; Fill mnchfac1(21,20)= 1/13749310575+34362352/200046075436832625*ep+679713656361172/ 2910577376180836566579375*ep^2+2050615923818229593216/ 8469509480990249590945289368125*ep^3+131922328694702874545333756656/ 616137123132497355410970853733312859375*ep^4+21941335822753927802913705\ 9552353536/1280644091116511415708479974338959444775234375*ep^5+ 16761492691577470766990888649876688290104512/13042943218370010344525055\ 4284106546137364877705859375*ep^6; Fill mnchfac1(22,0)= 4194304/23+55449783894016/171037867*ep+62148447012132082024448/ 171707978824687305*ep^2+18773640843278935056606227120128/ 57460238696848076587523025*ep^3+5041448329983946376409848137016655847424 /19228454342647346039835476757497625*ep^4+25238480256124189915183972630\ 4251570188585611264/1286919319489547947773009251294531753830125*ep^5+ 43208773716402314365724491929872346118892115358985406464/30760984761789\ 6628576382938294123183144388655759375*ep^6; Fill mnchfac1(22,2)= -1048576/253-14216885108736/1881416537*ep-16185865646494692933632/ 1888787767071560355*ep^2-4939611430400022842765148762112/ 632062625665328842462753275*ep^3-13354979068614011175609644733439262351\ 36/211512997769120806438190244332473875*ep^4-67159019652865511163476517\ 453240188013484381184/14156112514385027425503101764239849292131375*ep^5 -1647410043030677534927152648628894859139012208775308288/48338690339955\ 1844905744617319336430655467887621875*ep^6; Fill mnchfac1(22,4)= 524288/5313+21882303447040/118529241831*ep+8441631814548135510016/ 39664543108502767455*ep^2+2604324848699357943102458894336/ 13273315138971905691717818775*ep^3+101321343397331258710314036451040088\ 064/634538993307362419314570732997421625*ep^4+7167983351101874733275580\ 885186961755973448192/59455672560417115187113027409807367026951775*ep^5 +43217128157661483349691907463896316521620720902405037056/4974051235981\ 38848408011211221597187144476456362909375*ep^6; Fill mnchfac1(22,6)= -65536/26565-14041955012608/2963231045775*ep-5510969387405605061632/ 991613577712569186375*ep^2-1719912378720983085985487541248/ 331832878474297642292945469375*ep^3-67436913073875512185452978431109980\ 416/15863474832684060482864268324935540625*ep^4-11989820446380228297642\ 1606865374599415825975808/371597953502606969919456421311296043918448593\ 75*ep^5-29016837689164161775189595060355807051671221091269944832/ 12435128089953471210200280280539929678611911409072734375*ep^6; Fill mnchfac1(22,8)= 32768/504735+7213354010624/56301389869725*ep+2882530576483548740096/ 18840657976538814541125*ep^2+910725032979212811114814879744/ 6304824691011655203565963918125*ep^3+3600991813154125875858030821225567\ 2448/301406021820997149174421098173775271875*ep^4+643886989601390919023\ 46347637310732074867965824/70603611165495324284696720049146248344505232\ 8125*ep^5+15642470921943931856938603300843064339023769706166925696/ 236267433709115952993805325330258663893626316772381953125*ep^6; Fill mnchfac1(22,10)= -8192/4542615-5562313573888/1520137526482575*ep-2265307307282547469952/ 508697765366547992610375*ep^2-725158267118879226334680363328/ 170230266657314690496281025789375*ep^3-28933362872653294042582652859042\ 781376/8137962589166923027709369650691932340625*ep^4-520568399479444585\ 25126066033796625460291034688/19062975014683737556868114413269487053016\ 412859375*ep^5-12699645677051080547117814240906398768455443776609817152/ 6379220710146130730832743783916983925127910552854312734375*ep^6; Fill mnchfac1(22,12)= 4096/77224455+2861785174784/25842337950203775*ep+1188986936108863222336/ 8647862011231315874376375*ep^2+385983943086118989229844859104/ 2893914533174349738436777438419375*ep^3+1555210495275940680030962700858\ 3453568/138345364015837691471059284061762849790625*ep^4+281713858062515\ 97501802751344470734586349460384/32407057524962353846675794502558127990\ 1279018609375*ep^5+6904367130707357876096731176747405396863924588894719\ 936/108446752072484222424156644326588726727174479398523316484375*ep^6; Fill mnchfac1(22,14)= -128/77224455-92107901152/25842337950203775*ep-39082274505059099408/ 8647862011231315874376375*ep^2-12879402295078230664046341312/ 2893914533174349738436777438419375*ep^3-5244850139955206056350879524507\ 37104/138345364015837691471059284061762849790625*ep^4-95714287544315204\ 8186356880274330079482289952/324070575249623538466757945025581279901279\ 018609375*ep^5-235780074498604806653923410329417045348156910237070208/ 108446752072484222424156644326588726727174479398523316484375*ep^6; Fill mnchfac1(22,16)= 64/1158366825+47481744944/387635069253056625*ep+20600421127746044632/ 129717930168469738115645625*ep^2+1379856370959773100966653608/ 8681743599523049215310332315258125*ep^3+2842308011395603339349332996328\ 38192/2075180460237565372065889260926442746859375*ep^4+5229583433396126\ 73898170304288726912690368704/48610586287443530770013691753837191985191\ 85279140625*ep^5+129556865019910360937793395257963062233911832671889152/ 1626701281087263336362349664898830900907617190977849747265625*ep^6; Fill mnchfac1(22,18)= -16/8108567775-12252881156/2713445484771396375*ep-5442983541528756628/ 908025511179288166809519375*ep^2-370984610303709300320350024/ 60772205196661344507172326206806875*ep^3-541741770621990984093718349138\ 928736/101683842551640703231228573785395694596109375*ep^4-2052696215611\ 2824890581469675838190357916928/486105862874435307700136917538371919851\ 9185279140625*ep^5-35823780429819038845933790843591299215393469184799808 /11386908967610843354536447654291816306353320336844948230859375*ep^6; Fill mnchfac1(22,20)= 8/105411381075+6332372458/35274791302028152875*ep+2884496441406398444/ 11804331645330746168523751875*ep^2+40068509905531577410044976/158007733\ 511319495718648048137697875*ep^3+296656458978635304970034464545198368/ 1321889953171329142005971459210144029749421875*ep^4+1135439219076379187\ 7198815926286703123515104/631937621736765900010177992799883495807494086\ 28828125*ep^5+19957842628748162433017141557085541526770654970625984/ 148029816578940963608973819505793611982593164378984327001171875*ep^6; Fill mnchfac1(22,22)= -1/316234143225-819433166/105824373906084458625*ep-383413267272815608/ 35412994935992238505571255625*ep^2-27181237845756473555515984/237011600\ 2669792435779720722065468125*ep^3-40872020098055931250366286319046096/ 3965669859513987426017914377630432089248265625*ep^4-1582125028602134326\ 134975265181511626491808/1895812865210297700030533978399650487422482258\ 86484375*ep^5-2803571040256992259702239379013002878077204164761088/ 444089449736822890826921458517380835947779493136952981003515625*ep^6; Fill mnchfac1(23,0)= 1048576/3+42519666950144/66927861*ep+16117764640820675428352/ 22396692890176605*ep^2+4916822256033218930723353403392/ 7494813743067140424459525*ep^3+1329188644911598202334432724426974703616/ 2508059262084436439978540446630125*ep^4+6684197693303930940701575099321\ 0783356571215872/167859041672549732318218597994938924412625*ep^5+ 11477890342832701810009410232447772818601434197345468416/40123023602334\ 342857789078907929110844920259446875*ep^6; Fill mnchfac1(23,2)= -524288/69-21768376582144/1539340803*ep-8375602077385422217216/ 515123936474061915*ep^2-2580272243587601374400838496256/ 172380716090544229762569075*ep^3-702136083773405432930109465944111392768 /57685363027942038119506430272492875*ep^4-35464139171644473586629231542\ 322423028880960512/3860757958468643843319027753883595261490375*ep^5- 6107507124361145387865589070758260748688938202817707008/922829542853689\ 885729148814882369549433165967278125*ep^6; Fill mnchfac1(23,4)= 131072/759+5575008821248/16932748833*ep+2178701295587778279424/ 5666363301214681065*ep^2+678208019413177329505688858624/ 1896187876995986527388259825*ep^3+1858501600461628204774155352676723307\ 52/634538993307362419314570732997421625*ep^4+94314235964746337981245997\ 30291304463861871104/42468337543155082276509305292719547876394125*ep^5+ 1629348373216418551652563707856703809682953192335665152/101511249713905\ 88743020636963706065043764825640059375*ep^6; Fill mnchfac1(23,6)= -65536/15939-2857126383616/355587725493*ep-1134879542427718740992/ 118993629325508302365*ep^2-357188547865480560572893852672/ 39819945416915717075153456325*ep^3-140881361081385936278502498027720404\ 48/1903616979922087257943712198992264875*ep^4-5030008069968843820082382\ 281017387077860976128/891835088406256727806695411147110505404276625* ep^5-6103490354990504280213952370180361692140664253673759232/ 1492215370794416545224033633664791561433429369088728125*ep^6; Fill mnchfac1(23,8)= 8192/79695+1831393409536/8889693137325*ep+739942524904759583744/ 2974840733137707559125*ep^2+235623535029629047272867730816/ 995498635422892926878836408125*ep^3+93682914676148940087435818609981918\ 72/47590424498052181448592804974806621875*ep^4+168160247096686642863145\ 60283190599155321505536/111479386050782090975836926393388813175534578125 *ep^5+4096046612954382604986251504590101321781433941752134144/ 37305384269860413630600840841619789035835734227218203125*ep^6; Fill mnchfac1(23,10)= -4096/1514205-939743767808/168904169609175*ep-386522588838556133632/ 56521973929616443623375*ep^2-124619433330379533202860160448/ 18914474073034965610697891754375*ep^3-713956974388359284595787048185700\ 288/129174009351855921074751899217332259375*ep^4-9024169471663381838066\ 971604906370551893193408/2118108334964859728540901601474387450335156984\ 375*ep^5-2206962348592962423137354906048766578341138269627840832/ 708802301127347858981415975990775991680878950317145859375*ep^6; Fill mnchfac1(23,12)= 1024/13627845+723845084096/4560412579447725*ep+303348998066114433184/ 1526093296099643977831125*ep^2+99104158213634143122765270176/ 510690799971944071488843077368125*ep^3+40114816284533352217379827941640\ 84192/24413887767500769083128108952075797021875*ep^4+729017132425649450\ 4369169602590177376686926496/571889250440512126706043432398084611590492\ 38578125*ep^5+1790753865071395315279594978383125109153700162510187584/ 19137662130438392192498231351750951775383731658562938203125*ep^6; Fill mnchfac1(23,14)= -512/231673365-372001090528/77527013850611325*ep-158997215879735569712/ 25943586033693947623129125*ep^2-52681886037342346539747501568/ 8681743599523049215310332315258125*ep^3-3076981832204068338373832353577\ 01008/59290870292501867773311121740755507053125*ep^4-394187550936056140\ 6886762921062081164462936928/972211725748870615400273835076743839703837\ 055828125*ep^5-972971431409164673146292110227091066502112899598902912/ 325340256217452667272469932979766180181523438195569949453125*ep^6; Fill mnchfac1(23,16)= 16/231673365+11959673384/77527013850611325*ep+5218799045569783936/ 25943586033693947623129125*ep^2+1755459894013456818451059704/ 8681743599523049215310332315258125*ep^3+ 72554030069535752494552348768961968/41503609204751307441317785218528854\ 9371875*ep^4+133805860378888157790961535029886365752008384/972211725748\ 870615400273835076743839703837055828125*ep^5+33203900989168781648065234\ 904854991307205271110961536/3253402562174526672724699329797661801815234\ 38195569949453125*ep^6; Fill mnchfac1(23,18)= -8/3475100475-6158310988/1162905207759169875*ep-2746787050051437524/ 389153790505409214346936875*ep^2-187801761526841858742203048/ 26045230798569147645930996945774375*ep^3- 39269674604059214268914222105985824/62255413807126961161976677827793282\ 40578125*ep^4-73035479277414057528318685430352458034836608/145831758862\ 33059231004107526151157595557555837421875*ep^5-182313199629667736512663\ 89633155947151057261441459264/48801038432617900090870489946964927027228\ 51572933549241796875*ep^6; Fill mnchfac1(23,20)= 2/24325703325+1587383362/8140336454314189125*ep+724639681443448196/ 2724076533537864500428558125*ep^2+50414624944191277558592816/1823166155\ 89984033521516978620420625*ep^3+74747185933232136723910458944129792/ 305051527654922109693685721356187083788328125*ep^4+28636482022688957141\ 43569100709471740271456/14583175886233059231004107526151157595557555837\ 421875*ep^5+5036974612827574755265838725329433102805105633953856/ 34160726902832530063609342962875448919059961010534844692578125*ep^6; Fill mnchfac1(23,22)= -1/316234143225-819433166/105824373906084458625*ep-383413267272815608/ 35412994935992238505571255625*ep^2-27181237845756473555515984/237011600\ 2669792435779720722065468125*ep^3-40872020098055931250366286319046096/ 3965669859513987426017914377630432089248265625*ep^4-1582125028602134326\ 134975265181511626491808/1895812865210297700030533978399650487422482258\ 86484375*ep^5-2803571040256992259702239379013002878077204164761088/ 444089449736822890826921458517380835947779493136952981003515625*ep^6; Fill mnchfac1(24,0)= 16777216/25+17366559184912384/13943304375*ep+33374413283574558039605248/ 23329888427267296875*ep^2+51388229764415700241549844693549056/ 39035488245141356377393359375*ep^3+699102033793153959975854773105822721\ 42098432/65314043283448865624441157464326171875*ep^4+882770314528551867\ 80029445308724636035459266770427904/10928323025556623197800689973628836\ 2247802734375*ep^5+1520327694244988289926166464482031364650297330164279\ 1425552384/26121760157769754464706431580683014872994960577392578125* ep^6; Fill mnchfac1(24,2)= -1048576/75-1109777639604224/41829913125*ep-2163270667311263626313728/ 69989665281801890625*ep^2-3362580067075132823134658137071616/ 117106464735424069132180078125*ep^3-46038150980098947145816902319951920\ 74186752/195942129850346596873323472392978515625*ep^4-58382764417923112\ 67587421620328656385351071491794944/32784969076669869593402069920886508\ 6743408203125*ep^5-1008351141369762085874363677139625419703391032097304\ 620724224/78365280473309263394119294742049044618984881732177734375*ep^6 ; Fill mnchfac1(24,4)= 524288/1725+567602397478912/962088001875*ep+1122927088396648522686464/ 1609762301481443484375*ep^2+1762980368412942069384954078507008/ 2693448688914753590040141796875*ep^3+2430160271877632332748289205190748\ 340299776/4506668986557971728086439865038505859375*ep^4+309592673055262\ 1270505975210069553065942453252918272/754054288763407000648247608180389\ 6995098388671875*ep^5+5363500666303174233064469485898407918283291100409\ 36775078912/1802401450886113058064743779067128026236652279840087890625* ep^6; Fill mnchfac1(24,6)= -131072/18975-145223466262528/10582968020625*ep- 291776653876385611913216/17707385316295878328125*ep^2- 462935986800603525774110865661952/29627935578062289490441559765625*ep^3 -642748380897236068970162766542701626489344/495733588521376890089508385\ 15423564453125*ep^4-822865517063911307294927287502098931283514146426368/ 82945971763974770071307236899842866946082275390625*ep^5-204325540713922\ 87012590247688576120915974453057666981397504/28323451371067490912445973\ 67105486898371882154034423828125*ep^6; Fill mnchfac1(24,8)= 65536/398475+74352282456064/222242328433125*ep+151812421253969222622208/ 371855091642213444890625*ep^2+243563803671443546017933042994176/ 622186647139308079299272755078125*ep^3+48682912308434151749099266693325\ 836439296/148720076556413067026852515546270693359375*ep^4+4385847850990\ 72903946768832054823142382739886761984/17418654070434701714974519748967\ 00205867727783203125*ep^5+535542267051284391980146420502135852504439842\ 698986050472448/2914483146082844814890690690751546018424666736501422119\ 140625*ep^6; Fill mnchfac1(24,10)= -8192/1992375-9522482405888/1111211642165625*ep-19773201880291424884736/ 1859275458211067224453125*ep^2-32099698092641797157463570411392/ 3110933235696540396496363775390625*ep^3-6469000490712535990591857792568\ 828946432/743600382782065335134262577731353466796875*ep^4-5861146633683\ 3341491034609209990010193613787587328/870932703521735085748725987448350\ 1029338638916015625*ep^5-7184620847140775032186517390201139558008843866\ 6533523490816/145724157304142240744534534537577300921233336825071105957\ 03125*ep^6; Fill mnchfac1(24,12)= 4096/37855125+4881476518144/21113021201146875*ep+ 10316478284726114560768/35326233706010277264609375*ep^2+ 16958348815596777287143833570496/59107731478234267533430911732421875* ep^3+3447843480754722082198545358730521614016/1412840727285924136755098\ 8976895715869140625*ep^4+3143112464816398324851349371973076879323124839\ 6864/165477213669129666292257937615186519557434139404296875*ep^5+ 38691022579817023813646849535609005489013322930058586255808/ 276875898877870257414615615621396871750343339967635101318359375*ep^6; Fill mnchfac1(24,14)= -1024/340696125-3756293679808/570051572430965625*ep- 8086526354207597490976/953808310062277486144453125*ep^2- 13470447600318753590385639736672/1595908749912325223402634616775390625* ep^3-2764761230526739398154976684264569825312/3814669963671995169238767\ 02376184328466796875*ep^4-253723391629899013232748141118521045330525067\ 46848/4467884769066500989890964315610036028050721763916015625*ep^5- 31376761919231440721579377184594082040017781193730891264256/ 7475649269702496950194621621777715537259270179126147735595703125*ep^6; Fill mnchfac1(24,16)= 512/5791834125+1928539582304/9690876731326415625*ep+ 4233076455188269586288/16214741271058717264455703125*ep^2+ 7151857259858219788871659235936/27130448748509528797844788485181640625* ep^3+1482939125469174701963423585027682142256/6484938938242391787705903\ 940395133583935546875*ep^4+13707860178003829175849276299278965120913963\ 021824/75954041074130516828146393365370612476862269986572265625*ep^5+ 17037554136969949091008784064515771869768269876400411276928/ 127086037584942448153308567570221164133407593045144511505126953125*ep^6 ; Fill mnchfac1(24,18)= -16/5791834125-61940058472/9690876731326415625*ep-138761007386736375184/ 16214741271058717264455703125*ep^2-238006441580881033030299665848/ 27130448748509528797844788485181640625*ep^3-498974865189540813194347336\ 44664484608/6484938938242391787705903940395133583935546875*ep^4- 464896762271884549775772339295584685219758288832/7595404107413051682814\ 6393365370612476862269986572265625*ep^5-5810400447251276799619002399723\ 98698627315835525865896704/12708603758494244815330856757022116413340759\ 3045144511505126953125*ep^6; Fill mnchfac1(24,20)= 8/86877511875+31862400716/145363150969896234375*ep+72934640903779435052/ 243221119065880758966835546875*ep^2+127138819971262290521514472544/ 406956731227642931967671827277724609375*ep^3+26974726419177199367947256\ 852787753824/97274084073635876815588559105927003759033203125*ep^4+ 253510923106059000447337558037496898864952866496/1139310616111957752422\ 195900480559187152934049798583984375*ep^5+31879826206860384838051402982\ 6887724705598956463592690112/190629056377413672229962851355331746200111\ 3895677167672576904296875*ep^6; Fill mnchfac1(24,22)= -2/608142583125-8204628254/1017542056789273640625*ep- 19214228474766974288/1702547833461165312767848828125*ep^2- 34081075015282440599196185936/2848697118593500523773702790944072265625* ep^3-51278938110976877572771554928190645792/476643011960815796396383939\ 6190423184192626953125*ep^4-9929469101267174259957074014856473052081788\ 832/1139310616111957752422195900480559187152934049798583984375*ep^5- 88006542114818516629293318902134755718649435660641276928/ 13344033946418957056097399594873222234007797269740173708038330078125* ep^6; Fill mnchfac1(24,24)= 1/7905853580625+4231021552/13228046738260557328125*ep+ 10151678126460910744/22133121834995149065982034765625*ep^2+ 18347133858726828484613167168/37033062541715506809058136282272939453125 *ep^3+28000881410575482659056990331383145296/61963591554906053531529912\ 150475501394504150390625*ep^4+54795804569315211501470196008285538573907\ 54816/14811038009455450781488546706247269432988142647381591796875*ep^5+ 48940109892253114734625888300797575093534786728536600064/ 173472441303446441729266194733351889042101364506622258204498291015625* ep^6; Fill mnchfac1(25,0)= 16777216/13+17712055548116992/7250518275*ep+34491779685453570345140224/ 12131541982178994375*ep^2+53593899818198107634118071655497728/ 20298453887473505316244546875*ep^3+733688319219147658390615420291054329\ 89679616/33963302507393410124709401881449609375*ep^4+930412045105300862\ 62166663638758767230080445615562752/56827279732894440628563587862869948\ 368857421875*ep^5+16069977079718367584102878631428363160574577275994006\ 292180992/13583315282040272321647344421955167733957379500244140625*ep^6 ; Fill mnchfac1(25,2)= -8388608/325-9043171637460992/181262956875*ep- 17851129977077916838068224/303288549554474859375*ep^2- 27991687854897857821366825432137728/507461347186837632906113671875*ep^3 -38557839754865374916996972737086095287279616/8490825626848352531177350\ 47036240234375*ep^4-491011959948389470172409917481478713454600280155627\ 52/1420681993322361015714089696571748709221435546875*ep^5- 8504451114212946329673763558460208400409407457437244532180992/ 339582882051006808041183610548879193348934487506103515625*ep^6; Fill mnchfac1(25,4)= 524288/975+577382072614912/543788870625*ep+1155948693463060153278464/ 909865648663424578125*ep^2+1830069213305311216515905477931008/ 1522384041560512898718341015625*ep^3+2537451045021249702792224781605490\ 404427776/2547247688054505759353205141108720703125*ep^4+324572701096439\ 9753322113371825958228491643393334272/426204597996708304714226908971524\ 6127664306640625*ep^5+5638540229469059942115710396620679429583699525021\ 26069414912/1018748646153020424123550831646637580046803462518310546875* ep^6; Fill mnchfac1(25,6)= -262144/22425-295047825145856/12507144024375*ep- 599438390024697636524032/20926909919258765296875*ep^2- 958642355832695553893071148591104/35014832955891796670521843359375*ep^3 -1338464525053976141924670515472327543897088/58586696825253632465123718\ 245500576171875*ep^4-17202336877498558904915464910546424699027952879375\ 36/98027057539242910084272189063450660936279052734375*ep^5- 299804583079235568194116179027981619713711523850836076025856/ 23431218861519469754841669127872664341076479637921142578125*ep^6; Fill mnchfac1(25,8)= 65536/246675+75423389732864/137578584268125*ep+155595877215481169271808/ 230196009111846418265625*ep^2+251494338097322514320018965605376/ 385163162514809763375740276953125*ep^3+35374337910720381469773665028558\ 2324361472/644453665077789957116360900700506337890625*ep^4+456962157967\ 642655587386481337432281235836903542784/1078297632931672010926994079697\ 957270299069580078125*ep^5+79915999631938507332753634980409489638730640\ 783972307172864/2577434074767141673032583604065993077518412760171325683\ 59375*ep^6; Fill mnchfac1(25,10)= -32768/5180175-38581969528832/2889150269630625*ep- 80871996576469041288704/4834116191348774783578125*ep^2- 132190728269687918905454294924288/8088426412811005030890545816015625* ep^3-26772017331997966959682467740219443710848/193336099523336987134908\ 2702101519013671875*ep^4-2434126944395342510016950807108360659360597779\ 05792/22644250291565112229466875673657102676280461181640625*ep^5- 299100154639266467635805054724526805895980390009819406141824/ 37888280899076982593578978979770098239520667574518487548828125*ep^6; Fill mnchfac1(25,12)= 4096/25900875+4936969740544/14445751348153125*ep+ 10522025602754048781568/24170580956743873917890625*ep^2+ 17404111867435445105731789948096/40442132064055025154452729080078125* ep^3+507786533476804764497124361201045329088/13809721394524070509636305\ 01501085009765625*ep^4+325081721299169868303589631303078712259514036352\ 64/113221251457825561147334378368285513381402305908203125*ep^5+ 40107147362002255999627000921177563352768017670297230380608/ 189441404495384912967894894898850491197603337872592437744140625*ep^6; Fill mnchfac1(25,14)= -2048/492116625-2528602527872/274469275614909375*ep- 5483689062573953129984/459241038178133604439921875*ep^2- 9184965906542946023002847716448/768400509217045477934601852521484375* ep^3-1892803641883637217461370864686853982208/1836692945471701377781628\ 56699644306298828125*ep^4-174208875035242472955120734266124632484225366\ 59232/2151203777698685661799353188997424754246643812255859375*ep^5- 21587708861701796201291997794954719362118261470407146325504/ 3599386685412313346390003003078159332754463419579256317138671875*ep^6; Fill mnchfac1(25,16)= 512/4429049625+1944045041504/7410670441602553125*ep+ 4293476208479796712688/12399508030809607319877890625*ep^2+ 7287826067251574594606357176736/20746813748860227904234250018080078125* ep^3+1516380233401059269544231645110564979056/4959070952773593720010397\ 130890396270068359375*ep^4+14052355347628595977625339906445914877772590\ 209024/58082501997864512868582536102930468364659382930908203125*ep^5+ 17497023431593976805435203706405435625696190418249136435328/ 97183440506132460352530081083110301984370512328639920562744140625*ep^6; Fill mnchfac1(25,18)= -256/75293843625-997218891952/125981397507243403125*ep- 2244887703338629936744/210791636523763324437924140625*ep^2- 3864862345639988856622062742168/352695833730623874371982250307361328125 *ep^3-812531917089842057090928920189967099328/8430420619715109324017675\ 1225136736591162109375*ep^4-7585982324454544041698773314869250793781564\ 283712/987402533963696718765903113749817962199209509825439453125*ep^5- 9495149319561033438660533771273421416230966089628746600064/ 1652118488604251825993011378412875133734298709586878649566650390625* ep^6; Fill mnchfac1(25,20)= 8/75293843625+31999688636/125981397507243403125*ep+73499101218509509892/ 210791636523763324437924140625*ep^2+128463100848089237871361181024/ 352695833730623874371982250307361328125*ep^3+39015379129390238080542234\ 00222114272/12043458028164441891453821603590962370166015625*ep^4+ 257054069153340815768955484004441647654117754816/9874025339636967187659\ 03113749817962199209509825439453125*ep^5+323604789689062266525971775272\ 039722345976704632081657152/1652118488604251825993011378412875133734298\ 709586878649566650390625*ep^6; Fill mnchfac1(25,22)= -4/1129407654375-16446030058/1889720962608651046875*ep- 38584046632127498176/3161874547856449866568862109375*ep^2- 68535463273732197822682393072/5290437505959358115579733754610419921875* ep^3-14747509352323477015594779484270299712/126456309295726639860265126\ 8377051048867431640625*ep^4-1400422592303363076797360013947912573918447\ 64448/14811038009455450781488546706247269432988142647381591796875*ep^5- 177423609611020992235723560332763853504216033863629971456/ 24781777329063777389895170676193127006014480643803179743499755859375* ep^6; Fill mnchfac1(25,24)= 1/7905853580625+4231021552/13228046738260557328125*ep+ 10151678126460910744/22133121834995149065982034765625*ep^2+ 18347133858726828484613167168/37033062541715506809058136282272939453125 *ep^3+28000881410575482659056990331383145296/61963591554906053531529912\ 150475501394504150390625*ep^4+54795804569315211501470196008285538573907\ 54816/14811038009455450781488546706247269432988142647381591796875*ep^5+ 48940109892253114734625888300797575093534786728536600064/ 173472441303446441729266194733351889042101364506622258204498291015625* ep^6; Fill mnchfac1(26,0)= 67108864/27+649630401232371712/135528918525*ep+ 3843556378482312345660424192/680299546539114376875*ep^2+180743658470891\ 38731789559108881743872/3414824511684965855894371078125*ep^3+7468254618\ 4320506403371326748725723314168266752/171410175193083202944783373649377\ 60546875*ep^4+285308665580901526549564629704738404621481549505087864832/ 86040872844812405760924392300374553364940048828125*ep^5+148252276811607\ 597936431740727223027010185818920115315444956758016/6169855262224584925\ 5458003136310053809419177085378173828125*ep^6; Fill mnchfac1(26,2)= -16777216/351-165646628713136128/1761875940825*ep- 992869021182976308479131648/8843894105008486899375*ep^2-471027588439038\ 1684697921828195565568/44392718651904556126626824015625*ep^3-1958000776\ 6259352182949778819218946289555980288/222833227751008163828218385744190\ 887109375*ep^4-75107304966838246289844549830396417787583469300600823808/ 1118531346982561274892017099904869193744220634765625*ep^5- 39134540878824355427996869965867437394545897295653160929497698304/ 802081184089196040320954040772030699522449302109916259765625*ep^6; Fill mnchfac1(26,4)= 8388608/8775+84507609127190528/44046898520625*ep+ 513402251142808971175067648/221097352625212172484375*ep^2+2458220685699\ 909872266034716730605568/1109817966297613903165670600390625*ep^3+ 10283574240209220858405536189237034176480780288/55708306937752040957054\ 59643604772177734375*ep^4+396184253654148331785112741383093866520390000\ 47160823808/27963283674564031872300427497621729843605515869140625*ep^5+ 20703660353367331212131116729703003870777057888570311776377698304/ 20052029602229901008023851019300767488061232552747906494140625*ep^6; Fill mnchfac1(26,6)= -524288/26325-5391380177911808/132140695561875*ep- 33215245518755050561200128/663292057875636517453125*ep^2-16058574702861\ 9713632277089045557248/3329453898892841709497011801171875*ep^3- 676309829249678251199848655980832380285319168/1671249208132561228711637\ 8930814316533203125*ep^4-2617601492353915199566412615108467816415046820\ 499237888/83889851023692095616901282492865189530816547607421875*ep^5- 1372188802814768646866394850862074364218208873352994907440569344/ 60156088806689703024071553057902302464183697658243719482421875*ep^6; Fill mnchfac1(26,8)= 262144/605475+2752901188501504/3039235997923125*ep+ 17208424242282188730609664/15255717331139639901421875*ep^2+ 84048492076428854588327707688372224/76577439674535359318431271426953125 *ep^3+356497911782287490022566096607642301634397184/3843873178704890826\ 03676715408729280263671875*ep^4+138660392885050716302538845074032800223\ 4176695737260544/1929466573544918199188729497335899359208780594970703125 *ep^5+729325349394415674296458700758127563923360648171098074625385472/ 1383590042553863169553645720331752956676225046139605548095703125*ep^6; Fill mnchfac1(26,10)= -65536/6660225-703178198142976/33431595977154375*ep- 4462545422059900213974016/167812890642536038915640625*ep^2- 22030311495404297744336665105478656/842351836419888952502743985696484375 *ep^3-94150983487223421295080994127079981637808896/42282604965753799086\ 40443869496022082900390625*ep^4-368132768357556964903102637998760496059\ 468581216308736/21224132308994100191076024470694892951296586544677734375 *ep^5-194330528298366793986428018610659014675268324837017532625223168/ 15219490468092494865090102923649282523438475507535661029052734375*ep^6; Fill mnchfac1(26,12)= 32768/139864725+359421571033088/702063515520241875*ep+ 2317184557267464892932608/3524070703493256817228453125*ep^2+ 11569027911845518265656094947708928/17689388564817668002557623699626171\ 875*ep^3+7120116316428773510851087435844011648436864/126847814897261397\ 25921331608488066248701171875*ep^4+195979738057022906699919408289505608\ 761958373134851968/4457067784888761040125965138845927519772283174382324\ 21875*ep^5+727001508571058204571884403955886119727513180090116745509282\ 688/2237265098809596745168245129776444530945455899607742171270751953125 *ep^6; Fill mnchfac1(26,14)= -4096/699323625-45955708324096/3510317577601209375*ep- 301182009379201761761536/17620353517466284086142265625*ep^2- 1521718992703559452465003855542976/884469428240883400127881184981308593\ 75*ep^3-944574573781127318092000510949203801012288/63423907448630698629\ 606658042440331243505859375*ep^4-26156949096304498593664736165667554959\ 183875993950656/2228533892444380520062982569422963759886141587191162109\ 375*ep^5-97440046021263062179803634029601281555382094233630966984760896/ 11186325494047983725841225648882222654727279498038710856353759765625* ep^6; Fill mnchfac1(26,16)= 2048/13287148875+23518913080448/66696033974422978125*ep+ 156804441053492876519168/334786716831859397636703046875*ep^2+ 802285493068927876775258663585888/1680491913657678460242974251464486328\ 125*ep^3+502566564312988659998541405893129385633344/1205054241523983273\ 962526502806366293626611328125*ep^4+14007882190719792160187804171970039\ 100526623165581728/4234214395644322988119666881903631143783669015663208\ 0078125*ep^5+5242075034812443795692526079710392053986714262481061721234\ 2848/212540184386911690790983287328762230439818310462735506270721435546\ 875*ep^6; Fill mnchfac1(26,18)= -512/119584339875-6022507706912/600264305769806803125*ep- 40880583424538365276592/3013080451486734578730327421875*ep^2- 211971581621550334612143732270272/1512442722291910614218676826318037695\ 3125*ep^3-134086167596531257499293116131262095722736/108454881737158494\ 65662738525257296642639501953125*ep^4-376371514229854569249893138017096\ 7154630404903203232/381079295607989068930770019371326802940530211409688\ 720703125*ep^5-14154760103228410683438470291195232826469574180099755828\ 280512/1912861659482205217118849585958860073958364794164619556436492919\ 921875*ep^6; Fill mnchfac1(26,20)= 256/2032933777875+3086842967056/10204493198086715653125*ep+ 21351743757980733581896/51222367675274487838415566171875*ep^2+ 112290319656400544561279958507736/2571152627896248044171750604740664082\ 03125*ep^3+71779649495078114090017346539428225865168/184373298953169440\ 916266554929374042924871533203125*ep^4+20302181983327161878423116777213\ 26738673720012717216/64783480253358141718230903293125556499890135939647\ 08251953125*ep^5+767684252828045149218552981862060061632980793136188996\ 4529856/325186482111974886910204429613006212572922015007985324594203796\ 38671875*ep^6; Fill mnchfac1(26,22)= -8/2032933777875-98973637508/10204493198086715653125*ep- 698292432376584535628/51222367675274487838415566171875*ep^2- 3728143827628698030611531508248/257115262789624804417175060474066408203\ 125*ep^3-2410201117178919722503048101085575695024/184373298953169440916\ 266554929374042924871533203125*ep^4-68737290123529419116438949433637017\ 683010684673888/6478348025335814171823090329312555649989013593964708251\ 953125*ep^5-261465890566127780030965473188208552278789690817725341361408 /32518648211197488691020442961300621257292201500798532459420379638671875 *ep^6; Fill mnchfac1(26,24)= 4/30494006668125+50825375974/153067397971300734796875*ep+ 366154384680595325884/768335515129117317576233492578125*ep^2+ 1986601562626566082145836024744/385672894184437206625762590711099612304\ 6875*ep^3+1300071268050783868146646261394829985072/27655994842975416137\ 43998323940610643873072998046875*ep^4+374140296809015906866121121177766\ 08499088923521664/97175220380037212577346354939688334749835203909470623\ 779296875*ep^5+14325315017273017009624508659777911855278705590935046408\ 4224/487779723167962330365306644419509318859383022511977986891305694580\ 078125*ep^6; Fill mnchfac1(26,26)= -1/213458046676875-13064886106/1071471785799105143578125*ep- 96222908034165970396/5378348605903821223033634448046875*ep^2- 531150355374104609737853307736/2699710259291060446380338134977697286132\ 8125*ep^3-2465564489559828963828028953611730506176/13551437473057953907\ 3455917873089921549780576904296875*ep^4-1462502302973880420497516516740\ 466640748181173888/9717522038003721257734635493968833474983520390947062\ 3779296875*ep^5-3948386819989313335207424675985515930346418418766734952\ 9856/341445806217573631255714651093656523201568115758384590823913986206\ 0546875*ep^6; Fill mnchfac1(27,0)= 33554432/7+47229678395588608/5019589575*ep+1979928360456130264959287296/ 176373956510140764375*ep^2+9389791444050161230739377115371995136/ 885324873399805962639281390625*ep^3+39027799523170633104694270841561213\ 545231384576/4443967505005860817086976353872752734375*ep^4+ 149705299324728350277192879486515966589568437057794031616/2230689295976\ 6179271350768374171180502021494140625*ep^5+5460376526794955444973176337\ 54951718092392161385121222673031520256/11197144735148320790805341309922\ 9356913390358414204833984375*ep^6; Fill mnchfac1(27,2)= -16777216/189-24060419824943104/135528918525*ep- 1021275810882281951318376448/4762096825773800638125*ep^2-48847618484511\ 68542593702628956602368/23903771581794760991260597546875*ep^3- 20422029378283213423197924056964334712387289088/11998712263515824206134\ 8361554564323828125*ep^4-7864932395005210660143289762318316406030680592\ 4031684608/602286109913686840326470746102621873554580341796875*ep^5- 287640579176061823174708492913452617884441662704331636744960380928/ 3023229078490046613517442153679192636661539677183530517578125*ep^6; Fill mnchfac1(27,4)= 4194304/2457+6130784542130176/1761875940825*ep+ 263604266382867966991040512/61907258735059408295625*ep^2+12720822016305\ 21635868028390794452992/310749030563331892886387768109375*ep^3+ 5351096981411096217538523375250155301422620672/155983259425705714679752\ 8700209336209765625*ep^4+2069541985761706924123815917869192534462100799\ 6175255552/7829719428877928924244119699334084356209544443359375*ep^5+ 75905626092767095220806824147807483340208026986221099672462405632/ 39301978020370605975726747997829504276600015803385896728515625*ep^6; Fill mnchfac1(27,6)= -2097152/61425-446506522247168/6292414074375*ep- 136195040980547108025024512/1547681468376485207390625*ep^2-663386829130\ 166899583566670579412992/7768725764083297322159694202734375*ep^3- 2808745675173311792255651411663392877281820672/389958148564264286699382\ 17505233405244140625*ep^4-109116599492055863082443209317787466841478272\ 53375255552/195742985721948223106102992483352108905238611083984375*ep^5 -40143695227462643232988449269988176992596583550708282489502405632/ 982549450509265149393168699945737606915000395084647418212890625*ep^6; Fill mnchfac1(27,8)= 131072/184275+199262839463936/132140695561875*ep+ 8803920215517798507333632/4643044405129455622171875*ep^2+ 43303012909508135166238019420966912/23306177292249891966479082608203125 *ep^3+184603411038609380918400682156217598492411392/1169874445692792860\ 09814652515700215732421875*ep^4+720588470056967626388403724478848266876\ 907700831555072/587228957165844669318308977450056326715715833251953125* ep^5+2659691717223213300125600005886144356554875792891404850195965952/ 2947648351527795448179506099837212820745001185253942254638671875*ep^6; Fill mnchfac1(27,10)= -65536/4238325-101674673287168/3039235997923125*ep- 4557288625607446919689216/106790021317977479309953125*ep^2- 22646102910204729261398916270201856/536042077721747515229018899988671875 *ep^3-97244059522889073942514056296639369660260096/26907112250934235782\ 25737007861104961845703125*ep^4-381517072742039181430864805990623006807\ 202236053607936/13506266014814427394321106481351295514461464164794921875 *ep^5-1413109298655974325686795766568503864917637304228805883214629376/ 67795912085139295308128640296255894877135027260840671856689453125*ep^6; Fill mnchfac1(27,12)= 16384/46621575+25952700500992/33431595977154375*ep+ 1180772307953913413672704/1174690234497752272409484375*ep^2+ 5930934471526371104064463952116864/5896462854939222667519207899875390625 *ep^3+25664235646325991518880478773342074674887424/29597823476027659360\ 483107086472154580302734375*ep^4+10123490135372076508861214999409560015\ 3934033004720384/148568926162958701337532171294864250659076105812744140\ 625*ep^5+376375399912234042326236282520703174687866401843937851045311744 /745755032936532248389415043258814843648485299869247390423583984375* ep^6; Fill mnchfac1(27,14)= -8192/979053075-92792569743872/4914444608641693125*ep- 612566183297137674042752/24668494924452797720599171875*ep^2- 3111887751366797523268648454320832/123825719953723676017903365897383203\ 125*ep^3-13575946361988279990341912134559071242802112/62155429299658084\ 6570145248815915246186357421875*ep^4-7694640428867099183279788692341513\ 692845980419950656/4457067784888761040125965138845927519772283174382324\ 21875*ep^5-201062345582821961203412221803111702168043012720848403813326\ 272/15660855691667177216177715908435111716618191297254195198895263671875 *ep^6; Fill mnchfac1(27,16)= 1024/4895265375+11856074204224/24572223043208465625*ep+ 79546404235939669823584/123342474622263988602995859375*ep^2+ 408950483992422620757351273566944/6191285997686183800895168294869160156\ 25*ep^3+1799631474555513447100127969690364163700704/3107771464982904232\ 850726244079576230931787109375*ep^4+10263544206692497768945172746700011\ 25420502175483552/22285338924443805200629825694229637598861415871911621\ 09375*ep^5+269359504804390308965363059006957949960450336640687708477754\ 24/78304278458335886080888579542175558583090956486270975994476318359375 *ep^6; Fill mnchfac1(27,18)= -512/93010042125-6063301831712/466872237820960846875*ep- 41375059310840359101392/2343507017823015783456921328125*ep^2- 215406074437353465696286355267072/1176344339560374922170081976025140429\ 6875*ep^3-956723636521831115497390253535357921427952/590476578346751804\ 24163798637511948387703955078125*ep^4-549285180199595360080802404675998\ 228246291816860576/4234214395644322988119666881903631143783669015663208\ 0078125*ep^5-1448378066914705213357129865334926611457856412436323256213\ 3312/148778129070838183553688301130133561307872817323914854389505004882\ 8125*ep^6; Fill mnchfac1(27,20)= 128/837090379125+1551520317128/4201850140388647621875*ep+ 10776431228224334372048/21091563160407142051112291953125*ep^2+ 56856699823166106122696383938968/10587099056043374299530737784226263867\ 1875*ep^3+255036314558306052751393698923297325304688/531428920512076623\ 817474187737607535489335595703125*ep^4+14748143493722656852853628273912\ 7112448277681067744/381079295607989068930770019371326802940530211409688\ 720703125*ep^5+39088381624655743022590494802220956557400072323213502826\ 54528/13390031616375436519831947101712020517708553559152336895055450439\ 453125*ep^6; Fill mnchfac1(27,22)= -64/14230536445125-794657436964/71431452386607009571875*ep- 5622854095658091541924/358556573726921414868908963203125*ep^2- 30088609899836665359479802901384/17998068395273736309202254233184648574\ 21875*ep^3-136402420372062551060473816877345243797744/90342916487053026\ 04897061191539328103318705126953125*ep^4-794943659333559128571341881406\ 39028824500094239072/64783480253358141718230903293125556499890135939647\ 08251953125*ep^5-211872517732526711551752207223857030554524457165495417\ 5569664/227630537478382420837143100729104348801045410505589727215942657\ 470703125*ep^6; Fill mnchfac1(27,24)= 2/14230536445125+25460493602/71431452386607009571875*ep+ 183701767255499948132/358556573726921414868908963203125*ep^2+ 997900776608944786299770585912/1799806839527373630920225423318464857421\ 875*ep^3+4575641407573871164456114981038008685392/903429164870530260489\ 7061191539328103318705126953125*ep^4+2689268952456623435173809676750502\ 785372352391296/6478348025335814171823090329312555649989013593964708251\ 953125*ep^5+72115985840593163825190939980277609898429183982719196509952/ 227630537478382420837143100729104348801045410505589727215942657470703125 *ep^6; Fill mnchfac1(27,26)= -1/213458046676875-13064886106/1071471785799105143578125*ep- 96222908034165970396/5378348605903821223033634448046875*ep^2- 531150355374104609737853307736/2699710259291060446380338134977697286132\ 8125*ep^3-2465564489559828963828028953611730506176/13551437473057953907\ 3455917873089921549780576904296875*ep^4-1462502302973880420497516516740\ 466640748181173888/9717522038003721257734635493968833474983520390947062\ 3779296875*ep^5-3948386819989313335207424675985515930346418418766734952\ 9856/341445806217573631255714651093656523201568115758384590823913986206\ 0546875*ep^6; Fill mnchfac1(28,0)= 268435456/29+78000310823201800192/4221474832575*ep+ 13705259305863474244225322713088/614512060760831871763125*ep^2+ 1900396737535984816840884348536253822533632/ 89453351683298308723067654463234375*ep^3+230382762154814676375467511520\ 887291624131368898920448/13021554235190493870361816850537251196417578125 *ep^4+25729816395581576455947799313251900181505964546260353639004700672/ 1895522878788519733952317742889467458386124622586943359375*ep^5+ 27289635522302797832288155253916947310783942972000450169484212297924667\ 31008/27592765956468442630063600298956953571108538692545868211719262695\ 3125*ep^6; Fill mnchfac1(28,2)= -33554432/203-1417783381204140032/4221474832575*ep- 1764753420662213284351303745536/4301584425325823102341875*ep^2- 246724299274542653053615298304309506146304/6261734617830881610614735812\ 42640625*ep^3-30080530515622997281242807109947911026735570880659456/ 91150879646333457092532717953760758374923046875*ep^4-337261153531248372\ 0626053928112633307563318893937998542712029184/132686601515196381376662\ 24200226272208702872358108603515625*ep^5-358654181364220663685421256043\ 866028303257698614289182020678093854557003776/1931493616952790984104452\ 020926986749977597708478210774820348388671875*ep^6; Fill mnchfac1(28,4)= 16777216/5481+721813528789385216/113979820479525*ep+ 909617864250871366671252717568/116142779483797223763230625*ep^2+ 128266273419130427778935858604212079460352/1690668346814338034865978669\ 3551296875*ep^3+15731801458459062874861724605820545630008503263510528/ 2461073750451003341498383384751540476122922265625*ep^4+1771122375482489\ 131407724661446651322662802862307638412218785792/3582538240910302297169\ 88053406109349634977553668932294921875*ep^5+188875939383910813440224908\ 531820882541963917016391549687688903358380658688/5215032765772535657082\ 0204565028642249395138128911690920149406494140625*ep^6; Fill mnchfac1(28,6)= -4194304/71253-26258298598326272/211676809461975*ep- 234608164454328735642686881792/1509856133289363908921998125*ep^2- 33380086208576460347295268416750675058688/21978688508586394453257722701\ 6166859375*ep^3-4119837889599764895736232768953401979543098167468032/ 31993958755863043439478984001770026189597989453125*ep^4-465846630959792\ 453736529939313491466314995641188990371886082048/4657299713183392986320\ 844694279421545254708197696119833984375*ep^5-49827154379713270548642654\ 399168610951407143016167049098435601437146243072/6779542595504296354206\ 62659345372349242136795675851981961942284423828125*ep^6; Fill mnchfac1(28,8)= 2097152/1781325+93648493249429504/37043441655845625*ep+ 121121107470650236830707105792/37746403332234097723049953125*ep^2+ 17395297872399901608477004384985194098688/54946721271465986133144306754\ 04171484375*ep^3+2161206961590891590428243191768898111291015018668032/ 799848968896576085986974600044250654739949736328125*ep^4+24550742692312\ 6342085296753657468481809159160377989587166082048/116432492829584824658\ 021117356985538631367704942402995849609375*ep^5+26343099153947978477562\ 844840295136893832757162784491675006807038986243072/1694885648876074088\ 5516566483634308731053419891896299549048557110595703125*ep^6; Fill mnchfac1(28,10)= -131072/5343975-852371667361792/15875760709648125*ep- 7823395382930901194566387712/113239209996702293169149859375*ep^2- 1134657649660520077732580028467088621568/164840163814397958399432920262\ 12514453125*ep^3-141957516581658579287876649573624941830158927652352/ 2399546906689728257960923800132751964219849208984375*ep^4- 16205234417672867554634353773111996056245312858677300630358528/ 349297478488754473974063352070956615894103114827208987548828125*ep^5- 17447339115616684769472758028915657154741195100062336784156491596938577\ 92/50846569466282222656549699450902926193160259675688898647145671331787\ 109375*ep^6; Fill mnchfac1(28,12)= 65536/122911425+3042555188867072/2555997474253348125*ep+ 4046493030439453208866272256/2604501829924152742890446765625*ep^2+ 592939272338791215948109044484611728384/3791323767731153043186957166028\ 87832421875*ep^3+74731499243488271618484688052859726572116536952576/ 55189578853863749933101247403053295177056531806640625*ep^4+ 8575596434109272443868329469424284560328032645973229880868864/ 8033842005241352901403457097632002165564371641025806713623046875*ep^5+ 926642314882651641635907942273793082993356515274839440196239684569463296 /1169471097724491121100643087370767302442685972540844668884350440631103\ 515625*ep^6; Fill mnchfac1(28,14)= -16384/1352025675-776125730413568/28115972216786829375*ep- 1047571167743066070097694464/28649520129165680171794914421875*ep^2- 155166315451404006305025424054237421696/4170456144504268347505652882631\ 766156640625*ep^3-19709568691031151545789183684673364711169292972544/ 607085367392501249264113721433586246947621849873046875*ep^4- 2274312036724961045725499054881936992570480425260942746818816/ 88372262057654881915438028073952023821208088051283873849853515625*ep^5- 246709091298181424800556057734774361190507103539894426009582839461268224 /1286418207496940233210707396107844032686954569794929135772785484694213\ 8671875*ep^6; Fill mnchfac1(28,16)= 8192/28392539175+2773225478169088/4133047915867663918125*ep+ 543009067551576672294069632/601639922712479283607693202859375*ep^2+ 81347195677309554873120073670653344448/87579579034589635297618710535267\ 089289453125*ep^3+10418667989608048871227025895483961490140450436672/ 12748792715242526234546388150105311185900058847333984375*ep^4+ 172768041259637764103201967883768041289678558529754183262144/ 265116786172964645746314084221856071463624264153851621549560546875*ep^5 +1317377173508245057603091998144393670224200055624180334524059623712725\ 12/27014782357435744897424855318264724686426045965693511851228495178578\ 4912109375*ep^6; Fill mnchfac1(28,18)= -1024/141962695875-354106271372096/20665239579338319590625*ep- 70453462258868250376632544/3008199613562396418038466014296875*ep^2- 10681188283445737339429109293960454816/43789789517294817648809355267633\ 5446447265625*ep^3-1380075511667490842832798797457569474979701912224/ 63743963576212631172731940750526555929500294236669921875*ep^4- 67145682818095580610947258788168820024392305099369131936/ 3864676183279368013794665950755919409090732713612997398681640625*ep^5- 17640615700109101983678667796127957672172913901196619315294425458757504/ 13507391178717872448712427659132362343213022982846755925614247589289245\ 60546875*ep^6; Fill mnchfac1(28,20)= 512/2697291221625+180975812844448/392639552007428072221875*ep+ 36613273487379026559129872/57155792657685531942730854271640625*ep^2+ 5621105961260356986446440771733187808/832006000828601535327377750085037\ 3482498046875*ep^3+733103740129022916779999616698035214430591121712/ 1211135307948039992281906874260004562660505590496728515625*ep^4+ 12317864429235793766898841203148111664821038654717446948224/ 25186094686431641345899838001076326789044305094615904047208251953125* ep^5+948091925251122620597947110262867630209779014607167910071036606087\ 6352/256640432395639576525536125523514884521047436674088362586670704196\ 49566650390625*ep^6; Fill mnchfac1(28,22)= -128/24275620994625-46279104127912/3533755968066852649996875*ep- 9527582880178278290327168/514402133919169787484577688444765625*ep^2- 1482327163387780881921592259551637752/748805400745741381794639975076533\ 61342482421875*ep^3-195263687549274516490614347715060845607056304128/ 10900217771532359930537161868340041063944550314470556640625*ep^4- 3305054706845087125787362265778634187966339558508958639456/ 226674852177884772113098542009686941101398745851543136424874267578125* ep^5-255732835116729038131395101627374211551410581347662751296292833844\ 4288/230976389156075618872982512971163396068942693006679526328003633776\ 846099853515625*ep^6; Fill mnchfac1(28,24)= 64/412685556908625+23687573137556/60073851457136495049946875*ep+ 4966624084805107263915484/8744836276625886387237820703561015625*ep^2+ 783691935805179696109766787296812976/1272969181267760349050887957630107\ 142822201171875*ep^3+104342464025131271643791488517218271068620824464/ 185303702116050118819131751761780698087057355345999462890625*ep^4+ 1780165454219690475543600437156611801564780054910904374528/ 3853472487024041125922675214164677998723778679476233319222862548828125* ep^5+138536694564379745585493940167218309081679863298020415294600162817\ 2544/392659861565328552084070272050977773317202578111355194757606177420\ 6383697509765625*ep^6; Fill mnchfac1(28,26)= -2/412685556908625-758432672758/60073851457136495049946875*ep- 162107227736906342974712/8744836276625886387237820703561015625*ep^2- 25965225541476206236959582507462568/12729691812677603490508879576301071\ 42822201171875*ep^3-3496933781271290560942870060005166753083796352/ 185303702116050118819131751761780698087057355345999462890625*ep^4- 8596455469392886447004131095711487921421294473234579072/ 550496069574863017988953602023525428389111239925176188460408935546875* ep^5-471250366639899962264741295683171401955803852941646732231550468817\ 92/39265986156532855208407027205097777331720257811135519475760617742063\ 83697509765625*ep^6; Fill mnchfac1(28,28)= 1/6190283353629375+388920876224/901107771857047425749203125*ep+ 84827912008321292632636/131172544149388295808567310553415234375*ep^2+ 13805828622791011074395112263112704/19094537719016405235763319364451607\ 142333017578125*ep^3+1882446104598762122550738656233208736235589056/ 2779555531740751782286976276426710471305860330189991943359375*ep^4+ 32697347461181348958224518309789769409688869127892160512/ 57802087305360616888840128212470169980856680192143499788342938232421875 *ep^5+25783707310834906055388638332911578193458006963614675719440400645\ 376/5889897923479928281261054080764666599758038671670327921364092661309\ 5755462646484375*ep^6; Fill mnchfac1(29,0)= 268435456/15+79257917585266573312/2183521465125*ep+ 14082891378046516465513244131328/317851065910775106084375*ep^2+ 1968269941312660162454311760742311570440192/ 46268975008602573477448786791328125*ep^3+239944704573899557950976765485\ 369914839729017078284288/6735286673374393381221629405450302342974609375 *ep^4+26901942430543726177519644383992455040845896943743748686603026432/ 980442868338889517561543660115241788820409287544970703125*ep^5+ 28608814063094621616929834374093885937016264591586418731850654086302322\ 19648/14272120322311263429343241533943251847125106220282345626751342773\ 4375*ep^6; Fill mnchfac1(29,2)= -134217728/435-40302676700882272256/63322122488625*ep- 7243748584835602279875151396864/9217680911412478076446875*ep^2- 1020495615536691873520063422624401007312896/134180027524947463084601481\ 6948515625*ep^3-125094821440030965533796911652229219856791820063801344/ 195323313527857408055427252758058767946263671875*ep^4-14078895876858729\ 011030453479892953337926483684809407404514902016/2843284318182779600928\ 4766143342011875791869338804150390625*ep^5-1501110982125721640738010242\ 999887437541830459199997823862163514406776193024/4138914893470266394509\ 540044843543035666280803881880231757889404296875*ep^6; Fill mnchfac1(29,4)= 16777216/3045+732150999339237376/63322122488625*ep+ 932113030150616026686788599808/64523766379887346535128125*ep^2+ 132407877678411666109085172454083248422912/9392601926746322415922103718\ 639609375*ep^3+16325222782533530750689856727553302830634968355258368/ 1367263194695001856387990769306411375623845703125*ep^4+1844734542627840\ 279531629439906198990462907784022918218881687552/1990299022727945720649\ 93363003394083130543085371629052734375*ep^5+197229390554490058841721263\ 859277755317074912891755655258652815116503011328/2897240425429186476156\ 6780313904801249663965627173161622305225830078125*ep^6; Fill mnchfac1(29,6)= -8388608/82215-372536418763276288/1709697307192875*ep- 480115993762648425853104226304/1742141692256958356448459375*ep^2- 68792441501256607010885907383211104813056/25360025202215070522989680040\ 3269453125*ep^3-8533499718813307797737510939859624665709024859971584/ 36916106256765050122475750771273107141843833984375*ep^4-968374875779764\ 607343255206490316787606519468083508988605157376/5373807361365453445754\ 820801091640244524663305033984423828125*ep^5-10383560225885705779679585\ 4009299423142981828867980393611178852407077976064/782254914865880348562\ 303068475429633740927071933675363802241097412109375*ep^6; Fill mnchfac1(29,8)= 2097152/1068795+94811458686287872/22226064993507375*ep+ 123744793277249931884093259776/22647841999340458633829971875*ep^2+ 17890929381258590269640353169567465304064/32968032762879591679886584052\ 42502890625*ep^3+2233542181844387633388370485630640498230493212164096/ 479909381337945651592184760026550392843969841796875*ep^4+25459881457909\ 3322246107663394170283825446293965943694253446144/698594956977508947948\ 12670414191323178820622965441797509765625*ep^5+273843415304292133240321\ 03915152878935802574092783608203126866351582729216/10169313893256444531\ 309939890180585238632051935137779729429134266357421875*ep^6; Fill mnchfac1(29,10)= -1048576/26719875-48277953420787712/555651624837684375*ep- 63840160993574737232086245376/566196049983511465845749296875*ep^2- 9317188322273311630692688173220436056064/824200819071989791997164601310\ 62572265625*ep^3-1171022506112315848914280713211627039319855251204096/ 11997734533448641289804619000663759821099246044921875*ep^4- 134117948031521896243662013999611493424938497173937427442246144/ 1746487392443772369870316760354783079470515574136044937744140625*ep^5- 14473102547575532796867996263719745999378649743891141497653477660238729\ 216/2542328473314111132827484972545146309658012983784444932357283566589\ 35546875*ep^6; Fill mnchfac1(29,12)= 65536/80159625+3074157510520832/1666954874513053125*ep+ 4120530679820038543209051136/1698588149950534397537247890625*ep^2+ 607316678995118540338298005147498824704/2472602457215969375991493803931\ 87716796875*ep^3+76872487200670492079149577557250388361510102157056/ 35993203600345923869413857001991279463297738134765625*ep^4+ 8848629323859593078415040855675252190618655480091820715075584/ 5239462177331317109610950281064349238411546722408134813232421875*ep^5+ 958238831627865068688602874876986237001342032309995517595871976961573376 /7626985419942333398482454917635438928974038951353334797071850699768066\ 40625*ep^6; Fill mnchfac1(29,14)= -32768/1843671375-1566705931810816/38339962113800221875*ep- 2129675636204318022550880768/39067527448862291143356701484375*ep^2- 317137158237866136784951153195206065152/5686985651596729564780435749043\ 317486328125*ep^3-40443419810193577721448122688991439608311518457728/ 827843682807956248996518711045799427655847977099609375*ep^4- 4680282996070722134095062352447908248706786647032089264606592/ 120507630078620293521051856464480032483465574615387100704345703125*ep^5 -5087411502625701222062029367539867003831574383754565813600912625983898\ 88/17542066465867366816509646310561509536640289588112670033265256609466\ 552734375*ep^6; Fill mnchfac1(29,16)= 8192/20280385125+399419949551104/421739583251802440625*ep+ 550918891578679085471019392/429742801937485202576923716328125*ep^2+ 82929572060390529289934380309550385088/62556842167564025212584793239476\ 492349609375*ep^3+10659577681904434410649399593486097501706236317632/ 9106280510887518738961705821503793704214327748095703125*ep^4+ 1240602314707394842083085718121281131944103338459917193456448/ 1325583930864823228731570421109280357318121320769258107747802734375* ep^5+135394020243967855161420817019445591882651804930829000344090092618\ 804672/1929627311245410349816061094161766049030431854692393703659178227\ 04132080078125*ep^6; Fill mnchfac1(29,18)= -4096/425888087625-1426362534289664/61995718738014958771875*ep- 285346725823217559206696896/9024598840687189254115398042890625*ep^2- 43442756509046482665985073453396493344/13136936855188445294642806580290\ 06339341796875*ep^3-5630925956322699129602666919245718765310350510016/ 191231890728637893518195822251579667788500882710009765625*ep^4- 94190527102301505391768969675610231373927636452786569286432/ 3976751792594469686194711263327841071954363962307774323243408203125* ep^5-722673887384131143320999300159805770166156516759282087866502091188\ 17536/40522173536153617346137282977397087029639068948540267776842742767\ 86773681640625*ep^6; Fill mnchfac1(29,20)= 512/2129440438125+182021860086688/309978593690074793859375*ep+ 36993169523306404038399632/45122994203435946270576990214453125*ep^2+ 5699595829354635323848872785757564448/656846842759422264732140329014503\ 1696708984375*ep^3+745349710660113300552135263436505170185622386672/ 956159453643189467590979111257898338942504413550048828125*ep^4+ 12548809741240576471552120191292257784413977252767866262144/ 19883758962972348430973556316639205359771819811538871616217041015625* ep^5+967277081904290419053196331379835200004845498616917542038346637127\ 2512/202610867680768086730686414886985435148195344742701338884213713839\ 33868408203125*ep^6; Fill mnchfac1(29,22)= -256/40459368324375-92972268622544/5889593280111421083328125*ep- 19208889829017034792830616/857336889865282979140962814074609375*ep^2- 2996966417354089544553996419174488424/124800900124290230299106662512755\ 602237470703125*ep^3-395636050075851119848821969352883752133494815136/ 18167029619220599884228603113900068439907583857450927734375*ep^4- 6707427330629255807000958198416402866443748497728469344672/ 377791420296474620188497570016144901835664576419238560708123779296875* ep^5-519610709676834831630190455284231793368172406826739330957879626762\ 9056/384960648593459364788304188285272326781571155011132543880006056294\ 743499755859375*ep^6; Fill mnchfac1(29,24)= 64/364134314919375+23760642614036/53006339521002789749953125*ep+ 4994377543079856463428004/7716032008787546812268665326671484375*ep^2+ 789631717561682112027013979882638256/1123208101118612072691959962614800\ 420137236328125*ep^3+105294856240590388546697084741673514182601462384/ 163503266572985398958057428025100615959168254717058349609375*ep^4+ 1798504228831165896033031633178018829749773850320307418368/ 3400122782668271581696478130145304116520981187773147046373114013671875* ep^5+140083976723429652116797928857912161173732156870952118196087355533\ 2864/346464583734113428309473769456745094103414039510019289492005450665\ 2691497802734375*ep^6; Fill mnchfac1(29,26)= -32/6190283353629375-12154331843818/901107771857047425749203125*ep- 2601264240070237729885952/131172544149388295808567310553415234375*ep^2- 417090040367725115703183962138163928/1909453771901640523576331936445160\ 7142333017578125*ep^3-56218898928266882659244528212543918768728123392/ 2779555531740751782286976276426710471305860330189991943359375*ep^4- 968022519208615774851882801669285770568613657945415123584/ 57802087305360616888840128212470169980856680192143499788342938232421875 *ep^5-75844296458151975550788922019058025932062179333969944978620650451\ 7632/588989792347992828126105408076466659975803867167032792136409266130\ 95755462646484375*ep^6; Fill mnchfac1(29,28)= 1/6190283353629375+388920876224/901107771857047425749203125*ep+ 84827912008321292632636/131172544149388295808567310553415234375*ep^2+ 13805828622791011074395112263112704/19094537719016405235763319364451607\ 142333017578125*ep^3+1882446104598762122550738656233208736235589056/ 2779555531740751782286976276426710471305860330189991943359375*ep^4+ 32697347461181348958224518309789769409688869127892160512/ 57802087305360616888840128212470169980856680192143499788342938232421875 *ep^5+25783707310834906055388638332911578193458006963614675719440400645\ 376/5889897923479928281261054080764666599758038671670327921364092661309\ 5755462646484375*ep^6; Fill mnchfac1(30,0)= 1073741824/31+9979074250129694261248/139890941865675*ep+ 55561575535333391193766474444439552/631273406969860079023974375*ep^2+ 242579953380780498786203325032020785111727341568/2848691337927977150697\ 798735087609421875*ep^3+92171906492868117670384297402405443859850510839\ 1338520870912/12855035946688212509626306180978461918178258730859375* ep^4+321573588208152967151109544887892296919447341058747348917434752997\ 3137408/580097769773975201525456094929659981188758593748499301373730468\ 75*ep^5+106289853282720462094841819733484468255437601141487116179120983\ 97149645240626751209472/26177555931567382290692474565949893082829400811\ 9009291129825421517782958984375*ep^6; Fill mnchfac1(30,2)= -268435456/465-2535146722500146102272/2098364127985125*ep- 14271731585745417099392829681041408/9469101104547901185359615625*ep^2- 62791747456575801927692462892683153545910812672/42730370068919657260466\ 981026314141328125*ep^3-23987492396667781197054759288926113779909771713\ 2906831413248/192825539200323187644394592714676928772673880962890625* ep^4-840016044760872457195230616985502179756529733361823291638486607084\ 716032/8701466546609628022881841423944899717831378906227489520605957031\ 25*ep^5-278360185430874000136716516656785767159305475408040202347912320\ 2803674843514029375488/392663338973510734360387118489248396242441012178\ 5139366947381322766744384765625*ep^6; Fill mnchfac1(30,4)= 134217728/13485+1288458616405791604736/60852559711568625*ep+ 7336359329473321050467830573563904/274603932031889134375428853125*ep^2+ 32537464625356927413998478954159333709511131136/12391807319986700605535\ 42449763110098515625*ep^3+125000528248480466303815289139379376825242311\ 284551844429824/5591940636809372441687443188725630934407542547923828125 *ep^4+43945901418286876090335817874352991257660633666066972602149926099\ 6386816/252342529851679212663573401294402091817109988280597196097572753\ 90625*ep^5+146018394762756526113411617647580112558050340828800699188648\ 5942809235110359107026944/113872368302318112964512264361882034910307893\ 531769041641474058360235587158203125*ep^6; Fill mnchfac1(30,6)= -16777216/94395-23394460241631379456/60852559711568625*ep- 943437441003849812089947793522688/1922227524223223940628001971875*ep^2- 4219231871042162864050436205165916811992072192/867426512399069042387479\ 7148341770689609375*ep^3-1630505718358282598808255046216665081958880976\ 2757977980928/39143584457665607091812102321079416540852797835466796875* ep^4-575601760892008666063646866943995795712771921736318069812413368433\ 13152/17663977089617544886450138090608146427197699179641803726830092773\ 4375*ep^5-1917996607887825408256340990298835355943425332138494594708855\ 52145618836563080941568/79710657811622679075158585053317424437215525472\ 2383291490318408521649110107421875*ep^6; Fill mnchfac1(30,8)= 8388608/2548665+11897518612719075328/1643019112212352875*ep+ 485638058126995029210380974751744/51900143154027046396956053240625*ep^2 +2190782441324191059393974498566489182422941696/23420515834774864144461\ 9523005227808619453125*ep^3+8518682258624894431622791452917672120477811\ 687634133540864/1056876780356971391478926762669144246603025541557603515\ 625*ep^4+30203847285476720175703822368096409068156651355034023726515298\ 608050176/4769273814196737119341537284464199535343378778503287006244125\ 048828125*ep^5+10094791240721367127043706479149166202867332874974569010\ 3289407210954293333367773184/215218776091381233502928179643957045980481\ 91877504348870238597030084525972900390625*ep^6; Fill mnchfac1(30,10)= -2097152/33132645-3026377627039301632/21359248458760587375*ep- 125086362815637269475044303323136/674701861002351603160428692128125* ep^2-569405844957389010843482851516773535543988224/30446670585207323387\ 80053799067961512052890625*ep^3-222849776063005693106133279099365716741\ 2168045891561660416/137393981446406280892260479146988752058393320402488\ 45703125*ep^4-793774426638169395943856912383896366905419620251710434076\ 3184865209344/620005595845575825514399846980345939594639241205427310811\ 73625634765625*ep^5-266146685753927436252517602236351506019674624119739\ 35667805653154030463348655594496/27978440891879560355380663353714415977\ 4626494407556535313101761391098837647705078125*ep^6; Fill mnchfac1(30,12)= 1048576/828316125+1540227759926607872/533981211469014684375*ep+ 64489307064807723157632960372736/16867546525058790079010717303203125* ep^2+296343528808450223189375221763085687456180224/76116676463018308469\ 501344976699037801322265625*ep^3+11677402033612373620143784831535823011\ 01743571706528700416/34348495361601570223065119786747188014598330100622\ 1142578125*ep^4+4179654425968419054611269355339229407463931138023686547\ 390302838009344/1550013989613939563785999617450864848986598103013568277\ 029340640869140625*ep^5+14061780473917996745570540788493031785123459164\ 391707162047504525655487297871594496/6994610222969890088845165838428603\ 994365662360188913382827544034777470941192626953125*ep^6; Fill mnchfac1(30,14)= -65536/2484948375-98024583068782592/1601943634407044053125*ep- 4159599512464964778362237572096/50602639575176370237032151909609375* ep^2-19303581160182341180962373722201988251710464/228350029389054925408\ 504034930097113403966796875*ep^3-76613327427655839239109308352236140593\ 818553672929656576/1030454860848047106691953593602415640437949903018663\ 427734375*ep^4-27563365771619571644578456828473600956555429460110273762\ 0545618870784/465004196884181869135799885235259454695979430904070483108\ 8021922607421875*ep^5-9306874247647668615944460379566680248290861393591\ 60051905151613427294783783251456/20983830668909670266535497515285811983\ 096987080566740148482632104332412823577880859375*ep^6; Fill mnchfac1(30,16)= 32768/57153812625+49930734007453696/36844703591362013221875*ep+ 2148374793902090112834545013248/1163860710229056515451739493921015625* ep^2+10073302744746764976823981444043721952940032/525205067594826328439\ 5592803392233608291236328125*ep^3+4028305054224406844546265659811795142\ 6939694500786671488/237004617995050834539149326528555597300728477694292\ 58837890625*ep^4+145720382689201803194366775255126019235347475793515734\ 520907721144192/1069509652833618299012339736041096745800752691079362111\ 15024504219970703125*ep^5+493934121335285314488992366902399302840066317\ 298498769161534711014367457903084928/4826281053849224161303164428515736\ 75611230702853035023415100538399645494942291259765625*ep^6; Fill mnchfac1(30,18)= -8192/628691938875-12722730966413824/405291739504982145440625*ep- 555361387223274046608681264512/12802467812519621669969134433131171875* ep^2-2632240682571576364976485157432666176575808/5777255743543089612835\ 1520837314569691203599609375*ep^3-1061068437793944096830858104292656645\ 5328157102267915072/260705079794555917993064259181411157030801325463721\ 847216796875*ep^4-38606545278560498066837095779632369427121833430854438\ 429399863030848/1176460618116980128913573709645206420380827960187298322\ 265269546419677734375*ep^5-13140245405991759883341580636831112143179510\ 6603380086690926529501432282624154432/530890915923414657743348087136731\ 0431723537731383385257566105922396100444365203857421875*ep^6; Fill mnchfac1(30,20)= 4096/13202530716375+45409732419133184/59577885707232375379771875*ep+ 287438620244480061132327211456/268851824062912055069351823095754609375* ep^2+1377886945455635176939362480484709707140704/1213223706144048818695\ 381937583605963515275591796875*ep^3+56014311330314820205015346061515824\ 47844337503041012736/54748066756856742778543494428096342976468278347381\ 58791552734375*ep^4+292956330155078587213408905911051381961300322846231\ 3849011785976032/352938185435094038674072112893561926114248388056189496\ 6795808639259033203125*ep^5+7010788691715294894372209626497762466713047\ 0809852598583900944336963428956308416/111487092343917078126103098298713\ 519066194292359051090408888224370318109331669281005859375*ep^6; Fill mnchfac1(30,22)= -512/66012653581875-5791739394706528/297889428536161876898859375*ep- 37236620883731024772630291152/1344259120314560275346759115478773046875* ep^2-180637587484083746197841950938659651013568/60661185307202440934769\ 09687918029817576377958984375*ep^3-740936250095857415988023244601047423\ 299645130910220912/2737403337842837138927174721404817148823413917369079\ 3957763671875*ep^4-3900779633593622484006607602695851297329674336255356\ 10987824325344/17646909271754701933703605644678096305712419402809474833\ 979043196295166015625*ep^5-93795804063662123746399727623494736767304620\ 79226291935047578640827896233769472/55743546171958539063051549149356759\ 5330971461795255452044441121851590546658346405029296875*ep^6; Fill mnchfac1(30,24)= 256/1254240418055625+2956671193308464/5659899142187075661078328125*ep+ 19320537127806141023822664376/25540923285976645231588423194096687890625 *ep^2+94907534210903578211849391543155806490984/11525625208368463777606\ 1284070442566533951181220703125*ep^3+3930092190223125343002029020998314\ 02488123181006938256/52010663419013905639616319706691525827644864430012\ 5085197509765625*ep^4+2976765016029416621650160150000880714650210342271\ 3059732175600896/478987537376199052486240724641262614012194240933400031\ 20800260104229736328125*ep^5+503621975544884753327265884970504261681694\ 5103125390610799916073794961403201536/105912737726721224219797943383777\ 84311288457774109853588844381315180220386508581695556640625*ep^6; Fill mnchfac1(30,26)= -64/11288163762500625-755212637537516/50939092279683680949704953125*ep- 5019466552872653062484062444/229868309573789807084295808746870191015625 *ep^2-24985266892769995625068909234641658719896/10373062687531617399845\ 51556633983098805560630986328125*ep^3-104516126473131649169952945713863\ 118431753957930017664/4680959707711251507565468773602237324488037798701\ 125766777587890625*ep^4-55836567343361282277724404493124282107879182910\ 821380054771168768/3017621485470054030663316565239954468276823717880420\ 196610416386566473388671875*ep^5-13570427703558731776019144942055402312\ 56641862301257393265823247163391848073984/95321463954049101797818149045\ 400058801596119966988682299599431836621983478577235260009765625*ep^6; Fill mnchfac1(30,28)= 32/191898783962510625+386100645409558/865964568754622576144984203125*ep +2612222807634216617065555172/39077612627544267204330287486967932472656\ 25*ep^2+13186042002216019682283767030369636429248/176342065688037495797\ 37376462777712679694530726767578125*ep^3+557582678573824279794689776716\ 64356259388587424700032/79576315031091275628612969151238034516296642577\ 919138035218994140625*ep^4+42903855118381948393143647676680347530180964\ 28120601984630474112/73285093218558455030394830870113179943865718862810\ 20477482439795947149658203125*ep^5+734326162105216794673641156751346459\ 833444411463144928944024730808624668584192/1620464887218834730562908533\ 771800999627134039438807599093190341222573719135812999420166015625*ep^6 ; Fill mnchfac1(30,30)= -1/191898783962510625-12347683358294/865964568754622576144984203125*ep- 85114480994316988246696096/3907761262754426720433028748696793247265625* ep^2-436069346667442343847318558027528918464/17634206568803749579737376\ 462777712679694530726767578125*ep^3-18654340794626727598833755208267321\ 35180736766528576/79576315031091275628612969151238034516296642577919138\ 035218994140625*ep^4-10136823521329120662307781492859245838866065811126\ 61666970474112/51299565252990918521276381609079225960706003203967143342\ 377078571630047607421875*ep^5-24948972511246495142796358164207857912831\ 761190063538178659686989159424083456/1620464887218834730562908533771800\ 999627134039438807599093190341222573719135812999420166015625*ep^6; *--#] harmo1 : *--#[ harmo2 : #procedure harmo2(P,Q,TT) * * Routine to generate the harmonic projection for * P(mnci1)*P(mnci2)*...*P(in) = TT(mnci1,mnci2,...,in) at P->Q * The object mnchfac2 is a table to give better speed. * *id `P'.`P' = 0; *id `Q'.`P' = `Q'.`Q'; ToTensor,`TT',`P'; * * Next generate the splits between indices that connect to a Q and * the indices that go to d_. * id 'TT'(?a) = sum_(mncj,0,nargs_(?a),2,`Q'.`Q'^(mncj/2)* acc(mnchfac2(nargs_(?a),mncj))*distrib_(1,mncj,mncdd,`TT',?a)); * * The indices in TT contract with Q and the indices in mncdd go to d_'mncs. * We used mncdd as an intemediary to have the mnchfac2 worked out before * the dd_ is expanded. At that moment there are fewer terms. * tovector,`TT',`Q'; id mncdd = 1; id mncdd(?a) = dd_(?a); id D = acc(4-2*ep); * #endprocedure * * Table is good up to D12 or P10. * We have only terms up to ep^3 as the integrals at this point can have * divergences up to ep^-3 only. * CTable,relax,mnchfac2(2:12,0:12); Fill mnchfac2(2,0) = - 1/3 - 2/9*ep - 4/27*ep^2 - 8/81*ep^3; Fill mnchfac2(2,2) = 1/3 + 2/9*ep + 4/27*ep^2 + 8/81*ep^3; Fill mnchfac2(3,0) = - 1 - 2/3*ep - 4/9*ep^2 - 8/27*ep^3; Fill mnchfac2(3,2) = 1/3 + 2/9*ep + 4/27*ep^2 + 8/81*ep^3; Fill mnchfac2(4,0) = - 12/5 - 44/25*ep - 464/375*ep^2 - 4784/5625*ep^3; Fill mnchfac2(4,2) = 7/15 + 82/225*ep + 892/3375*ep^2 + 9352/50625*ep^3; Fill mnchfac2(4,4) = - 2/15 - 32/225*ep - 392/3375*ep^2 - 4352/50625*ep^3; Fill mnchfac2(5,0) = - 16/3 - 196/45*ep - 2176/675*ep^2 - 23056/10125*ep^3; Fill mnchfac2(5,2) = 11/15 + 146/225*ep + 1676/3375*ep^2 + 18056/50625*ep^3; Fill mnchfac2(5,4) = - 2/15 - 32/225*ep - 392/3375*ep^2 - 4352/50625*ep^3; Fill mnchfac2(6,0) = - 80/7 - 1516/147*ep - 123292/15435*ep^2 - 9367864/1620675*ep^3; Fill mnchfac2(6,2) = 128/105 + 13136/11025*ep + 1103012/1157625*ep^2 + 85160504/121550625* ep^3; Fill mnchfac2(6,4) = - 17/105 - 1994/11025*ep - 176048/1157625*ep^2 - 13936016/121550625* ep^3; Fill mnchfac2(6,6) = 1/35 + 142/3675*ep + 13864/385875*ep^2 + 1162288/40516875*ep^3; Fill mnchfac2(7,0) = - 24 - 828/35*ep - 23372/1225*ep^2 - 1815224/128625*ep^3; Fill mnchfac2(7,2) = 44/21 + 4904/2205*ep + 427988/231525*ep^2 + 33759896/24310125*ep^3; Fill mnchfac2(7,4) = - 23/105 - 2846/11025*ep - 259232/1157625*ep^2 - 20909744/121550625* ep^3; Fill mnchfac2(7,6) = 1/35 + 142/3675*ep + 13864/385875*ep^2 + 1162288/40516875*ep^3; Fill mnchfac2(8,0) = - 448/9 - 21472/405*ep - 5657152/127575*ep^2 - 1345089952/40186125*ep^3 ; Fill mnchfac2(8,2) = 232/63 + 83236/19845*ep + 22561876/6251175*ep^2 + 5445734776/1969120125* ep^3; Fill mnchfac2(8,4) = - 20/63 - 1564/3969*ep - 440248/1250235*ep^2 - 108447328/393824025*ep^3 ; Fill mnchfac2(8,6) = 31/945 + 13486/297675*ep + 4006936/93767625*ep^2 + 1017493936/ 29536801875*ep^3; Fill mnchfac2(8,8) = - 4/945 - 1984/297675*ep - 637984/93767625*ep^2 - 170185984/29536801875 *ep^3; Fill mnchfac2(9,0) = - 512/5 - 183872/1575*ep - 50077472/496125*ep^2 - 12133597472/156279375 *ep^3; Fill mnchfac2(9,2) = 296/45 + 112916/14175*ep + 31587116/4465125*ep^2 + 7765528616/1406514375 *ep^3; Fill mnchfac2(9,4) = - 152/315 - 62372/99225*ep - 18050072/31255875*ep^2 - 4521671072/ 9845600625*ep^3; Fill mnchfac2(9,6) = 13/315 + 5818/99225*ep + 1760968/31255875*ep^2 + 452621968/9845600625* ep^3; Fill mnchfac2(9,8) = - 4/945 - 1984/297675*ep - 637984/93767625*ep^2 - 170185984/29536801875 *ep^3; Fill mnchfac2(10,0) = - 2304/11 - 1074016/4235*ep - 3316968176/14674275*ep^2 - 8998169551936/ 50846362875*ep^3; Fill mnchfac2(10,2) = 5888/495 + 26082208/1715175*ep + 82610452688/5943081375*ep^2 + 227269629249568/20592776964375*ep^3; Fill mnchfac2(10,4) = - 376/495 - 1774196/1715175*ep - 5795428756/5943081375*ep^2 - 16224932111816/20592776964375*ep^3; Fill mnchfac2(10,6) = 64/1155 + 324824/4002075*ep + 1102890364/13867189875*ep^2 + 3158182574504/48049812916875*ep^3; Fill mnchfac2(10,8) = - 7/1485 - 38642/5145525*ep - 137831812/17829244125*ep^2 - 406815641432/ 61778330893125*ep^3; Fill mnchfac2(10,10) = 1/2079 + 6086/7203735*ep + 23133196/24960941775*ep^2 + 71203299656/ 86489663250375*ep^3; Fill mnchfac2(11,0) = - 1280/3 - 1133152/2079*ep - 3599216912/7203735*ep^2 - 9927387845632/ 24960941775*ep^3; Fill mnchfac2(11,2) = 3584/165 + 2380352/81675*ep + 1106110096/40429125*ep^2 + 3092405649056/ 140086918125*ep^3; Fill mnchfac2(11,4) = - 608/495 - 2988148/1715175*ep - 9998466428/5943081375*ep^2 - 28414250145208/20592776964375*ep^3; Fill mnchfac2(11,6) = 116/1485 + 606976/5145525*ep + 2101518836/17829244125*ep^2 + 6094659016696/61778330893125*ep^3; Fill mnchfac2(11,8) = - 59/10395 - 331354/36018675*ep - 1196154644/124804708875*ep^2 - 3559742486584/432448316251875*ep^3; Fill mnchfac2(11,10) = 1/2079 + 6086/7203735*ep + 23133196/24960941775*ep^2 + 71203299656/ 86489663250375*ep^3; Fill mnchfac2(12,0) = - 11264/13 - 61826944/53235*ep - 2620237967552/2397970575*ep^2 - 95436709262412736/108016584550875*ep^3; Fill mnchfac2(12,2) = 17152/429 + 1082775712/19324305*ep + 46930455150896/870463318725*ep^2 + 1731730784364142528/39210020191967625*ep^3; Fill mnchfac2(12,4) = - 4352/2145 - 288658016/96621525*ep - 12841800621088/4352316593625*ep^2 - 481207359158775584/196050100959838125*ep^3; Fill mnchfac2(12,6) = 736/6435 + 51568148/289864575*ep + 2365538731564/13056949780875*ep^2 + 90297525582720152/588150302879514375*ep^3; Fill mnchfac2(12,8) = - 28/3861 - 59572/4969107*ep - 2833804928/223833424815*ep^2 - 110654880654064/10082576620791675*ep^3; Fill mnchfac2(12,10) = 71/135135 + 5658958/6087156075*ep + 281153094644/274195945398375*ep^2 + 11294141213967592/12351156360469801875*ep^3; Fill mnchfac2(12,12) = - 2/45045 - 172096/2029052025*ep - 9011645528/91398648466125*ep^2 - 375318002197504/4117052120156600625*ep^3; *--#] harmo2 : *--#[ integral : #procedure integral(TOPO1) #switch `TOPO1' *--#[ la : #case la * * Reduction procedure for three loop graphs of the la or ladder type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<-----<-\ * P1 / | P2 | \ P3 * / | | \ * / | | \ * / | | \ * Q --<-- P7 ^ v P8 --<-- Q * \ | | / * \ | | / * \ | | / * P6 \ | P5 | / P4 * \->------>----->-/ * #call ladder(p1,p2,p3,p4,p5,p6,p7,p8,Q) multiply Q.Q; #call ACCU(Ladder recursion) * * Now use some symmetry relations to diminish the number of terms. * Note that these transformations are sign insensitive, because the * only `nonsquare' is p7.p8 and either both change sign or neither. * if ( ( count(p2.p2,1) > count(p5.p5,1) ) || ( ( count(p2.p2,1) == count(p5.p5,1) ) && ( ( count(p1.p1,1) < count(p6.p6,1) ) || ( ( count(p1.p1,1) == count(p6.p6,1) ) && ( count(p3.p3,1) < count(p4.p4,1) ) ) ) ) ); multiply replace_(p1,p6,p6,p1,p2,p5,p5,p2,p3,p4,p4,p3); endif; if ( ( count(p1.p1,1) < count(p3.p3,1) ) || ( ( count(p1.p1,1) == count(p3.p3,1) ) && ( ( count(p6.p6,1) < count(p4.p4,1) ) || ( ( count(p6.p6,1) == count(p4.p4,1) ) && ( count(p7.p7,1) < count(p8.p8,1) ) ) ) ) ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p6,p4,p4,p6); endif; if ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p6.p6/p7.p7/p8.p8) ); * * type BEbar or benzbar. Note the introduction of Q.p2. This will * need some sign corrections in future transformations. * id p5.p5 = p2.p2+Q.Q-2*Q.p2; endif; if ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p6.p6/p7.p7/p8.p8) ); id p7.p8 = p7.p7/2+p8.p8/2-mncx8/2; endif; #call ACCU2(AB Q.Q mncx8,Rearrange) Keep Brackets; if ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p6.p6/p7.p7/p8.p8) ); multiply acc(1/ep); #call triangle(p2,p7,p8,p1,p3) multiply ep; endif; #call ACCU(Second recursion) id mncx8 = p7.p7 + p8.p8 - 2*p7.p8; #call ACCU(Second recursion B) * * Now bring the integrals to a standard form again. We can make it * such that either p1.p1 is missing, or p2.p2 and p5.p5, or p8.p8. * `missing' means: not occurring in the denominator. * if ( ( count(p7.p7,1) >= 0 ) || ( count(p8.p8,1) >= 0 ) ); if ( count(p7.p7,1) > count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p6,p4,p4,p6); endif; if ( ( count(p1.p1,1) < count(p6.p6,1) ) || ( ( count(p1.p1,1) == count(p6.p6,1) ) && ( ( count(p3.p3,1) < count(p4.p4,1) ) || ( ( count(p3.p3,1) == count(p4.p4,1) ) && ( count(p2.p2,1) < count(p5.p5,1) ) ) ) ) ); id Q.p2 = -Q.p2; multiply replace_(p1,p6,p6,p1,p2,p5,p5,p2,p3,p4,p4,p3); endif; else; if ( ( count(p1.p1,1) >= 0 ) || ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p6,p4,p4,p6); endif; if ( count(p1.p1,1) < count(p6.p6,1) ); id Q.p2 = -Q.p2; multiply replace_(p1,p6,p6,p1,p2,p5,p5,p2,p3,p4,p4,p3); endif; if ( count(p1.p1,1) < count(p4.p4,1) ); id Q.p2 = -Q.p2; multiply replace_(p1,p4,p4,p1,p2,p5,p5,p2,p6,p3,p3,p6,p7,p8,p8,p7); endif; if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p6,p4,p4,p6); endif; if ( ( count(p1.p1,1) == count(p3.p3,1) ) && ( count(p4.p4,1) > count(p6.p6,1) ) ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p6,p4,p4,p6); else; if ( ( count(p1.p1,1) == count(p6.p6,1) ) && ( count(p4.p4,1) > count(p3.p3,1) ) ); id Q.p2 = -Q.p2; multiply replace_(p1,p6,p6,p1,p2,p5,p5,p2,p3,p4,p4,p3); endif; endif; else; if ( ( count(p2.p2,1) > count(p5.p5,1) ) || ( ( count(p2.p2,1) == count(p5.p5,1) ) && ( ( count(p1.p1,1) < count(p6.p6,1) ) || ( ( count(p1.p1,1) == count(p6.p6,1) ) && ( count(p3.p3,1) < count(p4.p4,1) ) ) ) ) ); id Q.p2 = -Q.p2; multiply replace_(p1,p6,p6,p1,p2,p5,p5,p2,p3,p4,p4,p3); endif; if ( ( count(p1.p1,1) < count(p3.p3,1) ) || ( ( count(p1.p1,1) == count(p3.p3,1) ) && ( ( count(p6.p6,1) < count(p4.p4,1) ) || ( ( count(p6.p6,1) == count(p4.p4,1) ) && ( count(p7.p7,1) < count(p8.p8,1) ) ) ) ) ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p6,p4,p4,p6); endif; endif; endif; #call ACCU(Use symmetry) repeat; if ( count(p1.p1,1) >= 0 ); id p1 = p6+Q; if ( count(p6.p6,1) >= 0 ) discard; elseif ( ( count(p2.p2,1) >= 0 ) && ( count(p5.p5,1) >= 0 ) ); if ( match(1/p7.p7/p8.p8) == 0 ) discard; repeat id p2.p2/p1.p1 = 1-2*p1.p7/p1.p1+p7.p7/p1.p1; repeat id p5.p5/p6.p6 = 1+p7.p7/p6.p6-2*p6.p7/p6.p6; if ( count(p7.p7,1) >= 0 ) discard; if ( ( count(p1.p1,1) < 0 ) && ( count(p6.p6,1) >= 0 ) ); multiply replace_(p1,p6,p6,p1,p2,p5,p5,p2,p3,p4,p4,p3,Q,-Q); endif; if ( count(p1.p1,1) < 0 ); id p2 = p1-p7; id p5 = p6-p7; if ( count(p7.p7,1) >= 0 ) discard; endif; else; if ( match(1/p3.p3/p4.p4) == 0 ) discard; id p8 = p3-p2; if ( count(p3.p3,1) >= 0 ) discard; endif; endrepeat; if ( count(p1.p1,1) >= 0 ); id p6.p7 = p6.p6/2+p7.p7/2-p5.p5/2; id p5.p7 = p6.p6/2-p7.p7/2-p5.p5/2; id p5.p6 = p6.p6/2+p5.p5/2-p7.p7/2; if ( match(1/p6.p6/p7.p7) == 0 ) discard; if ( count(p7.p2,1,p7.p3,1,p7.p4,1,p7.p8,1,p7.Q,1) > count(p6.p2,1,p6.p3,1,p6.p4,1,p6.p8,1,p6.Q,1) ); multiply replace_(p6,-p7,p7,-p6); endif; id p7 = p6-p5; elseif ( ( count(p2.p2,1) >= 0 ) && ( count(p5.p5,1) >= 0 ) ); id p7.p8 = p7.p7/2+p8.p8/2-mncp9.mncp9/2; if ( match(1/p7.p7/p8.p8) == 0 ) discard; if ( count(p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.Q,1) > count(p7.p1,1,p7.p3,1,p7.p4,1,p7.p6,1,p7.Q,1) ); multiply replace_(p7,-p8,p8,-p7); endif; id p8 = p7-mncp9; else; id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; id p3.Q = p3.p3/2+Q.Q/2-p4.p4/2; id p4.Q = p3.p3/2-p4.p4/2-Q.Q/2; if ( match(1/p3.p3/p4.p4) == 0 ) discard; if ( count(p4.p1,1,p4.p2,1,p4.p5,1,p4.p6,1,p4.p7,1) > count(p3.p1,1,p3.p2,1,p3.p5,1,p3.p6,1,p3.p7,1) ); multiply replace_(p3,-p4,p4,-p3); endif; id p4 = p3-Q; endif; #call ACCU(Prepare first loop) multiply mncint1*mncint2*mncint3; * * Now we do the first integral. * The order of the selection of the integrals determines the speed only. * On atari ST (4 Mbytes, 28msec hard disk): * 8, 1, 2+5: 426 sec. * 2+5, 8, 1: 416 sec. * 2+5, 1, 8: 408 sec. * 1, 2+5, 8: 408 sec. * It seems important to keep the p8.p8 for the last. * if ( count(p1.p1,1) >= 0 ); if ( count(p6.p6,1) >= 0 ) discard; if ( count(p7.p7,1) >= 0 ) discard; totensor,nosquare,mncFQ,p6; if ( count(mncFQ,1) == 0 ); id mncint2/p6.p6^mncx1?/p7.p7^mncx2? = p5.p5^2/p5.p5^mncx1/p5.p5^mncx2*mnce5*mncG(mncx1,0,mncx2,0,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncint2/p6.p6^mncx1?/p7.p7^mncx2?*mncFQ(mnci1?) = p5.p5^2/p5.p5^mncx1/p5.p5^mncx2*mnce5*mncG(mncx1,0,mncx2,0,1,0)*p5(mnci1); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncint2/p6.p6^mncx1?/p7.p7^mncx2?*mncFQ(mnci1?,mnci2?) = p5.p5^2/p5.p5^mncx1/p5.p5^mncx2*mnce5*( +mncG(mncx1,0,mncx2,0,2,0)*p5(mnci1)*p5(mnci2) +mncG(mncx1,0,mncx2,0,2,1)*p5.p5*d_(mnci1,mnci2)/2 ); else; id mncint2/p6.p6^mncx1?/p7.p7^mncx2?*mncFQ(?a) = p5.p5^2/p5.p5^mncx1/p5.p5^mncx2*mnce5 *sum_(mncj,0,integer_(nargs_(?a)/2),mncG(mncx1,0,mncx2,0,nargs_(?a),mncj) *p5.p5^mncj/2^mncj*mncy^mncj)*mncFQ(?a); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncj?*mncFQ(?a) = distrib_(1,2*mncj,mncdel,mncFQ,?a); tovector,mncFQ,p5; id mncdel(?a) = dd_(?a); endif; * #call one(p6,p7,p5,mnce6,mnce7,mnce5,mncint2) id 1/p8.p8 = 1/p7.p7; id p8 = -p7; multiply replace_(p2,p1,mnce2,mnce1,p5,p6,mnce5,mnce6); elseif ( ( count(p2.p2,1) >= 0 ) && ( count(p5.p5,1) >= 0 ) ); if ( count(p7.p7,1) >= 0 ) discard; if ( count(p8.p8,1) >= 0 ) discard; totensor,nosquare,mncFQ,p7; if ( count(mncFQ,1) == 0 ); id mncint2/p7.p7^mncx1?/p8.p8^mncx2? = mncp9.mncp9^2/mncp9.mncp9^mncx1/mncp9.mncp9^mncx2*mnce9*mncG(mncx1,0,mncx2,0,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncint2/p7.p7^mncx1?/p8.p8^mncx2?*mncFQ(mnci1?) = mncp9.mncp9^2/mncp9.mncp9^mncx1/mncp9.mncp9^mncx2*mnce9*mncG(mncx1,0,mncx2,0,1,0)*mncp9(mnci1); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncint2/p7.p7^mncx1?/p8.p8^mncx2?*mncFQ(mnci1?,mnci2?) = mncp9.mncp9^2/mncp9.mncp9^mncx1/mncp9.mncp9^mncx2*mnce9*( +mncG(mncx1,0,mncx2,0,2,0)*mncp9(mnci1)*mncp9(mnci2) +mncG(mncx1,0,mncx2,0,2,1)*mncp9.mncp9*d_(mnci1,mnci2)/2 ); else; id mncint2/p7.p7^mncx1?/p8.p8^mncx2?*mncFQ(?a) = mncp9.mncp9^2/mncp9.mncp9^mncx1/mncp9.mncp9^mncx2*mnce9 *sum_(mncj,0,integer_(nargs_(?a)/2),mncG(mncx1,0,mncx2,0,nargs_(?a),mncj) *mncp9.mncp9^mncj/2^mncj*mncy^mncj)*mncFQ(?a); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncj?*mncFQ(?a) = distrib_(1,2*mncj,mncdel,mncFQ,?a); tovector,mncFQ,mncp9; id mncdel(?a) = dd_(?a); endif; * #call one(p7,p8,mncp9,mnce7,mnce8,mnce9,mncint2) multiply replace_(mncp9,p7,mnce9,mnce7); elseif ( count(p8.p8,1) >= 0 ); * #call one(p3,p4,Q,mnce3,mnce4,mnceq,mncint2) if ( count(p3.p3,1) >= 0 ) discard; if ( count(p4.p4,1) >= 0 ) discard; totensor,nosquare,mncFQ,p3; if ( count(mncFQ,1) == 0 ); id mncint2/p3.p3^mncx1?/p4.p4^mncx2? = Q.Q^2/Q.Q^mncx1/Q.Q^mncx2*mnceq*mncG(mncx1,0,mncx2,0,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncint2/p3.p3^mncx1?/p4.p4^mncx2?*mncFQ(mnci1?) = Q.Q^2/Q.Q^mncx1/Q.Q^mncx2*mnceq*mncG(mncx1,0,mncx2,0,1,0)*Q(mnci1); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncint2/p3.p3^mncx1?/p4.p4^mncx2?*mncFQ(mnci1?,mnci2?) = Q.Q^2/Q.Q^mncx1/Q.Q^mncx2*mnceq*( +mncG(mncx1,0,mncx2,0,2,0)*Q(mnci1)*Q(mnci2) +mncG(mncx1,0,mncx2,0,2,1)*Q.Q*d_(mnci1,mnci2)/2 ); else; id mncint2/p3.p3^mncx1?/p4.p4^mncx2?*mncFQ(?a) = Q.Q^2/Q.Q^mncx1/Q.Q^mncx2*mnceq *sum_(mncj,0,integer_(nargs_(?a)/2),mncG(mncx1,0,mncx2,0,nargs_(?a),mncj) *Q.Q^mncj/2^mncj*mncy^mncj)*mncFQ(?a); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncj?*mncFQ(?a) = distrib_(1,2*mncj,mncdel,mncFQ,?a); tovector,mncFQ,Q; id mncdel(?a) = dd_(?a); endif; multiply replace_(p2,p3,mnce2,mnce3,p5,p4,mnce5,mnce4); else; print "Illegal symmetry in LA"; setexitflag; endif; #call ACCU(First loop integral) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * * Now approximate and convert to MSbar. * #call finish(3,`SCHEME') * #break *--#] la : *--#[ bu : #case bu * * Integral of type BU * It may as well be handled by BE * We only need renumbering. * multiply replace_(p1,p2,p2,p6,p3,p5,p4,p7,p5,p8,p6,p3,p7,p4,p8,p1); * *--#] bu : *--#[ fa : #case fa * * Integral of type FA. * This may as well be done by BE. * *--#] fa : *--#[ be : #case be * * Reduction procedure for three loop graphs of the BE or benz type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<------<-\ * P1 / \ P2 / \ P3 * / \ / \ * / P6 v ^ P7 \ * / \ / \ * Q --<-- \ / --<-- Q * \ | / * \ v P8 / * \ | / * P5 \ | / P4 * \---->------->----/ * #ifdef `BEPATH' #call benzred(p1,p2,p3,p4,p5,p6,p7,p8,Q) #else if ( count(p6.p6,1) < count(p7.p7,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p6.p6,1) == count(p7.p7,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p5.p5,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); endif; endif; #call ACCU2(AB p1.p3 p1.p1 p3.p3 p8.p8,Benz scalar 0) id p1.p3 = p1.p1/2+p3.p3/2-p8.p8/2; #call ACCU2(AB p2.p3 p2.p2 p3.p3 p7.p7,Benz scalar 1) id p2.p3 = p2.p2/2+p3.p3/2-p7.p7/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p6.p6,Benz scalar 2) id p1.p2 = p1.p1/2+p2.p2/2-p6.p6/2; #call ACCU2(AB Q.p1 p1.p1 Q.Q p5.p5,Benz scalar 3) id Q.p1 = p1.p1/2+Q.Q/2-p5.p5/2; #call ACCU2(AB Q.p3 p3.p3 Q.Q p4.p4,Benz scalar 4) id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( count(p6.p6,1) < count(p7.p7,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p6.p6,1) == count(p7.p7,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p5.p5,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); endif; endif; #call ACCU(Benz scalar 5) #endif multiply Q.Q; if ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7) > 0 ); multiply acc(1/ep); #call triangle(p2,p6,p7,p1,p3) multiply ep; endif; *#call ACCU(Benz recursion) * * Use the left-right symmetry relation. * if ( ( count(p1.p1,1) < count(p3.p3,1) ) || ( ( count(p1.p1,1) == count(p3.p3,1) ) && ( ( count(p5.p5,1) < count(p4.p4,1) ) || ( ( count(p5.p5,1) == count(p4.p4,1) ) && ( count(p6.p6,1) < count(p7.p7,1) ) ) ) ) ); multiply replace_(p1,-p3,p2,-p2,p3,-p1,p4,-p5,p5,-p4,p6,-p7,p7,-p6,Q,-Q); endif; #call ACCU2(AB p1.p1 p5.p5 p3.p3 p4.p4 Q.p8 Q.Q Q.p2 Q.p7,Benz recursion) *#call ACCU(Rearrange) * * Now we use the second level reduction. We have only BU left * because FA was treated already together with BE. * if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) > 0 ); id p1.p1 = p5.p5 + p3.p3 - p4.p4 -2*Q.p8; endif; if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) > 0 ); id Q.p2 = Q.p7 + p3.p3/2 + Q.Q/2 - p4.p4/2; endif; *if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) > 0 ); * if ( ( count(p3.p3,1) > count(p4.p4,1) ) * || ( ( count(p3.p3,1) == count(p4.p4,1) ) * && ( ( count(p7.p7,1) > count(p8.p8,1) ) * || ( ( count(p7.p7,1) == count(p8.p8,1) ) * && ( ( count(p5.p5,1) > count(p2.p2,1) ) * || ( ( count(p5.p5,1) == count(p2.p2,1) ) * && ( count(Q.p7,1) < count(Q.p8,1) ) ) ) ) ) ) ); * Multiply,replace_(p3,-p4,p4,-p3,p2,-p5,p5,-p2,p7,p8,p8,p7); * endif; *endif; #call ACCU(Prepare second) if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) > 0 ); multiply acc(1/ep); if ( count(p3.p3,1) > count(p4.p4,1) ); #call triangle(p7,p2,p6,p3,p8) else; #call triangle(p8,p5,p6,p4,p7) endif; multiply ep; endif; #call ACCU(Second recursion) if ( match(1/p6.p6/p7.p7) == 0 ); if ( ( count(p6.p6,1) < count(p7.p7,1) ) || ( ( count(p6.p6,1) == count(p7.p7,1) ) && ( ( count(p1.p1,1) < count(p3.p3,1) ) || ( ( count(p1.p1,1) == count(p3.p3,1) ) && ( count(p5.p5,1) < count(p4.p4,1) ) ) ) ) ); multiply replace_(p1,-p3,p2,-p2,p3,-p1,p4,-p5,p5,-p4,p6,-p7,p7,-p6,Q,-Q); endif; elseif ( ( count(p5.p5,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) ); if ( ( count(p4.p4,1) < count(p5.p5,1) ) || ( ( count(p4.p4,1) == count(p5.p5,1) ) && ( ( count(p1.p1,1) < count(p3.p3,1) ) || ( ( count(p1.p1,1) == count(p3.p3,1) ) && ( count(p6.p6,1) < count(p7.p7,1) ) ) ) ) ); multiply replace_(p1,-p3,p2,-p2,p3,-p1,p4,-p5,p5,-p4,p6,-p7,p7,-p6,Q,-Q); endif; elseif ( ( count(p1.p1,1) < count(p3.p3,1) ) || ( ( count(p1.p1,1) == count(p3.p3,1) ) && ( ( count(p5.p5,1) < count(p4.p4,1) ) || ( ( count(p5.p5,1) == count(p4.p4,1) ) && ( count(p6.p6,1) < count(p7.p7,1) ) ) ) ) ); multiply replace_(p1,-p3,p2,-p2,p3,-p1,p4,-p5,p5,-p4,p6,-p7,p7,-p6,Q,-Q); endif; #call ACCU(Use Symmetry) * #ifdef `POW' #if `POW' >= 1 if ( count(p6.p6,1) >= 0 ); * id p6.p6 = p1.p1+p2.p2-2*p1.p2; * id p6 = p2-p1; if ( ( count(p2.p2,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; elseif ( ( count(p8.p8,1) >= 0 ) && ( count(p1.p1,1) >= 0 ) ); * id p8 = p6-p7; * id p1 = p2-p6; if ( ( count(p6.p6,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) ) discard; elseif ( count(p2.p2,1) >= 0 ); * id p2.p2 = p1.p1+p6.p6+2*p1.p6; * id p2 = p1+p6; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; if ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ) discard; elseif ( count(p4.p4,1) >= 0 ); if ( count(p5.p5,1) >= 0 ) discard; id p4.p4 = Q.Q+p3.p3-2*Q.p3; id p4 = p3-Q; if ( count(p3.p3,1) >= 0 ); * repeat id p3.p3/p2.p2 = 1+p7.p7/p2.p2-2*p2.p7/p2.p2; * repeat id p2.p3/p2.p2 = 1-p2.p7/p2.p2; if ( count(p7.p7,1) >= 0 ) discard; if ( count(p8.p8,1) >= 0 ) discard; * if ( count(p2.p2,1) < 0 ); * id p3 = p2-p7; * endif; endif; elseif ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ); repeat id p3.p3/p4.p4 = 1+Q.Q/p4.p4+2*Q.p4/p4.p4; repeat id p3.p4/p4.p4 = 1+Q.p4/p4.p4; if ( count(p4.p4,1) < 0 ); repeat id p1.p1/p5.p5 = 1+Q.Q/p5.p5+2*Q.p5/p5.p5; repeat id p1.p5/p5.p5 = 1+Q.p5/p5.p5; if ( count(p5.p5,1) >= 0 ); multiply replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6 ,Q,-Q,p4,-p5,p5,-p4); else; id p1 = Q+p5; id p3 = Q+p4; endif; endif; else; exit "mincer integral Pre-Setup 1";* Just in case we forgot something endif; #call ACCU(Pre-setup 1) if ( count(p6.p6,1) >= 0 ); * id p6.p6 = p1.p1+p2.p2-2*p1.p2; * id p6 = p2-p1; if ( ( count(p2.p2,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; elseif ( ( count(p8.p8,1) >= 0 ) && ( count(p1.p1,1) >= 0 ) ); * id p8 = p6-p7; * id p1 = p2-p6; if ( ( count(p6.p6,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) ) discard; elseif ( count(p2.p2,1) >= 0 ); * id Q.p2 = Q.Q/2+p1.p1/2-p5.p5/2+Q.p6; * id p2.p2 = p1.p1+p6.p6+2*p1.p6; * id p2 = p1+p6; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; if ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ) discard; elseif ( count(p4.p4,1) >= 0 ); id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; if ( count(p5.p5,1) >= 0 ) discard; id p4.p4 = Q.Q+p3.p3-2*Q.p3; id p4 = p3-Q; if ( count(p3.p3,1) >= 0 ); repeat id p3.p3/p2.p2 = 1+p7.p7/p2.p2-2*p2.p7/p2.p2; repeat id p2.p3/p2.p2 = 1-p2.p7/p2.p2; if ( count(p7.p7,1) >= 0 ) discard; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p2.p2,1) < 0 ); id p3 = p2-p7; endif; endif; elseif ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ); repeat id p3.p3/p4.p4 = 1+Q.Q/p4.p4+2*Q.p4/p4.p4; repeat id p3.p4/p4.p4 = 1+Q.p4/p4.p4; if ( count(p4.p4,1) < 0 ); repeat id p1.p1/p5.p5 = 1+Q.Q/p5.p5+2*Q.p5/p5.p5; repeat id p1.p5/p5.p5 = 1+Q.p5/p5.p5; if ( count(p5.p5,1) >= 0 ); multiply replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6 ,Q,-Q,p4,-p5,p5,-p4); else; id p1 = Q+p5; id p3 = Q+p4; endif; endif; else; exit "mincer integral Pre-Setup 2";* Just in case we forgot something endif; #call ACCU(Pre-setup 2) #if `POW' >= 4 if ( count(p6.p6,1) >= 0 ); * id p6.p6 = p1.p1+p2.p2-2*p1.p2; * id p6 = p2-p1; * id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; * id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; * id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( ( count(p2.p2,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; elseif ( ( count(p8.p8,1) >= 0 ) && ( count(p1.p1,1) >= 0 ) ); * id p8.p8 = p6.p6-2*p6.p7+p7.p7; * id p1.p1 = p2.p2-2*p2.p6+p6.p6; * id p8 = p6-p7; * id p1 = p2-p6; * id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; * id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) ) discard; elseif ( count(p2.p2,1) >= 0 ); id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; id p2.p2 = p1.p1+p6.p6+2*p1.p6; id Q.p2 = Q.Q/2+p1.p1/2-p5.p5/2+Q.p6; id p2 = p1+p6; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; if ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ) discard; elseif ( count(p4.p4,1) >= 0 ); id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; if ( count(p5.p5,1) >= 0 ) discard; id p4.p4 = Q.Q+p3.p3-2*Q.p3; id p4 = p3-Q; if ( count(p3.p3,1) >= 0 ); repeat id p3.p3/p2.p2 = 1+p7.p7/p2.p2-2*p2.p7/p2.p2; repeat id p2.p3/p2.p2 = 1-p2.p7/p2.p2; if ( count(p7.p7,1) >= 0 ) discard; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p2.p2,1) < 0 ); id p3 = p2-p7; endif; endif; elseif ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ); repeat id p3.p3/p4.p4 = 1+Q.Q/p4.p4+2*Q.p4/p4.p4; repeat id p3.p4/p4.p4 = 1+Q.p4/p4.p4; if ( count(p4.p4,1) < 0 ); repeat id p1.p1/p5.p5 = 1+Q.Q/p5.p5+2*Q.p5/p5.p5; repeat id p1.p5/p5.p5 = 1+Q.p5/p5.p5; if ( count(p5.p5,1) >= 0 ); multiply replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6 ,Q,-Q,p4,-p5,p5,-p4); else; id p1 = Q+p5; id p3 = Q+p4; endif; endif; else; exit "mincer integral Pre-Setup 3";* Just in case we forgot something endif; #call ACCU(Pre-setup 3) #if `POW' >= 6 if ( count(p6.p6,1) >= 0 ); * id p6.p6 = p1.p1+p2.p2-2*p1.p2; * id p6 = p2-p1; * id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; * id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; * id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( ( count(p2.p2,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; elseif ( ( count(p8.p8,1) >= 0 ) && ( count(p1.p1,1) >= 0 ) ); id p8.p8 = p6.p6-2*p6.p7+p7.p7; id p1.p1 = p2.p2-2*p2.p6+p6.p6; id p8 = p6-p7; id p1 = p2-p6; id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) ) discard; elseif ( count(p2.p2,1) >= 0 ); id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; id p2.p2 = p1.p1+p6.p6+2*p1.p6; id Q.p2 = Q.Q/2+p1.p1/2-p5.p5/2+Q.p6; id p2 = p1+p6; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; if ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ) discard; elseif ( count(p4.p4,1) >= 0 ); id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; if ( count(p5.p5,1) >= 0 ) discard; id p4.p4 = Q.Q+p3.p3-2*Q.p3; id p4 = p3-Q; if ( count(p3.p3,1) >= 0 ); repeat id p3.p3/p2.p2 = 1+p7.p7/p2.p2-2*p2.p7/p2.p2; repeat id p2.p3/p2.p2 = 1-p2.p7/p2.p2; if ( count(p7.p7,1) >= 0 ) discard; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p2.p2,1) < 0 ); id p3 = p2-p7; endif; endif; elseif ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ); repeat id p3.p3/p4.p4 = 1+Q.Q/p4.p4+2*Q.p4/p4.p4; repeat id p3.p4/p4.p4 = 1+Q.p4/p4.p4; if ( count(p4.p4,1) < 0 ); repeat id p1.p1/p5.p5 = 1+Q.Q/p5.p5+2*Q.p5/p5.p5; repeat id p1.p5/p5.p5 = 1+Q.p5/p5.p5; if ( count(p5.p5,1) >= 0 ); multiply replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6 ,Q,-Q,p4,-p5,p5,-p4); else; id p1 = Q+p5; id p3 = Q+p4; endif; endif; else; exit "mincer integral Pre-Setup 4";* Just in case we forgot something endif; #call ACCU(Pre-setup 4) #endif #endif #endif #endif repeat; if ( count(p6.p6,1) >= 0 ); id p6.p6 = p1.p1+p2.p2-2*p1.p2; id p6 = p2-p1; id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( ( count(p2.p2,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; elseif ( ( count(p8.p8,1) >= 0 ) && ( count(p1.p1,1) >= 0 ) ); id p8.p8 = p6.p6-2*p6.p7+p7.p7; id p1.p1 = p2.p2-2*p2.p6+p6.p6; id p8 = p6-p7; id p1 = p2-p6; id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) ) discard; elseif ( count(p2.p2,1) >= 0 ); id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; id p2.p2 = p1.p1+p6.p6+2*p1.p6; * id Q.p2 = Q.Q/2+p1.p1/2-p5.p5/2+Q.p6; Reactivated 13-sep-1994 id Q.p2 = Q.Q/2+p1.p1/2-p5.p5/2+Q.p6; id p2 = p1+p6; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; if ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ) discard; elseif ( count(p4.p4,1) >= 0 ); id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; if ( count(p5.p5,1) >= 0 ) discard; id p4.p4 = Q.Q+p3.p3-2*Q.p3; id p4 = p3-Q; if ( count(p3.p3,1) >= 0 ); repeat id p3.p3/p2.p2 = 1+p7.p7/p2.p2-2*p2.p7/p2.p2; repeat id p2.p3/p2.p2 = 1-p2.p7/p2.p2; if ( count(p7.p7,1) >= 0 ) discard; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p2.p2,1) < 0 ); id p3 = p2-p7; endif; endif; elseif ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ); repeat id p3.p3/p4.p4 = 1+Q.Q/p4.p4+2*Q.p4/p4.p4; repeat id p3.p4/p4.p4 = 1+Q.p4/p4.p4; if ( count(p4.p4,1) < 0 ); repeat id p1.p1/p5.p5 = 1+Q.Q/p5.p5+2*Q.p5/p5.p5; repeat id p1.p5/p5.p5 = 1+Q.p5/p5.p5; if ( count(p5.p5,1) >= 0 ); multiply replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6 ,Q,-Q,p4,-p5,p5,-p4); else; id p1 = Q+p5; id p3 = Q+p4; endif; endif; else; exit "mincer integral setup first loop";* Just in case we forgot something endif; endrepeat; #call ACCU(setup first loop) if ( count(p6.p6,1) >= 0 ); multiply replace_(p2,mncp9,p7,p8,p8,-p7,p5,p6); multiply mncnaar(p3,mnce3); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-p3.p3/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - p3.mncq1; totensor,nosquare,mncp9,mncFQ; elseif ( ( count(p8.p8,1) >= 0 ) && ( count(p1.p1,1) >= 0 ) ); multiply replace_(p2,p4,p3,p6,p4,p1,p7,-p7,p5,mncp9,p6,-p8,Q,-Q); multiply mncnaar(p3,mnce3); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-p3.p3/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - p3.mncq1; totensor,nosquare,mncp9,mncFQ; elseif ( count(p2.p2,1) >= 0 ); multiply replace_(p5,p6,p8,-p7,p6,p8,p7,mncp9); label 2; multiply mncnaar(p7,mnce7); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-p7.p7/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - p7.mncq1; totensor,nosquare,mncp9,mncFQ; elseif ( count(p4.p4,1) >= 0 ); if ( count(p3.p3,1) >= 0 ); multiply replace_(p2,p3,p6,-p7,p5,p6,p7,-mncp9); goto 2; else; multiply replace_(p2,p1,p8,p4,p1,mncp9,p5,p8); multiply mncnaar(Q,mnceq,1); id Q.p8 = mncp9.mncp9/2-p8.p8/2-Q.Q/2; if ( count(p8.p8,1) >= 0 ) discard; id p8 = mncp9-Q; id mncp9.mncq1?{p1,p3,p4,p6,p7} = p1.mncq1-p6.mncq1; id Q.mncp9 = mncp9.mncp9/2+Q.Q/2-p8.p8/2; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p1.p1,1,p3.p3,1) > count(p4.p4,1,p6.p6,1) ); multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); endif; if ( count(p1.p1,1,p6.p6,1) > count(p3.p3,1,p4.p4,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4); id p7 = -p7; endif; totensor,nosquare,Q,mncFQ; id,many,mncq1?{p1,p3,p4,p6,p7}.mncq2?{p1,p3,p4,p6,p7}^D? = mncx^D*mncq1.mncq2^D; endif; elseif ( ( count(p1.p1,1) >= 0 ) && ( count(p3.p3,1) >= 0 ) ); multiply replace_(p5,-p1,p4,-p3,p7,p4,p8,p7,p2,-p8); multiply mncnaar(Q,mnceq,1); id Q.p8 = mncp9.mncp9/2-p8.p8/2-Q.Q/2; if ( count(p8.p8,1) >= 0 ) discard; id p8 = mncp9-Q; id mncp9.mncq1?{p1,p3,p4,p6,p7} = p1.mncq1-p6.mncq1; id Q.mncp9 = mncp9.mncp9/2+Q.Q/2-p8.p8/2; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p1.p1,1,p3.p3,1) > count(p4.p4,1,p6.p6,1) ); multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); endif; if ( count(p1.p1,1,p6.p6,1) > count(p3.p3,1,p4.p4,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4); id p7 = -p7; endif; totensor,nosquare,Q,mncFQ; id,many,mncq1?{p1,p3,p4,p6,p7}.mncq2?{p1,p3,p4,p6,p7}^D? = mncx^D*mncq1.mncq2^D; else; Print "Illegal case in BE"; SetExitFlag; endif; #call ACCU2(B p8 mncp9 mncnaar mncFQ mncx mncint3,Prepare first loop) keep brackets; * multiply mncint1*mncint2*mncint3; if ( match(mncnaar(Q,mnceq,1)) ); id mncnaar(Q,mnceq,1) = 1; id mncx^D? = mncp9.mncp9^D/Q.Q^D; multiply mncp9.mncp9^4/Q.Q^4; if ( count(p8.p8,1) >= 0 ) discard; if ( count(mncFQ,1) == 0 ); id mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq*mncG(mncx1,2,mncx2,0,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncint2*mncFQ(mnci1?)/mncp9.mncp9^mncx1?/p8.p8^mncx2? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq*Q(mnci1)*mncG(mncx1,2,mncx2,0,1,0); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncint2*mncFQ(mnci1?,mnci2?)/mncp9.mncp9^mncx1?/p8.p8^mncx2? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq* (mncG(mncx1,2,mncx2,0,2,0)*mncFFPP(mnci1,mnci2) +mncG(mncx1-1,2,mncx2,0,0,0)*acc(mncpoch(3,1))*d_(mnci1,mnci2)*Q.Q/2); else; id mncint2*mncFQ(?a)/mncp9.mncp9^mncx1?/p8.p8^mncx2? = mncFQ(?a)/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq* sum_(mncs,0,integer_(nargs_(?a)/2),mncG(mncx1-mncs,2,mncx2,0,nargs_(?a)-2*mncs,0) *acc(mncpoch(nargs_(?a)+2-mncs,mncs))*Q.Q^mncs *sum_(mncj,0,integer_(nargs_(?a)/2)-mncs,sign_(mncj)*Q.Q^mncj * the original mncy/4 becomes mncy/2 when we consider the normalization of * the distrib_ to expand the mncFQ. *mncy^mncj*mncy^mncs/2^mncj/2^mncs*acc(mncpoch(nargs_(?a)+1-2*mncs,mncj)) )); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncs?*mncFQ(?a) = fac_(mncs)*distrib_(1,2*mncs,mncdel,mncFQ,?a); tovector,mncFQ,Q; id mncdel(?a) = dd_(?a); else; id mncFFPP(mnci1?,mnci2?) = Q(mnci1)*Q(mnci2) - d_(mnci1,mnci2)*Q.Q/2*acc(mncpoch(3,1)); endif; else; id p8 = mncp9 - mncq9; id mncnaar(mncq1?,mncy?) = mncnaar(mncq1,mncy)*replace_(mncq9,mncq1); repeat; id mncFQ(mncp9) = mncp9.mncp9; id mncFQ(?a,mncp9,?b) = mncFQ(?a,?b)*mncp9.mncp9; endrepeat; totensor,nosquare,mncFQ,mncp9; if ( count(mncFQ,1) == 0 ); id mncnaar(mncq9?,mncy?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2? = mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncy *mncG(mncx1,0,mncx2,0,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncnaar(mncq9?,mncy?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mncFQ(mnci1?) = mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncy *mncG(mncx1,0,mncx2,0,1,0)*mncq9(mnci1); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncnaar(mncq9?,mncy?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mncFQ(mnci1?,mnci2?) = mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncy*( +mncG(mncx1,0,mncx2,0,2,0)*mncq9(mnci1)*mncq9(mnci2) +mncG(mncx1,0,mncx2,0,2,1)*mncq9.mncq9*d_(mnci1,mnci2)/2 ); else; id mncnaar(mncq9?,mncx?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mncFQ(?a) = mncnaar(mncq9,mncx)*mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncx *sum_(mncj,0,integer_(nargs_(?a)/2),mncG(mncx1,0,mncx2,0,nargs_(?a),mncj) *mncq9.mncq9^mncj/2^mncj*mncy^mncj)*mncFQ(?a); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncj?*mncFQ(?a) = distrib_(1,2*mncj,mncdel,mncFQ,?a); tovector,mncFQ,mncq9; id mncnaar(mncq1?,mncy?) = replace_(mncq9,mncq1); id mncdel(?a) = dd_(?a); endif; endif; #call ACCU(First loop integral) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * * Now approximate and convert to MSbar. * #call finish(3,`SCHEME') * #break *--#] be : *--#[ no : #case no * * Reduction procedure for three loop graphs of the NO or nonplanar type. * Notation is from S.mncG.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<-----<-\ * P1 / \ P2 / \ P3 * / v / \ * / P7 \ / \ * / \ / \ * Q --<-- / --<-- Q * \ / \ / * \ P8 / \ / * \ ^ \ / * P6 \ / P5 \ / P4 * \->------>----->-/ * multiply mncint3*Q.Q; #call newplane(p1,p2,p3,p4,p5,p6,p7,p8,Q,mncint3) #call ACCU(noplane recursion) repeat id Q.p2/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 = ( p1.p1/2+p3.p3/2-p4.p4/2-p6.p6/2-Q.p5 ) /p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8; repeat id Q.p2/p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p8.p8 = ( Q.p8+p3.p3/2+Q.Q/2-p4.p4/2 ) /p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p8.p8; repeat id Q.p2/p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7 = ( Q.p7+p1.p1/2+Q.Q/2-p6.p6/2 ) /p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7; if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); label 1; if ( count(p3.p3,1) < count(p4.p4,1) ); multiply replace_(p3,-p4,p4,-p3,p2,-p7,p7,-p2,p5,p8,p8,p5); * elseif ( ( count(p3.p3,1) == count(p4.p4,1) ) * && ( count(p5.p5,1) < count(p8.p8,1) ) ); * multiply replace_(p3,-p4,p4,-p3,p2,-p7,p7,-p2,p5,p8,p8,p5); endif; elseif ( match(1/p1.p1/p2.p2/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); goto 1; elseif ( match(1/p1.p1/p2.p2/p3.p3/p5.p5/p6.p6/p7.p7/p8.p8) ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p2,p5,p5,p2,p7,-p7,p8,-p8,Q,-Q); goto 1; elseif ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p7.p7/p8.p8) ); multiply replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7); goto 1; elseif ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); if ( count(p7.p7,1) > count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; elseif ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p6.p6/p7.p7/p8.p8) ); if ( count(p7.p7,1) < count(p8.p8,1) ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p2,p5,p5,p2,p7,-p7,p8,-p8,Q,-Q); else; multiply replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7); endif; if ( count(p7.p7,1) > count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; elseif ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p8.p8) ); multiply replace_(p3,-p4,p4,-p3,p2,-p7,p7,-p2,p5,p8,p8,p5); if ( count(p7.p7,1) > count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; elseif ( match(1/p1.p1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7) ); multiply replace_(p1,-p6,p6,-p1,p2,-p8,p8,-p2,p5,p7,p7,p5); if ( count(p7.p7,1) > count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; else; repeat; if ( count(p2.p2,1) < count(p5.p5,1) ) multiply replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7); if ( count(p7.p7,1) < count(p8.p8,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); if ( count(p2.p2,1) < count(p7.p7,1) ) multiply replace_(p3,-p4,p4,-p3,p2,-p7,p7,-p2,p5,p8,p8,p5); endrepeat; endif; #call ACCU(Move Q.p2) #ifdef `POW' #if `POW' >= 6 if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id p1.p1/p6.p6 = 1+mncx/p6.p6; id mncx = Q.Q+2*Q.p5+2*Q.p8; * repeat id Q.p7/p6.p6/p3.p3/p4.p4 = * (p3.p3/2-Q.Q/2-p4.p4/2-Q.p5)/p6.p6/p3.p3/p4.p4; * repeat id p7.p8/p6.p6/p3.p3/p4.p4/p2.p2/p5.p5 = * (p2.p2/2-p3.p3/2+p5.p5/2-p6.p6/2-Q.p8)/p6.p6/p3.p3/p4.p4/p2.p2/p5.p5; elseif ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id p2.p2/p5.p5/p7.p7/p8.p8 = (mncx-p5.p5+p7.p7+p8.p8)/p5.p5/p7.p7/p8.p8; id mncx = 2*p1.p3-2*Q.p5-Q.Q; repeat id p2.p5/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 = (p4.p4/2+p6.p6/2-p7.p7/2-p8.p8/2+Q.p5)/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8; * repeat id p7.p8/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 = * (p7.p7+p8.p8-mncy9)/2/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8; * if ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); * repeat id Q.p2/p1.p1/p3.p3/p4.p4/p6.p6 = * (p1.p1/2+p3.p3/2-p4.p4/2-p6.p6/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; * repeat id Q.p7/p1.p1/p3.p3/p4.p4/p6.p6 = * (p3.p3/2-Q.Q/2-p4.p4/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; * repeat id Q.p8/p1.p1/p3.p3/p4.p4/p6.p6 = * (p1.p1/2-Q.Q/2-p6.p6/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; * endif; endif; #call ACCU(Prepare second A) #if `POW' >= 8 if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id p1.p1/p6.p6 = 1+mncx/p6.p6; id mncx = Q.Q+2*Q.p5+2*Q.p8; repeat id Q.p7/p6.p6/p3.p3/p4.p4 = (p3.p3/2-Q.Q/2-p4.p4/2-Q.p5)/p6.p6/p3.p3/p4.p4; * repeat id p7.p8/p6.p6/p3.p3/p4.p4/p2.p2/p5.p5 = * (p2.p2/2-p3.p3/2+p5.p5/2-p6.p6/2-Q.p8)/p6.p6/p3.p3/p4.p4/p2.p2/p5.p5; elseif ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id p2.p2/p5.p5/p7.p7/p8.p8 = (mncx-p5.p5+p7.p7+p8.p8)/p5.p5/p7.p7/p8.p8; id mncx = 2*p1.p3-2*Q.p5-Q.Q; repeat id p2.p5/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 = (p4.p4/2+p6.p6/2-p7.p7/2-p8.p8/2+Q.p5)/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8; repeat id p7.p8/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 = (p7.p7+p8.p8-mncy9)/2/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8; if ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id Q.p2/p1.p1/p3.p3/p4.p4/p6.p6 = (p1.p1/2+p3.p3/2-p4.p4/2-p6.p6/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; * repeat id Q.p7/p1.p1/p3.p3/p4.p4/p6.p6 = * (p3.p3/2-Q.Q/2-p4.p4/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; * repeat id Q.p8/p1.p1/p3.p3/p4.p4/p6.p6 = * (p1.p1/2-Q.Q/2-p6.p6/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; endif; endif; #call ACCU(Prepare second B) #endif #endif #endif if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id p1.p1/p6.p6 = 1+mncx/p6.p6; id mncx = Q.Q+2*Q.p5+2*Q.p8; repeat id Q.p7/p6.p6/p3.p3/p4.p4 = (p3.p3/2-Q.Q/2-p4.p4/2-Q.p5)/p6.p6/p3.p3/p4.p4; repeat id p7.p8/p6.p6/p3.p3/p4.p4/p2.p2/p5.p5 = (p2.p2/2-p3.p3/2+p5.p5/2-p6.p6/2-Q.p8)/p6.p6/p3.p3/p4.p4/p2.p2/p5.p5; elseif ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id p2.p2/p5.p5/p7.p7/p8.p8 = (mncx-p5.p5+p7.p7+p8.p8)/p5.p5/p7.p7/p8.p8; id mncx = 2*p1.p3-2*Q.p5-Q.Q; repeat id p2.p5/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 = (p4.p4/2+p6.p6/2-p7.p7/2-p8.p8/2+Q.p5)/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8; repeat id p7.p8/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8 = (p7.p7+p8.p8-mncy9)/2/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8; if ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); repeat id Q.p2/p1.p1/p3.p3/p4.p4/p6.p6 = (p1.p1/2+p3.p3/2-p4.p4/2-p6.p6/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; repeat id Q.p7/p1.p1/p3.p3/p4.p4/p6.p6 = (p3.p3/2-Q.Q/2-p4.p4/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; repeat id Q.p8/p1.p1/p3.p3/p4.p4/p6.p6 = (p1.p1/2-Q.Q/2-p6.p6/2-Q.p5)/p1.p1/p3.p3/p4.p4/p6.p6; endif; endif; if ( ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) == 0 ) && ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) == 0 ) ); repeat; if ( count(p2.p2,1) < count(p5.p5,1) ) multiply replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7); if ( count(p7.p7,1) < count(p8.p8,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); if ( count(p2.p2,1) < count(p7.p7,1) ) multiply replace_(p3,-p4,p4,-p3,p2,-p7,p7,-p2,p5,p8,p8,p5,mncy9,mncx9,mncx9,mncy9); endrepeat; endif; #call ACCU(Prepare second) if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); id Q.p8 = Q.p2 - p3.p3/2 - Q.Q/2 + p4.p4/2; id p2.p5 = Q.p5+p4.p4/2+p6.p6/2-p7.p7/2-p8.p8/2; elseif ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); id mncy9 = p1.p1+p3.p3-2*p1.p3; endif; #call ACCU(Minimize second) if ( match(1/p2.p2/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); multiply acc(1/ep); #call triangle(p5,p6,p7,p8,p4) multiply ep; elseif ( match(1/p1.p1/p3.p3/p4.p4/p5.p5/p6.p6/p7.p7/p8.p8) ); multiply acc(1/ep); #call triangle(p5,p8,p7,p6,p4) multiply ep; endif; id mncx9 = p2.p2+p5.p5+2*p2.p5; id mncy9 = p7.p7+p8.p8-2*p7.p8; repeat; if ( count(p2.p2,1) < count(p5.p5,1) ) multiply replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7); if ( count(p7.p7,1) < count(p8.p8,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); if ( count(p2.p2,1) < count(p7.p7,1) ) multiply replace_(p3,-p4,p4,-p3,p2,-p7,p7,-p2,p5,p8,p8,p5); endrepeat; #call ACCU(Second recursion) * * Now we try to reduce the number of one loop integrals * if ( count(mncint3,1) ); if ( count(p2.p2,1) >= 0 ); if ( count(p8.p8,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); * Everybody flips sign -> nobody flips sign elseif ( count(p3.p3,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); * Everybody flips sign -> nobody flips sign elseif ( count(p4.p4,1) >= 0 ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; elseif ( count(p6.p6,1) >= 0 ); multiply replace_(p1,p6,p6,p1,p7,p8,p8,p7,p3,p4,p4,p3 ,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; endif; elseif ( count(p5.p5,1) >= 0 ); if ( count(p7.p7,1) >= 0 ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; elseif ( count(p8.p8,1) >= 0 ); multiply replace_(p1,p6,p6,p1,p7,p8,p8,p7,p3,p4,p4,p3 ,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; elseif ( count(p3.p3,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); * Everybody flips sign -> nobody flips sign elseif ( count(p4.p4,1) >= 0 ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; elseif ( count(p6.p6,1) >= 0 ); multiply replace_(p1,p6,p6,p1,p7,p8,p8,p7,p3,p4,p4,p3 ,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; endif; elseif ( count(p7.p7,1) >= 0 ); if ( count(p8.p8,1) >= 0 ); multiply replace_(p3,-p4,p4,-p3,p5,p8,p8,p5,p2,-p7,p7,-p2); elseif ( count(p1.p1,1) >= 0 ); multiply replace_(p3,-p4,p4,-p3,p5,p8,p8,p5,p2,-p7,p7,-p2); elseif ( count(p3.p3,1) >= 0 ); multiply replace_(p3,p4,p4,p3,p5,p8,p8,p5,p2,p7,p7,p2); id p3 = -p3; id p4 = -p4; id p2 = -p2; id p7 = -p7; multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; elseif ( count(p4.p4,1) >= 0 ); multiply replace_(p3,-p4,p4,-p3,p5,p8,p8,p5,p2,-p7,p7,-p2); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); * Everybody flips sign -> nobody flips sign elseif ( count(p6.p6,1) >= 0 ); multiply replace_(p1,-p6,p6,-p1,p5,p7,p7,p5,p2,-p8,p8,-p2); endif; elseif ( count(p8.p8,1) >= 0 ); if ( count(p1.p1,1) >= 0 ); multiply replace_(p3,-p4,p4,-p3,p5,p8,p8,p5,p2,-p7,p7,-p2); elseif ( count(p3.p3,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); * Everybody flips sign -> nobody flips sign multiply replace_(p3,-p4,p4,-p3,p5,p8,p8,p5,p2,-p7,p7,-p2); elseif ( count(p4.p4,1) >= 0 ); multiply replace_(p1,p4,p4,p1,p3,p6,p6,p3,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; multiply replace_(p3,-p4,p4,-p3,p5,p8,p8,p5,p2,-p7,p7,-p2); elseif ( count(p6.p6,1) >= 0 ); multiply replace_(p1,-p6,p6,-p1,p5,p7,p7,p5,p2,-p8,p8,-p2); endif; elseif ( count(p3.p3,1) >= 0 ); if ( count(p4.p4,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); * Everybody flips sign -> nobody flips sign elseif ( count(p6.p6,1) >= 0 ); multiply replace_(p1,p6,p6,p1,p5,p7,p7,p5,p2,p8,p8,p2); id p1 = -p1; id p6 = -p6; id p2 = -p2; id p8 = -p8; endif; elseif ( count(p4.p4,1) >= 0 ); if ( count(p1.p1,1) >= 0 ); multiply replace_(p3,-p4,p4,-p3,p5,p8,p8,p5,p2,-p7,p7,-p2); elseif ( count(p6.p6,1) >= 0 ); multiply replace_(p1,p6,p6,p1,p7,p8,p8,p7,p3,p4,p4,p3 ,p2,p5,p5,p2); id Q = -Q; id p7 = -p7; id p8 = -p8; endif; endif; endif; #call ACCU(Symmetry) if ( count(mncint3,1) ); if ( count(p2.p2,1) >= 0 ); if ( count(p1.p1,1) >= 0 ); * id p1.p1 = p6.p6+Q.Q+2*Q.p6; * id p2.p2 = p3.p3+p8.p8+2*p3.p8; * id p1 = p6+Q; * id p2 = p3+p8; if ( ( count(p6.p6,1) >= 0 ) || ( count(p8.p8,1) >= 0 ) ) discard; elseif ( count(p7.p7,1) >= 0 ); if ( count(p5.p5,1) >= 0 ) discard; * id p2.p2 = p3.p3+p8.p8+2*p3.p8; * id p7.p7 = p4.p4+p5.p5-2*p4.p5; * id p2 = p3+p8; * id p7 = p4-p5; if ( ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) ) discard; elseif( count(p5.p5,1) >= 0); repeat id p5.p5/p6.p6 = 1+p8.p8/p6.p6-2*p6.p8/p6.p6; if ( count(p8.p8,1) >= 0 ) discard; repeat id p5.p6/p6.p6 = 1-p6.p8/p6.p6; if ( count(p6.p6,1) >= 0 ); multiply replace_(p1,-p6,p6,-p1,p5,-p2,p2,-p5,p3,-p4,p4,-p3 ,p7,p8,p8,p7); else; repeat id p2.p2/p3.p3 = 1+p8.p8/p3.p3+2*p3.p8/p3.p3; repeat id p2.p3/p3.p3 = 1+p3.p8/p3.p3; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p3.p3,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); else; * id p5 = p6-p8; * id p2 = p3+p8; if ( count(p8.p8,1) >= 0 ) discard; endif; endif; else; exit "mincer integral Setup first loop"; endif; elseif ( count(p1.p1,1) >= 0 ); if ( count(p6.p6,1) >= 0 ); * id p1.p1 = p2.p2+p7.p7-2*p2.p7; if ( ( count(p2.p2,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; * id p6.p6 = p5.p5+p8.p8+2*p5.p8; if ( ( count(p5.p5,1) >= 0 ) || ( count(p8.p8,1) >= 0 ) ) discard; * id p1 = p2-p7; * id p6 = p5+p8; * if ( ( count(p2.p2,1) >= 0 ) || ( count(p8.p8,1) >= 0 ) ) discard; * if ( ( count(p5.p5,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; elseif ( count(p5.p5,1) >= 0 ); repeat id p1.p1/p2.p2/p7.p7 = 1/p7.p7+1/p2.p2-2*p2.p7/p2.p2/p7.p7; repeat id p1.p2/p2.p2 = 1-p2.p7/p2.p2; repeat id p1.p7/p7.p7 = p2.p7/p7.p7-1; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; if ( count(p2.p2,1) < 0 ); repeat id p5.p5/p4.p4 = 1+p7.p7/p4.p4-2*p4.p7/p4.p4; id p5.p7 = p4.p7-p7.p7; if ( count(p7.p7,1) >= 0 ) discard; repeat id p4.p5/p4.p4 = 1-p4.p7/p4.p4; if ( count(p4.p4,1) >= 0 ); multiply replace_(Q,-Q,p1,p4,p4,p1,p2,p5,p5,p2,p3,p6,p6,p3 ,p7,-p7,p8,-p8); else; * id p1 = p2-p7; * id p5 = p4-p7; endif; endif; elseif ( count(p3.p3,1) >= 0 ); repeat id p1.p1/p6.p6 = 1+Q.Q/p6.p6+2*Q.p6/p6.p6; repeat id p1.p6/p6.p6 = 1+Q.p6/p6.p6; if ( count(p6.p6,1) < 0 ); repeat id p3.p3/p4.p4 = 1+Q.Q/p4.p4+2*Q.p4/p4.p4; repeat id p3.p4/p4.p4 = 1+Q.p4/p4.p4; if ( count(p4.p4,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p4,p6,p6,p4); else; id p1 = Q+p6; id p3 = Q+p4; endif; endif; else; exit "mincer integral Setup first loop"; endif; else; exit "mincer integral Setup first loop"; endif; endif; #call ACCU(Setup first loop) if ( count(mncint3,1) ); repeat; if ( count(p2.p2,1) >= 0 ); if ( count(p1.p1,1) >= 0 ); id p1.p1 = p6.p6+Q.Q+2*Q.p6; id p2.p2 = p3.p3+p8.p8+2*p3.p8; id p1 = p6+Q; id p2 = p3+p8; if ( ( count(p6.p6,1) >= 0 ) || ( count(p8.p8,1) >= 0 ) ) discard; elseif ( count(p7.p7,1) >= 0 ); if ( count(p5.p5,1) >= 0 ) discard; id p2.p2 = p3.p3+p8.p8+2*p3.p8; id p7.p7 = p4.p4+p5.p5-2*p4.p5; id p2 = p3+p8; id p7 = p4-p5; if ( ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) ) discard; elseif( count(p5.p5,1) >= 0); repeat id p5.p5/p6.p6 = 1+p8.p8/p6.p6-2*p6.p8/p6.p6; if ( count(p8.p8,1) >= 0 ) discard; repeat id p5.p6/p6.p6 = 1-p6.p8/p6.p6; if ( count(p6.p6,1) >= 0 ); multiply replace_(p1,-p6,p6,-p1,p5,-p2,p2,-p5,p3,-p4,p4,-p3 ,p7,p8,p8,p7); else; repeat id p2.p2/p3.p3 = 1+p8.p8/p3.p3+2*p3.p8/p3.p3; repeat id p2.p3/p3.p3 = 1+p3.p8/p3.p3; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p3.p3,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); else; id p5 = p6-p8; id p2 = p3+p8; if ( count(p8.p8,1) >= 0 ) discard; endif; endif; else; exit "mincer integral Prepare first loop"; endif; elseif ( count(p1.p1,1) >= 0 ); if ( count(p6.p6,1) >= 0 ); id p1.p1 = p2.p2+p7.p7-2*p2.p7; if ( ( count(p2.p2,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; id p6.p6 = p5.p5+p8.p8+2*p5.p8; if ( ( count(p5.p5,1) >= 0 ) || ( count(p8.p8,1) >= 0 ) ) discard; id p1 = p2-p7; id p6 = p5+p8; if ( ( count(p2.p2,1) >= 0 ) || ( count(p8.p8,1) >= 0 ) ) discard; if ( ( count(p5.p5,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; elseif ( count(p5.p5,1) >= 0 ); repeat id p1.p1/p2.p2/p7.p7 = 1/p7.p7+1/p2.p2-2*p2.p7/p2.p2/p7.p7; repeat id p1.p2/p2.p2 = 1-p2.p7/p2.p2; repeat id p1.p7/p7.p7 = p2.p7/p7.p7-1; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; if ( count(p2.p2,1) < 0 ); repeat id p5.p5/p4.p4 = 1+p7.p7/p4.p4-2*p4.p7/p4.p4; id p5.p7 = p4.p7-p7.p7; if ( count(p7.p7,1) >= 0 ) discard; repeat id p4.p5/p4.p4 = 1-p4.p7/p4.p4; if ( count(p4.p4,1) >= 0 ); multiply replace_(Q,-Q,p1,p4,p4,p1,p2,p5,p5,p2,p3,p6,p6,p3 ,p7,-p7,p8,-p8); else; id p1 = p2-p7; id p5 = p4-p7; endif; endif; elseif ( count(p3.p3,1) >= 0 ); repeat id p1.p1/p6.p6 = 1+Q.Q/p6.p6+2*Q.p6/p6.p6; repeat id p1.p6/p6.p6 = 1+Q.p6/p6.p6; if ( count(p6.p6,1) < 0 ); repeat id p3.p3/p4.p4 = 1+Q.Q/p4.p4+2*Q.p4/p4.p4; repeat id p3.p4/p4.p4 = 1+Q.p4/p4.p4; if ( count(p4.p4,1) >= 0 ); multiply replace_(p1,p3,p3,p1,p7,p8,p8,p7,p4,p6,p6,p4); else; id p1 = Q+p6; id p3 = Q+p4; endif; endif; else; exit "mincer integral Prepare first loop"; endif; else; exit "mincer integral Prepare first loop"; endif; endrepeat; if ( count(p2.p2,1) >= 0 ); if ( count(p1.p1,1) >= 0 ); multiply replace_(p5,p6,p6,mncp9,p7,-p7); multiply mncnaar(p6,mnce6); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-p6.p6/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - p6.mncq1; totensor,nosquare,mncp9,mncFQ; elseif ( count(p7.p7,1) >= 0 ); multiply replace_(p8,p7,p5,p4,p3,mncp9,p4,p8); multiply mncnaar(Q,mnceq); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-Q.Q/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - Q.mncq1; totensor,nosquare,mncp9,mncFQ; else; * must be p5 multiply replace_(p7,-mncp9,p8,-p8); multiply mncnaar(p7,mnce7); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-p7.p7/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - p7.mncq1; totensor,nosquare,mncp9,mncFQ; endif; else; if ( count(p6.p6,1) >= 0 ); multiply replace_(p7,-p8,p8,p7,p2,p1,p5,mncp9); multiply mncnaar(p4,mnce4); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-p4.p4/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - p4.mncq1; totensor,nosquare,mncp9,mncFQ; elseif ( count(p5.p5,1) >= 0 ); multiply replace_(p8,p7,p7,-p8,p2,p1,p6,mncp9); multiply mncnaar(p6,mnce6); id p8.mncp9 = mncp9.mncp9/2+p8.p8/2-p6.p6/2; if ( ( count(p8.p8,1) >= 0 ) || ( count(mncp9.mncp9,1) >= 0 ) ) discard; if ( count(p8.Q,1,p8.p1,1,p8.p3,1,p8.p4,1,p8.p6,1,p8.p7,1) > count(mncp9.Q,1,mncp9.p1,1,mncp9.p3,1,mncp9.p4,1,mncp9.p6,1,mncp9.p7,1) ) multiply replace_(p8,-mncp9,mncp9,-p8); id p8.mncq1?!{p8} = mncp9.mncq1 - p6.mncq1; totensor,nosquare,mncp9,mncFQ; else; if ( count(p2.p2,1) >= 0 ) discard; multiply replace_(p7,-p1,p4,-p3,p8,p4,p5,p7,p2,-p8); multiply mncnaar(Q,mnceq,1); id Q.p8 = mncp9.mncp9/2-p8.p8/2-Q.Q/2; if ( count(p8.p8,1) >= 0 ) discard; id p8 = mncp9-Q; id mncp9.mncq1?{p1,p3,p4,p6,p7} = p1.mncq1-p6.mncq1; id Q.mncp9 = mncp9.mncp9/2+Q.Q/2-p8.p8/2; if ( count(p8.p8,1) >= 0 ) discard; if ( count(p1.p1,1,p3.p3,1) > count(p4.p4,1,p6.p6,1) ); multiply replace_(p1,-p6,p6,-p1,p3,-p4,p4,-p3,p7,-p7); endif; if ( count(p1.p1,1,p6.p6,1) > count(p3.p3,1,p4.p4,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4); id p7 = -p7; endif; totensor,nosquare,Q,mncFQ; id,many,mncq1?{p1,p3,p4,p6,p7}.mncq2?{p1,p3,p4,p6,p7}^D? = mncx^D*mncq1.mncq2^D; endif; endif; endif; if ( ( count(mncint3,1) > 0 ) && ( count(mncnaar,1) == 0 ) ); Print "Illegal case in NO"; SetExitFlag; endif; #call ACCU2(B p8 mncp9 mncnaar mncFQ mncx mncint3,Prepare first loop) keep brackets; if ( count(mncint3,1) ); id mncint3 = mncint1*mncint2*mncint3; if ( match(mncnaar(Q,mnceq,1)) ); id mncnaar(Q,mnceq,1) = 1; id mncx^D? = mncp9.mncp9^D/Q.Q^D; multiply mncp9.mncp9^4/Q.Q^4; if ( count(p8.p8,1) >= 0 ) discard; if ( count(mncFQ,1) == 0 ); id mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq* mncG(mncx1,2,mncx2,0,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncint2*mncFQ(mnci1?)/mncp9.mncp9^mncx1?/p8.p8^mncx2? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq*Q(mnci1)* mncG(mncx1,2,mncx2,0,1,0); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncint2*mncFQ(mnci1?,mnci2?)/mncp9.mncp9^mncx1?/p8.p8^mncx2? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq* (mncG(mncx1,2,mncx2,0,2,0)*mncFFPP(mnci1,mnci2) +mncG(mncx1-1,2,mncx2,0,0,0)*acc(mncpoch(3,1))*d_(mnci1,mnci2)*Q.Q/2); else; id mncint2*mncFQ(?a)/mncp9.mncp9^mncx1?/p8.p8^mncx2? = mncFQ(?a)/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq* sum_(mncs,0,integer_(nargs_(?a)/2),mncG(mncx1-mncs,2,mncx2,0,nargs_(?a)-2*mncs,0) *acc(mncpoch(nargs_(?a)+2-mncs,mncs))*Q.Q^mncs *sum_(mncj,0,integer_(nargs_(?a)/2)-mncs,sign_(mncj)*Q.Q^mncj * the original mncy/4 becomes mncy/2 when we consider the normalization of * the distrib_ to expand the mncFQ. *mncy^mncj*mncy^mncs/2^mncj/2^mncs*acc(mncpoch(nargs_(?a)+1-2*mncs,mncj)) )); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncs?*mncFQ(?a) = fac_(mncs)*distrib_(1,2*mncs,mncdel,mncFQ,?a); tovector,mncFQ,Q; id mncdel(?a) = dd_(?a); else; id mncFFPP(mnci1?,mnci2?) = Q(mnci1)*Q(mnci2) - d_(mnci1,mnci2)*Q.Q/2*acc(mncpoch(3,1)); endif; else; id p8 = mncp9 - mncq9; id mncnaar(mncq1?,mncy?) = mncnaar(mncq1,mncy)*replace_(mncq9,mncq1); repeat; id mncFQ(mncp9) = mncp9.mncp9; id mncFQ(?a,mncp9,?b) = mncFQ(?a,?b)*mncp9.mncp9; endrepeat; totensor,nosquare,mncFQ,mncp9; if ( count(mncFQ,1) == 0 ); id mncnaar(mncq9?,mncy?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2? = mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncy *mncG(mncx1,0,mncx2,0,0,0); elseif ( match(mncFQ(mnci1?)) ); id mncnaar(mncq9?,mncy?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mncFQ(mnci1?) = mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncy *mncG(mncx1,0,mncx2,0,1,0)*mncq9(mnci1); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncnaar(mncq9?,mncy?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mncFQ(mnci1?,mnci2?) = mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncy*( +mncG(mncx1,0,mncx2,0,2,0)*mncq9(mnci1)*mncq9(mnci2) +mncG(mncx1,0,mncx2,0,2,1)*mncq9.mncq9*d_(mnci1,mnci2)/2 ); else; id mncnaar(mncq9?,mncx?)*mncint2/mncp9.mncp9^mncx1?/p8.p8^mncx2?*mncFQ(?a) = mncnaar(mncq9,mncx)*mncq9.mncq9^2/mncq9.mncq9^mncx1/mncq9.mncq9^mncx2*mncx *sum_(mncj,0,integer_(nargs_(?a)/2),mncG(mncx1,0,mncx2,0,nargs_(?a),mncj) *mncq9.mncq9^mncj/2^mncj*mncy^mncj)*mncFQ(?a); endif; #call simplify if ( count(mncFQ,1) ); id mncy^mncj?*mncFQ(?a) = distrib_(1,2*mncj,mncdel,mncFQ,?a); tovector,mncFQ,mncq9; id mncnaar(mncq1?,mncy?) = replace_(mncq9,mncq1); id mncdel(?a) = dd_(?a); endif; endif; else; multiply ep; endif; #call ACCU(First loop integral) #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; #call finish(3,`SCHEME') * #break *--#] no : *--#[ o1 : #case o1 * * Integral of type O1. * id p6.p7 = p5.p5/2-p6.p6/2-p7.p7/2; id p7.mncq1?!{p7} = p5.mncq1-p6.mncq1; id p5.p6 = p5.p5/2+p6.p6/2-p7.p7/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; #call ACCU(Momenta 1) multiply mncint1*mncint2*mncint3*Q.Q; #call one(p6,p7,p5,mnce6,mnce7,mnce5,mncint2) #call ACCU2(B mncG,Integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * multiply replace_(p2,p3,p3,p4,p4,p6,p5,p7,mnce5,mnce7); #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] o1 : *--#[ o2 : #case o2 * * Integral of type O2. * *id p7 = p4-p6; id p4.p6 = p4.p4/2+p6.p6/2-p7.p7/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; #call ACCU(Momenta 1) multiply mncint1*mncint2*mncint3*Q.Q; #call one(p6,p7,p4,mnce6,mnce7,mnce4,mncint2) #call ACCU2(B mncG,Integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * multiply replace_(p2,p3,p3,p4,p4,p6,p5,p7,mnce4,mnce6); #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] o2 : *--#[ o3 : #case o3 * * Integral of type O3. * id p7 = Q-p6; id Q.p6 = Q.Q/2+p6.p6/2-p7.p7/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; #call ACCU(Momenta 1) multiply mncint1*mncint2*mncint3*Q.Q; #call one(p6,p7,Q,mnce6,mnce7,mnceq,mncint2) #call ACCU2(B mncG,Integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * multiply replace_(p2,p3,p3,p4,p4,p6,p5,p7); #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] o3 : *--#[ o4 : #case o4 * * Integral of type O4 * Note that this is a hacked up version of BE * The multiplicative constant is for the Bjorken sumrule * id p6.p1 = p1.p1/2+p6.p6/2-p4.p4/2; #call ACCU(scalars 1) id p6.p2 = p2.p2/2+p6.p6/2-p3.p3/2; #call ACCU(scalars 2) id p1.p2 = p1.p1/2+p2.p2/2-p5.p5/2; #call ACCU(scalars 3) id Q.p6 = Q.Q/2+p6.p6/2-p7.p7/2; if ( count(p7.p7,1) >= 0 ) discard; #call ACCU(scalars 4) id,many,mncq1?{p1,p2,p3,p4,p5}.mncq2?{p1,p2,p3,p4,p5}^mncx1? = mncq1.mncq2^mncx1*p6.p6^mncx1/Q.Q^mncx1; totensor,nosquare,mncFQ,Q; #call ACCU2(B p6 p7 mncFQ,Prepare first loop) keep brackets; multiply mncint1*mncint2*mncint3*mnce6^2/mnceq^2*p6.p6^4/Q.Q^3; if ( count(mncFQ,1) == 0 ); id mncint2/p6.p6^mncx1?/p7.p7^mncx2?*mnce6^mncy1? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq*mnceq^mncy1* mncG(mncx1,mncy1,mncx2,0,0,0); #call simplify elseif ( match(mncFQ(mnci1?)) ); id mncint2*mncFQ(mnci1?)/p6.p6^mncx1?/p7.p7^mncx2?*mnce6^mncy1? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq*mnceq^mncy1*Q(mnci1)* mncG(mncx1,mncy1,mncx2,0,1,0); #call simplify elseif ( match(mncFQ(mnci1?,mnci2?)) ); id mncint2*mncFQ(mnci1?,mnci2?)/p6.p6^mncx1?/p7.p7^mncx2?*mnce6^mncy1? = 1/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq*mnceq^mncy1* (mncG(mncx1,mncy1,mncx2,0,2,0)*Q(mnci1)*Q(mnci2) -mncG(mncx1,mncy1,mncx2,0,2,0)*d_(mnci1,mnci2)*Q.Q/2*acc(mncpoch(3,1)) +mncG(mncx1-1,mncy1,mncx2,0,0,0)*acc(mncpoch(3,1))*d_(mnci1,mnci2)*Q.Q/2); #call simplify else; id mncint2*mncFQ(?a)/p6.p6^mncx1?/p7.p7^mncx2?*mnce6^mncy1? = mncFQ(?a)/Q.Q^mncx1/Q.Q^mncx2*Q.Q^2*mnceq*mnceq^mncy1* sum_(mncs,0,integer_(nargs_(?a)/2),mncG(mncx1-mncs,mncy1,mncx2,0,nargs_(?a)-2*mncs,0) *acc(mncpoch(nargs_(?a)+2-mncs,mncs))*Q.Q^mncs *sum_(mncj,0,integer_(nargs_(?a)/2)-mncs,sign_(mncj)*Q.Q^mncj * the original mncy/4 becomes mncy/2 when we consider the normalization of * the distrib_ to expand the mncFQ. *mncy^mncj*mncy^mncs/2^mncj/2^mncs*acc(mncpoch(nargs_(?a)+1-2*mncs,mncj)) )); #call simplify id mncy^mncs?*mncFQ(?a) = fac_(mncs)*distrib_(1,2*mncs,mncdel,mncFQ,?a); tovector,mncFQ,Q; id mncdel(?a) = dd_(?a); endif; *#call one4(p6,p7,Q,mnce6,mnce7,mnceq,p1,p2,p3,p4,p5,mncint2) #call ACCU(First loop integral) *#call simplify *#call ACCU(Simplify first mncG) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * multiply replace_(p2,p3,p3,p4,p4,p6,p5,p7); #call dotwo{} #call ACCU(Simplify mncG\(3\)); repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] o4 : *--#[ o5 : #case o5 * * Integral of type O5 which is a flipped version of O2. * *id p7 = p3-p6; id p3.p6 = p3.p3/2+p6.p6/2-p7.p7/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; #call ACCU(Momenta 1) multiply mncint1*mncint2*mncint3*Q.Q; #call one(p6,p7,p3,mnce6,mnce7,mnce3,mncint2) #call ACCU2(B mncG,Integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * multiply replace_(p2,p3,p3,p4,p4,p6,p5,p7,mnce3,mnce4); #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] o5 : *--#[ o6 : #case o6 * * Integral of type O3. * id p7 = Q-p6; id Q.p6 = Q.Q/2+p6.p6/2-p7.p7/2; if ( ( count(p6.p6,1) >= 0 ) || ( count(p7.p7,1) >= 0 ) ) discard; #call ACCU(Momenta 1) multiply mncint1*mncint2*mncint3*Q.Q; #call one(p6,p7,Q,mnce6,mnce7,mnceq,mncint2) #call ACCU2(B mncG,Integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) * * The rest is standard. Note that the momenta that still exist * have to be called p1,p3,p4,p6,p7. * multiply replace_(p2,p3,p3,p4,p4,p6,p5,p7); #call dotwo{} #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] o6 : *--#[ y1 : #case y1 * * File inpy1 does 3-loop diagrams of type Y1. * The algorithm here is designed especially for these diagrams * so that things may proceed faster. * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; id p2.p5 = p2.p2/2+p5.p5/2-p6.p6/2; if ( ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) ) discard; #call ACCU(Momenta substitutions) multiply mncint1*mncint2*mncint3/mnceq^3; #call one(p3,p4,p1,mnce3,mnce4,mnce1,mncint1) #call ACCU2(B mncG,integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) #call one(p5,p6,p2,mnce5,mnce6,mnce2,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; #call ACCU(Momenta 3) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint3) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 3) Keep Brackets; #call simplify #call ACCU(Simplify 3) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] y1 : *--#[ y2 : #case y2 * * File inpy2 does 3-loop diagrams of type Y2. * The algorithm here is designed especially for these diagrams * so that things may proceed faster. * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; id p1.p5 = p1.p1/2+p5.p5/2-p6.p6/2; if ( ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) ) discard; #call ACCU(Momenta substitutions) multiply mncint1*mncint2*mncint3/mnceq^3; #call one(p3,p4,p1,mnce3,mnce4,mnce1,mncint1) #call ACCU2(B mncG,integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) #call one(p5,p6,p1,mnce5,mnce6,mnce1,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; #call ACCU(Momenta 3) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint3) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 3) Keep Brackets; #call simplify #call ACCU(Simplify 3) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] y2 : *--#[ y3 : #case y3 * * File inpy3 does 3-loop diagrams of type Y3. * The algorithm here is designed especially for these diagrams * so that things may proceed faster. * id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id p4.mncq1?!{p4} = p1.mncq1-p3.mncq1; id p6.mncq1?!{p6} = p3.mncq1-p5.mncq1; id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; id p3.p5 = p3.p3/2+p5.p5/2-p6.p6/2; if ( ( count(p5.p5,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) ) discard; #call ACCU(Momenta substitutions) multiply mncint1*mncint2*mncint3/mnceq^3; #call one(p5,p6,p3,mnce5,mnce6,mnce3,mncint1) #call ACCU2(B mncG,Integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; if ( count(p4.p4,1) >= 0 ) discard; #call one(p3,p4,p1,mnce3,mnce4,mnce1,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,Integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; #call ACCU(Momenta 3) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint3) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 3) Keep Brackets; #call simplify #call ACCU(Simplify 3) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] y3 : *--#[ y4 : #case y4 * * File inpy4 does 3-loop diagrams of type Y4. * The algorithm here is designed especially for these diagrams * so that things may proceed faster. * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; id Q.p5 = Q.Q/2+p5.p5/2-p6.p6/2; if ( ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) ) discard; #call ACCU(Momenta substitutions) multiply mncint1*mncint2*mncint3/mnceq^3; #call one(p5,p6,Q,mnce5,mnce6,mnceq,mncint1) #call ACCU2(B mncG,integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) #call one(p3,p4,p1,mnce3,mnce4,mnce1,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; if ( count(p2.p2,1) >= 0 ) discard; #call ACCU(Momenta 3) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint3) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral3) Keep Brackets; #call simplify #call ACCU(Simplify 3) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] y4 : *--#[ y5 : #case y5 * * File inpy5 does 3-loop diagrams of type Y5. * The algorithm here is designed especially for these diagrams * so that things may proceed faster. * id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id p4.mncq1?!{p4} = Q.mncq1-p3.mncq1; id p6.mncq1?!{p6} = Q.mncq1-p5.mncq1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; id Q.p3 = Q.Q/2+p3.p3/2-p4.p4/2; id Q.p5 = Q.Q/2+p5.p5/2-p6.p6/2; if ( ( count(p1.p1,1) >= 0 ) || ( count(p2.p2,1) >= 0 ) || ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) ) discard; #call ACCU(Momenta substitutions) multiply mncint1*mncint2*mncint3/mnceq^3; #call one(p3,p4,Q,mnce3,mnce4,mnceq,mncint1) id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; id Q.p5 = Q.Q/2+p5.p5/2-p6.p6/2; if ( ( count(p1.p1,1) >= 0 ) || ( count(p2.p2,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) ) discard; #call ACCU2(B mncG,integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) #call one(p5,p6,Q,mnce5,mnce6,mnceq,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) *id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; if ( ( count(p1.p1,1) >= 0 ) || ( count(p2.p2,1) >= 0 ) ) discard; #call ACCU(Momenta 3) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint3) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral3) Keep Brackets; #call simplify #call ACCU(Simplify 3) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] y5 : *--#[ y6 : #case y6 * * File inpy4 does 3-loop diagrams of type Y6. (flipped Y4) * The algorithm here is designed especially for these diagrams * so that things may proceed faster. * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; id Q.p5 = Q.Q/2+p5.p5/2-p6.p6/2; if ( ( count(p3.p3,1) >= 0 ) || ( count(p4.p4,1) >= 0 ) || ( count(p5.p5,1) >= 0 ) || ( count(p6.p6,1) >= 0 ) ) discard; #call ACCU(Momenta substitutions) multiply mncint1*mncint2*mncint3/mnceq^3; #call one(p5,p6,Q,mnce5,mnce6,mnceq,mncint1) #call ACCU2(B mncG,integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) #call one(p3,p4,p1,mnce3,mnce4,mnce1,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; if ( count(p2.p2,1) >= 0 ) discard; #call ACCU(Momenta 3) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint3) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral3) Keep Brackets; #call simplify #call ACCU(Simplify 3) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(3,`SCHEME') * #break *--#] y6 : *--#[ t1 : #case t1 * * This is inpt1. It does two loop topologies of type T1. * multiply replace_(p2,p3,p3,p4,p4,p6,p5,p7,mnce2,mnce3,mnce3,mnce4,mnce4,mnce6,mnce5,mnce7) *mncint1*mncint3*Q.Q*mnceq; *Print +f ">%t"; #call dotwo{} ; *#message We are at the print statement #call ACCU(Simplify mncG\(3\)) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * * Now approximate and convert to MSbar. * #call finish(2,`SCHEME') multiply ep; * #break *--#] t1 : *--#[ t2 : #case t2 * * This is inpt2. It does two loop topologies of type T2. * multiply mncint1*mncint2/mnceq^2; if ( count(mnce3,1) < count(mnce4,1) ) multiply replace_(p3,p4,p4,p3,mnce3,mnce4,mnce4,mnce3); id p4.mncq1?!{p4} = p1.mncq1-p3.mncq1; id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; if ( ( count(p3.p3,1) >= 0 ) && ( count(mnce3,1) == 0 ) ) discard; if ( ( count(p4.p4,1) >= 0 ) && ( count(mnce4,1) == 0 ) ) discard; #call ACCU(momenta) #call one(p3,p4,p1,mnce3,mnce4,mnce1,mncint1) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 1) Keep Brackets; #call simplify #call ACCU(simplify 1) id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; if ( ( count(p2.p2,1) >= 0 ) && ( count(mnce2,1) == 0 ) ) discard; #call ACCU(momenta 2) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * * Now approximate and convert to MSbar. * #call finish(2,`SCHEME') multiply ep; * #break *--#] t2 : *--#[ t3 : #case t3 * * This is inpt3. It does two loop topologies of type T3. * multiply mncint1*mncint2/mnceq^2; id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id p4.mncq1?!{p4} = Q.mncq1-p3.mncq1; id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; if ( ( count(p1.p1,1) >= 0 ) && ( count(mnce1,1) == 0 ) ) discard; if ( ( count(p2.p2,1) >= 0 ) && ( count(mnce2,1) == 0 ) ) discard; if ( ( count(p3.p3,1) >= 0 ) && ( count(mnce3,1) == 0 ) ) discard; if ( ( count(p4.p4,1) >= 0 ) && ( count(mnce4,1) == 0 ) ) discard; #call ACCU(momenta 1) #call one(p3,p4,Q,mnce3,mnce4,mnceq,mncint2) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 1) Keep Brackets; #call simplify #call ACCU(Simplify 1) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; if ( ( count(p1.p1,1) >= 0 ) && ( count(mnce1,1) == 0 ) ) discard; if ( ( count(p2.p2,1) >= 0 ) && ( count(mnce2,1) == 0 ) ) discard; #call ACCU(momenta 2) #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint1) #call ACCU2(B mncG mncexp10 mncexp20 mncexp11,integral 2) Keep Brackets; #call simplify #call ACCU(Simplify 2) repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * #call finish(2,`SCHEME') multiply ep; * #break *--#] t3 : *--#[ l1 : #case l1 * * This is inpl1. It does the one loop topology of type L1. * multiply mncint1/mnceq; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; .sort:prepare 1; id Q.p2 = Q.Q/2-p1.p1/2+p2.p2/2; .sort:prepare 2; id p1.p2 = Q.Q/2-p1.p1/2-p2.p2/2; .sort:prepare 3; id P.p2 = Q.P-P.p1; .sort:prepare 4; #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint1) #call ACCU(integral 1) #call simplify repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * * Now approximate and convert to MSbar. * #call finish(1,`SCHEME') multiply ep^2; * #break *--#] l1 : *--#[ l2 : #case l2 * * This is file inpl2. It does topologies of type L2 which are * meant to have an entire expanded gluon propagator in two loops. * It is done to avoid enormous problems with the gluon insertion * inside the three loop graph. * multiply mnce2^2*mncint1/ep^5/mnceq^3; id p2 = Q-p1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; if ( count(p1.p1,1) >= 0 ) discard; #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint1) #call ACCU(integral 1) #call simplify repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-1; id acc(mncx1?) = mncx1; .sort #call finish(1,`SCHEME') multiply,ep^2; print +f +s; B ep; .sort multiply, + ep^-2*ca*nf * ( - 55/18 - 1/3*mncxi ) + ep^-2*ca^2 * ( 175/36 + 35/24*mncxi ) + ep^-2*nf^2 * ( 4/9 ) + ep^-1*cf*nf * ( - 1 ) + ep^-1*ca*nf * ( - 1199/108 - 2/9*mncxi ) + ep^-1*ca^2 * ( 4229/216 - 97/144*mncxi + 5/8*mncxi^2 - 1/8*mncxi^3 ) + ep^-1*nf^2 * ( 40/27 ) + ep*cf*nf * ( - 1711/36 + 76/3*z3 + 12*z4 ) + ep*ca*nf * ( - 337315/3888 + 50/9*z3*mncxi + 286/27*z3 - 6*z4 + 37/81* mncxi ) + ep*ca^2 * ( 1659373/7776 - 134/9*z3*mncxi - 3/2*z3*mncxi^2 - 1184/27*z3 - 3 *z4*mncxi - 3/2*z4 - 165073/5184*mncxi + 113/8*mncxi^2 - 33/16*mncxi^3 ) + ep*nf^2 * ( 2432/243 - 56/27*z3 ) + cf*nf * ( - 55/6 + 8*z3 ) + ca*nf * ( - 2371/72 - 4*z3 + 5/27*mncxi ) + ca^2 * ( 9821/144 - 2*z3*mncxi - z3 - 6121/864*mncxi + 27/8*mncxi^2 - 9/16* mncxi^3 ) + nf^2 * ( 4 ); id ep = 0; * #break *--#] l2 : *--#[ l3 : #case l3 * * This is file inpl3. It does topologies of type L3 which are * meant to have an entire expanded gluon propagator in one loop. * It is done to avoid enormous problems with the gluon insertion * inside the two loop graph. * multiply mnce1*mncint1/ep^5/mnceq^2; id p2 = Q-p1; id Q.p1 = Q.Q/2+p1.p1/2-p2.p2/2; if ( count(p2.p2,1) >= 0 ) discard; #call one(p1,p2,Q,mnce1,mnce2,mnceq,mncint1) #call ACCU(integral 1) #call simplify repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); multiply ep^-1; id acc(mncx1?) = mncx1; .sort #call finish(1,`SCHEME') multiply,ep; *B ep; .sort multiply,ep^-1*( +ca*(5/3+mncxi/2-ep*mncxi+ep*mncxi^2/4+31/9*ep-2*ep^2*mncxi+ep^2*mncxi^2/2+188/27*ep^2 -7/6*ep^3*z3*mncxi-35/9*ep^3*z3-4*ep^3*mncxi+ep^3*mncxi^2+1132/81*ep^3) +nf*(-2/3-10/9*ep-56/27*ep^2+14/9*ep^3*z3-328/81*ep^3)); id ep = 0; multiply ep; * #break *--#] l3 : *--#[ tr : #case tr * * This is inptr. It does the tree level topology tr. * multiply 1/ep^6; id acc(mncx1?) = mncx1; id ep = 0; .sort: Expression G scheme; * * Now approximate and convert to MSbar. * #call finish(0,`SCHEME') multiply ep^3; * #break *--#] tr : #endswitch * #endprocedure *--#] integral : *--#[ intpow : #procedure intpow(TOPO) #switch `TOPO' #case la #case be #case no #case fa #case bu #case o1 #case o2 #case o3 #case o4 #case o5 #case o6 #case y1 #case y2 #case y3 #case y4 #case y5 #case y6 Multiply,i_^3; #break #case t1 #case t2 #case t3 Multiply,i_^2; #break #case l1 #case l2 #case l3 Multiply,i_; #break #endswitch #endprocedure *--#] intpow : *--#[ ladder : #procedure ladder(P1,P2,P3,P4,P5,P6,P7,P8,Q) * * Reduction procedure for three loop graphs of the LA or ladder type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<-----<-\ * P1 / | P2 | \ P3 * / | | \ * / | | \ * / | | \ * Q --<-- P7 ^ v P8 --<-- Q * \ | | / * \ | | / * \ | | / * P6 \ | P5 | / P4 * \->------>----->-/ * * We start with reducing the dotproducts in the numerator to sums * of denominators. Only one dotproduct is irreducible: P7.P8 * The easiest reduction (and quite fast) is by writing everything * in terms of Q,P1,P2,P3 and then rewriting * the few remaining dotproducts in terms of denominators. * There are variations to this principle. * * Routine coded and tested by J.A.M.Vermaseren 8-jul-1990. * modified 13-nov-1990. Variations added april 1993. * Backward reduction added 15-may-1993 * #ifdef `LATRANS' #if ( `LATRANS' == 1 ) #call ACCU2(AB `P3'.`P7' `P2'.`P7' `P7'.`P8',Ladder scalar 0) id `P3'.`P7' = `P2'.`P7'+`P7'.`P8'; #call ACCU2(AB `Q'.`P3' `P3'.`P3' `Q'.`Q' `P4'.`P4',Ladder scalar 1) id `Q'.`P3' = `P3'.`P3'/2-`P4'.`P4'/2+`Q'.`Q'/2; #call ACCU2(AB `Q'.`P2' `P2'.`P2' `Q'.`Q' `P5'.`P5',Ladder scalar 2) id `Q'.`P2' = `P2'.`P2'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `P2'.`P7' `P1'.`P1' `P2'.`P2' `P7'.`P7',Ladder scalar 3) id `P2'.`P7' = `P1'.`P1'/2-`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P3' `P3'.`P3' `P2'.`P2' `P8'.`P8',Ladder scalar 4) id `P2'.`P3' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; #call ACCU2(AB `Q'.`P7' `P1'.`P1' `P2'.`P2' `P5'.`P5' `P6'.`P6',Ladder scalar 5) id `Q'.`P7' = `P1'.`P1'/2-`P2'.`P2'/2+`P5'.`P5'/2-`P6'.`P6'/2; #call ACCU(Ladder scalar 6) #else #if ( `LATRANS' == 2 ) #call ACCU2(AB `P3'.`P7' `P1'.`P7' `P7'.`P8' `P7'.`P7',Ladder scalar 0) id `P3'.`P7' = `P1'.`P7'-`P7'.`P7'+`P7'.`P8'; #call ACCU2(AB `Q'.`P3' `P3'.`P3' `Q'.`Q' `P4'.`P4',Ladder scalar 1) id `Q'.`P3' = `P3'.`P3'/2-`P4'.`P4'/2+`Q'.`Q'/2; #call ACCU2(AB `Q'.`P1' `P1'.`P1' `Q'.`Q' `P6'.`P6',Ladder scalar 2) id `Q'.`P1' = `P1'.`P1'/2+`Q'.`Q'/2-`P6'.`P6'/2; #call ACCU2(AB `P1'.`P7' `P1'.`P1' `P2'.`P2' `P7'.`P7',Ladder scalar 3) id `P1'.`P7' = `P1'.`P1'/2-`P2'.`P2'/2+`P7'.`P7'/2; #call ACCU2(AB `Q'.`P7' `P1'.`P1' `P2'.`P2' `P5'.`P5' `P6'.`P6',Ladder scalar 4) id `Q'.`P7' = `P1'.`P1'/2-`P2'.`P2'/2+`P5'.`P5'/2-`P6'.`P6'/2; #call ACCU2(AB `P1'.`P3' `P1'.`P1' `P3'.`P3' `P7'.`P7' `P8'.`P8' `P7'.`P8',Ladder scalar 5) id `P1'.`P3' = `P1'.`P1'/2+`P3'.`P3'/2-`P7'.`P7'/2-`P8'.`P8'/2+`P7'.`P8'; #call ACCU(Ladder scalar 6) #else #if ( `LATRANS' == 3 ) if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) > count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU2(AB `Q'.`P2' `P2'.`P2' `Q'.`Q' `P5'.`P5',Ladder scalar 0) id `Q'.`P2' = `P2'.`P2'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `P2'.`P7' `P1'.`P1' `P2'.`P2' `P7'.`P7',Ladder scalar 1) id `P2'.`P7' = `P1'.`P1'/2-`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P8' `P3'.`P3' `P2'.`P2' `P8'.`P8',Ladder scalar 2) id `P2'.`P8' = `P3'.`P3'/2-`P2'.`P2'/2-`P8'.`P8'/2; #call ACCU2(AB `Q'.`P7' `P1'.`P1' `P2'.`P2' `P5'.`P5' `P6'.`P6',Ladder scalar 3) id `Q'.`P7' = `P1'.`P1'/2-`P2'.`P2'/2+`P5'.`P5'/2-`P6'.`P6'/2; #call ACCU2(AB `Q'.`P8' `P3'.`P3' `P2'.`P2' `P5'.`P5' `P4'.`P4',Ladder scalar 4) id `Q'.`P8' = `P3'.`P3'/2-`P2'.`P2'/2+`P5'.`P5'/2-`P4'.`P4'/2; #call ACCU(Ladder scalar 5) #else if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) > count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU2(AB `Q'.`P1' `P1'.`P1' `P6'.`P6' `Q'.`Q',Ladder scalar 0) id `Q'.`P1' = `P1'.`P1'/2-`P6'.`P6'/2+`Q'.`Q'/2; #call ACCU2(AB `Q'.`P3' `P3'.`P3' `P4'.`P4' `Q'.`Q',Ladder scalar 1) id `Q'.`P3' = `P3'.`P3'/2-`P4'.`P4'/2+`Q'.`Q'/2; if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) > count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU2(AB `Q'.`P2' `P2'.`P2' `Q'.`Q' `P5'.`P5',Ladder scalar 2) id `Q'.`P2' = `P2'.`P2'/2+`Q'.`Q'/2-`P5'.`P5'/2; if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) > count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P7'.`P7',Ladder scalar 3) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P3' `P3'.`P3' `P2'.`P2' `P8'.`P8',Ladder scalar 4) id `P2'.`P3' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; #call ACCU2(AB `P1'.`P3' `P1'.`P1' `P3'.`P3' `P7'.`P7' `P8'.`P8' `P7'.`P8',Ladder scalar 5) id `P1'.`P3' = `P1'.`P1'/2+`P3'.`P3'/2-`P7'.`P7'/2-`P8'.`P8'/2+`P7'.`P8'; #call ACCU(Ladder scalar 6) #endif #endif #endif #else if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) > count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU2(AB `Q'.`P1' `P1'.`P1' `P6'.`P6' `Q'.`Q',Ladder scalar 0) id `Q'.`P1' = `P1'.`P1'/2-`P6'.`P6'/2+`Q'.`Q'/2; #call ACCU2(AB `Q'.`P3' `P3'.`P3' `P4'.`P4' `Q'.`Q',Ladder scalar 1) id `Q'.`P3' = `P3'.`P3'/2-`P4'.`P4'/2+`Q'.`Q'/2; #call ACCU2(AB `Q'.`P2' `P2'.`P2' `Q'.`Q' `P5'.`P5',Ladder scalar 2) id `Q'.`P2' = `P2'.`P2'/2+`Q'.`Q'/2-`P5'.`P5'/2; #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P7'.`P7',Ladder scalar 3) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P3' `P3'.`P3' `P2'.`P2' `P8'.`P8',Ladder scalar 4) id `P2'.`P3' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; #call ACCU2(AB `P1'.`P3' `P1'.`P1' `P3'.`P3' `P7'.`P7' `P8'.`P8' `P7'.`P8',Ladder scalar 5) id `P1'.`P3' = `P1'.`P1'/2+`P3'.`P3'/2-`P7'.`P7'/2-`P8'.`P8'/2+`P7'.`P8'; #call ACCU(Ladder scalar 6) #endif if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P7',`P8',`P8',`P7',`P6',`P4',`P4',`P6'); endif; * * The rule of the triangle is applied in the procedure `triangle' * We apply it in the triangle at the right side. The above reordering * makes it the simplest triangle. * if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ); multiply acc(1/ep); #call triangle(`P8',`P4',`P3',`P5',`P2') multiply ep; else; repeat; if ( match(`P2'.`P2'/`P7'.`P7'/`P1'.`P1'^2) ); id `P7'.`P8'^mncx9?*`P2'.`P2'/`P1'.`P1'^mncx1?/`P7'.`P7'^mncx7?/`P6'.`P6'^mncx6? = `P1'.`P1'*`P7'.`P8'^mncx9/`P1'.`P1'^mncx1/`P7'.`P7'^mncx7/`P6'.`P6'^mncx6 *( +`P7'.`P7'/`P1'.`P1' +mncx6/(mncx1-1)*(`P7'.`P7'-`P5'.`P5')/`P6'.`P6' -acc(5-2*mncx7+mncx9-mncx1-mncx6-2*ep)/(mncx1-1) ); endif; if ( match(`P2'.`P2'/`P8'.`P8'/`P3'.`P3'^2) ); id `P7'.`P8'^mncx9?*`P2'.`P2'/`P3'.`P3'^mncx3?/`P8'.`P8'^mncx8?/`P4'.`P4'^mncx4? = `P3'.`P3'*`P7'.`P8'^mncx9/`P3'.`P3'^mncx3/`P8'.`P8'^mncx8/`P4'.`P4'^mncx4 *( +`P8'.`P8'/`P3'.`P3' +mncx4/(mncx3-1)*(`P8'.`P8'-`P5'.`P5')/`P4'.`P4' -acc(5-2*mncx8+mncx9-mncx3-mncx4-2*ep)/(mncx3-1) ); endif; if ( match(`P5'.`P5'/`P7'.`P7'/`P6'.`P6'^2/`P2'.`P2') ); id `P7'.`P8'^mncx9?*`P5'.`P5'/`P1'.`P1'^mncx1?/`P7'.`P7'^mncx7?/`P6'.`P6'^mncx6? = `P6'.`P6'*`P7'.`P8'^mncx9/`P1'.`P1'^mncx1/`P7'.`P7'^mncx7/`P6'.`P6'^mncx6 *( +`P7'.`P7'/`P6'.`P6' +mncx1/(mncx6-1)*(`P7'.`P7'-`P2'.`P2')/`P1'.`P1' -acc(5-2*mncx7+mncx9-mncx1-mncx6-2*ep)/(mncx6-1) ); endif; if ( match(`P5'.`P5'/`P8'.`P8'/`P4'.`P4'^2/`P2'.`P2') ); id `P7'.`P8'^mncx9?*`P5'.`P5'/`P3'.`P3'^mncx3?/`P8'.`P8'^mncx8?/`P4'.`P4'^mncx4? = `P4'.`P4'*`P7'.`P8'^mncx9/`P3'.`P3'^mncx3/`P8'.`P8'^mncx8/`P4'.`P4'^mncx4 *( +`P8'.`P8'/`P4'.`P4' +mncx3/(mncx4-1)*(`P8'.`P8'-`P2'.`P2')/`P3'.`P3' -acc(5-2*mncx8+mncx9-mncx3-mncx4-2*ep)/(mncx4-1) ); endif; endrepeat; endif; * #endprocedure *--#] ladder : *--#[ makepochs : * #procedure makepochs(nval) #do mncj = 0,`nval'-2 L mncFp`mncj' = mncpoc(`nval',`mncj'); #enddo repeat; id mncpoc(mncn?,mncj?pos_) = mncpoc(mncn,mncj-1)/mncj*mncden(mncn-mncj,-ep); id mncpoc(mncn?,0) = 1; endrepeat; #do jj = 1,1 id,once,mncden(mncx?,-ep) = mncden1(mncx,-ep); repeat id mncden1(mncx?,-ep) = 1/mncx+ep/mncx*mncden1(mncx,-ep); if ( count(mncden,1) ) redefine jj "0"; .sort #enddo Format nospaces; Format 80; .sort #do mncj = 0,`nval'-2 #write <> "Fill mncpoch(`nval',`mncj') = %e",mncFp`mncj'; Drop mncFp`mncj'; #enddo #endprocedure * *--#] makepochs : *--#[ momsubs : #procedure momsubs(TOPO) #switch `TOPO' *--#[ la : #case la * #ifdef `LATRANS' #if ( `LATRANS' == 1 ) id p5.mncq1?!{p5} = p2.mncq1-Q.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1\(1\)) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p8.mncq1?!{p8} = p3.mncq1-p2.mncq1; #call ACCU(moms2\(1\)) id p1.mncq1?!{p1} = p2.mncq1+p7.mncq1; #call ACCU2(AB P Q p7 p2 p3,moms3\(1\)) #else #if ( `LATRANS' == 2 ) id p5.mncq1?!{p5} = p6.mncq1-p7.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1\(2\)) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p8.mncq1?!{p8} = p3.mncq1-p2.mncq1; #call ACCU(moms2\(2\)) id p2.mncq1?!{p2} = p1.mncq1-p7.mncq1; #call ACCU2(AB P Q p1 p7 p3,moms3\(2\)) #else #if ( `LATRANS' == 3 ) id p5.mncq1?!{p5} = p2.mncq1-Q.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1\(3\)) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p3.mncq1?!{p3} = p2.mncq1+p8.mncq1; #call ACCU(moms2\(3\)) id p1.mncq1?!{p1} = p2.mncq1+p7.mncq1; #call ACCU2(AB P Q p7 p2 p8,moms3\(3\)) #else id p5.mncq1?!{p5} = p2.mncq1-Q.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1\(0\)) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p8.mncq1?!{p8} = p3.mncq1-p2.mncq1; #call ACCU(moms2\(0\)) id p7.mncq1?!{p7} = p1.mncq1-p2.mncq1; #call ACCU2(AB P Q p1 p2 p3,moms3\(0\)) #endif #endif #endif #else id p5.mncq1?!{p5} = p2.mncq1-Q.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p8.mncq1?!{p8} = p3.mncq1-p2.mncq1; #call ACCU(moms2) id p7.mncq1?!{p7} = p1.mncq1-p2.mncq1; #call ACCU2(AB P Q p1 p2 p3,moms3) #endif * #break *--#] la : *--#[ be : #case be * #ifndef `BEPATH' id p6.p7 = p6.p6/2+p7.p7/2-p8.p8/2; id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; id p7.p8 = p6.p6/2-p7.p7/2-p8.p8/2; * id p4.p5 = p4.p4/2+p5.p5/2-p8.p8/2; id p4.p8 = p4.p4/2+p8.p8/2-p5.p5/2; id p5.p8 = p4.p4/2-p5.p5/2-p8.p8/2; id p6.mncq1?!{p6} = p2.mncq1-p1.mncq1; id p7.mncq1?!{p7} = p2.mncq1-p3.mncq1; id p8.mncq1?!{p8} = p3.mncq1-p1.mncq1; #call ACCU(moms1) id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; id p5.mncq1?!{p5} = p1.mncq1-Q.mncq1; #call ACCU2(AB P Q p1 p2 p3,moms2) #else #if ( `BEPATH' == 0 ) id p6.p7 = p6.p6/2+p7.p7/2-p8.p8/2; id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; id p7.p8 = p6.p6/2-p7.p7/2-p8.p8/2; * id p4.p5 = p4.p4/2+p5.p5/2-p8.p8/2; id p4.p8 = p4.p4/2+p8.p8/2-p5.p5/2; id p5.p8 = p4.p4/2-p5.p5/2-p8.p8/2; id p6.mncq1?!{p6} = p2.mncq1-p1.mncq1; id p7.mncq1?!{p7} = p2.mncq1-p3.mncq1; id p8.mncq1?!{p8} = p3.mncq1-p1.mncq1; #call ACCU(moms1 \(0\)) id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; id p5.mncq1?!{p5} = p1.mncq1-Q.mncq1; #call ACCU2(AB P Q p1 p2 p3,moms2) #endif #if ( `BEPATH' == 1 ) id p4.p5 = p4.p4/2+p5.p5/2-p8.p8/2; id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; id p2.p3 = p2.p2/2+p3.p3/2-p7.p7/2; id p2.p7 = p2.p2/2+p7.p7/2-p3.p3/2; id p3.p7 = p2.p2/2-p3.p3/2-p7.p7/2; id p4.mncq1?!{p4} = p5.mncq1+p8.mncq1; id p3.mncq1?!{p3} = p1.mncq1+p8.mncq1; id p2.mncq1?!{p2} = p1.mncq1+p6.mncq1; #call ACCU(moms1 \(1\)) id p5.mncq1?!{p5} = p1.mncq1-Q.mncq1; id p7.mncq1?!{p7} = p6.mncq1-p8.mncq1; #call ACCU2(AB P Q p1 p6 p8,moms2) #endif #if ( `BEPATH' == 2 ) id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; id p4.p5 = p4.p4/2+p5.p5/2-p8.p8/2; id p4.p8 = p4.p4/2+p8.p8/2-p5.p5/2; id p5.p8 = p4.p4/2-p5.p5/2-p8.p8/2; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; id p8.mncq1?!{p8} = p6.mncq1-p7.mncq1; id p5.mncq1?!{p5} = p1.mncq1-Q.mncq1; #call ACCU(moms1 \(2\)) id p6.mncq1?!{p6} = p2.mncq1-p1.mncq1; id p3.mncq1?!{p3} = p2.mncq1-p7.mncq1; #call ACCU2(AB P Q p1 p2 p7,moms2) #endif #if ( `BEPATH' == 3 ) id p1.p5 = p1.p1/2+p5.p5/2-Q.Q/2; id p3.p7 = p2.p2/2-p3.p3/2-p7.p7/2; id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; id p3.mncq1?!{p3} = p2.mncq1-p7.mncq1; id p4.mncq1?!{p4} = p8.mncq1+p5.mncq1; id p5.mncq1?!{p5} = p1.mncq1-Q.mncq1; #call ACCU(moms1 \(3\)) id p7.mncq1?!{p7} = p6.mncq1-p8.mncq1; id p1.mncq1?!{p1} = p2.mncq1-p6.mncq1; #call ACCU2(AB P Q p2 p6 p8,moms2) #endif #if ( `BEPATH' == 4 ) id p1.p2 = p1.p1/2+p2.p2/2-p6.p6/2; id p1.p5 = p1.p1/2+p5.p5/2-Q.Q/2; id p2.p3 = p2.p2/2+p3.p3/2-p7.p7/2; id p2.p7 = p2.p2/2+p7.p7/2-p3.p3/2; id p3.p7 = p2.p2/2-p3.p3/2-p7.p7/2; id p1.mncq1?!{p1} = Q.mncq1+p5.mncq1; id p2.mncq1?!{p2} = p3.mncq1+p7.mncq1; id p7.mncq1?!{p7} = p6.mncq1-p8.mncq1; #call ACCU(moms1 \(4\)) id p3.mncq1?!{p3} = Q.mncq1+p4.mncq1; id p5.mncq1?!{p5} = p4.mncq1-p8.mncq1; #call ACCU2(AB P Q p4 p6 p8,moms2) #endif #if ( `BEPATH' == 5 ) id p2.p3 = p2.p2/2+p3.p3/2-p7.p7/2; id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; id p4.p5 = p4.p4/2+p5.p5/2-p8.p8/2; id p4.p8 = p4.p4/2+p8.p8/2-p5.p5/2; id p5.p8 = p4.p4/2-p5.p5/2-p8.p8/2; id p4.mncq1?!{p4} = -Q.mncq1+p3.mncq1; id p5.mncq1?!{p5} = -Q.mncq1+p1.mncq1; id p8.mncq1?!{p8} = p6.mncq1-p7.mncq1; #call ACCU(moms1 \(5\)) id p3.mncq1?!{p3} = p2.mncq1-p7.mncq1; id p2.mncq1?!{p2} = p1.mncq1+p6.mncq1; #call ACCU2(AB P Q p1 p6 p7,moms2) #endif #if ( `BEPATH' == 6 ) id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; id p1.p2 = p1.p1/2+p2.p2/2-p6.p6/2; id p2.p3 = p2.p2/2+p3.p3/2-p7.p7/2; id p2.p7 = p2.p2/2+p7.p7/2-p3.p3/2; id p3.p7 = p2.p2/2-p3.p3/2-p7.p7/2; id p3.mncq1?!{p3} = Q.mncq1+p4.mncq1; id p2.mncq1?!{p2} = p1.mncq1+p6.mncq1; id p7.mncq1?!{p7} = p6.mncq1-p8.mncq1; #call ACCU(moms1 \(6\)) id p1.mncq1?!{p1} = Q.mncq1+p5.mncq1; id p4.mncq1?!{p4} = p5.mncq1+p8.mncq1; #call ACCU2(AB P Q p5 p6 p8,moms2) #endif #if ( `BEPATH' == 7 ) id p1.p6 = p2.p2/2-p1.p1/2-p6.p6/2; id p3.p7 = p2.p2/2-p3.p3/2-p7.p7/2; id p6.p7 = p6.p6/2+p7.p7/2-p8.p8/2; id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; id p7.p8 = p6.p6/2-p7.p7/2-p8.p8/2; id p6.mncq1?!{p6} = p2.mncq1-p1.mncq1; id p7.mncq1?!{p7} = p2.mncq1-p3.mncq1; id p8.mncq1?!{p8} = p4.mncq1-p5.mncq1; #call ACCU(moms1 \(7\)) id p1.mncq1?!{p1} = Q.mncq1+p5.mncq1; id p3.mncq1?!{p3} = Q.mncq1+p4.mncq1; #call ACCU2(AB P Q p2 p4 p5,moms2) #endif #if ( `BEPATH' == 8 ) id p1.p5 = p1.p1/2+p5.p5/2-Q.Q/2; id p3.p4 = p3.p3/2+p4.p4/2-Q.Q/2; id p4.p5 = p4.p4/2+p5.p5/2-p8.p8/2; id p4.p8 = p4.p4/2+p8.p8/2-p5.p5/2; id p5.p8 = p4.p4/2-p5.p5/2-p8.p8/2; id p4.mncq1?!{p4} = -Q.mncq1+p3.mncq1; id p5.mncq1?!{p5} = -Q.mncq1+p1.mncq1; id p8.mncq1?!{p8} = p6.mncq1-p7.mncq1; #call ACCU(moms1 \(8\)) id p3.mncq1?!{p3} = p2.mncq1-p7.mncq1; id p1.mncq1?!{p1} = p2.mncq1-p6.mncq1; #call ACCU2(AB P Q p2 p6 p7,moms2) #endif #endif * #break *--#] be : *--#[ no : #case no * #ifndef `NOSPEC' id p5.mncq1?!{p5} = p6.mncq1-p8.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p7.mncq1?!{p7} = p2.mncq1-p1.mncq1; #call ACCU(moms2) id p8.mncq1?!{p8} = p2.mncq1-p3.mncq1; #call ACCU2(AB P Q p1 p2 p3,moms3) #else #if ( `NOSPEC' == 0 ) id p5.mncq1?!{p5} = p6.mncq1-p8.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p7.mncq1?!{p7} = p2.mncq1-p1.mncq1; #call ACCU(moms2) id p8.mncq1?!{p8} = p2.mncq1-p3.mncq1; #call ACCU2(AB P Q p1 p2 p3,moms3) #endif #if ( `NOSPEC' == 1 ) id p5.mncq1?!{p5} = p6.mncq1-p8.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p1.mncq1?!{p1} = p2.mncq1-p7.mncq1; #call ACCU(moms2) id p3.mncq1?!{p3} = p2.mncq1-p8.mncq1; #call ACCU2(AB P Q p7 p2 p8,moms3) #endif #if ( `NOSPEC' == 2 ) id p5.mncq1?!{p5} = p6.mncq1-p8.mncq1; id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; #call ACCU(moms1) id p6.mncq1?!{p6} = p1.mncq1-Q.mncq1; id p7.mncq1?!{p7} = p2.mncq1-p1.mncq1; #call ACCU(moms2) id p3.mncq1?!{p3} = p2.mncq1-p8.mncq1; #call ACCU2(AB P Q p1 p2 p8,moms3) #endif #endif * #break *--#] no : *--#[ fa : #case fa * id p6.mncq1?!{p6} = p2.mncq1-p1.mncq1; id p7.mncq1?!{p7} = p2.mncq1-p3.mncq1; id p8.mncq1?!{p8} = p3.mncq1-p1.mncq1; #call ACCU(moms1) id p4.mncq1?!{p4} = p3.mncq1-Q.mncq1; id p5.mncq1?!{p5} = p1.mncq1-Q.mncq1; #call ACCU2(AB P Q p1 p2 p3,moms2) * #break *--#] fa : *--#[ bu : #case bu * id p2.mncq1?!{p2} = p1.mncq1-p8.mncq1; id p4.mncq1?!{p4} = p1.mncq1-p6.mncq1; id p5.mncq1?!{p5} = p6.mncq1-p8.mncq1; #call ACCU(moms1) id p7.mncq1?!{p7} = p6.mncq1-Q.mncq1; id p3.mncq1?!{p3} = p8.mncq1-Q.mncq1; #call ACCU2(AB P Q p1 p6 p8,moms2) * #break *--#] bu : *--#[ o1 : #case o1 * #ifndef `O1PATH' id p7.mncq1?!{p7} = p5.mncq1-p6.mncq1; id p3.mncq1?!{p3} = p2.mncq1-Q.mncq1; #call ACCU(moms1) id p4.mncq1?!{p4} = p1.mncq1-Q.mncq1; id p5.mncq1?!{p5} = p1.mncq1-p2.mncq1; #call ACCU2(AB P Q p1 p2 p6,moms2) #else #if ( `O1PATH' == 0 ) id p7.mncq1?!{p7} = p5.mncq1-p6.mncq1; id p3.mncq1?!{p3} = p2.mncq1-Q.mncq1; #call ACCU(moms1) id p4.mncq1?!{p4} = p1.mncq1-Q.mncq1; id p5.mncq1?!{p5} = p1.mncq1-p2.mncq1; #call ACCU2(AB P Q p1 p2 p6,moms2) #endif #if ( `O1PATH' == 1 ) id p3.mncq1?!{p3} = p4.mncq1-p5.mncq1; id p2.mncq1?!{p2} = p1.mncq1-p5.mncq1; #call ACCU(moms1) id p5.mncq1?!{p5} = p6.mncq1+p7.mncq1; id p4.mncq1?!{p4} = p1.mncq1-Q.mncq1; #call ACCU2(AB P Q p1 p6 p7,moms2) #endif #if ( `O1PATH' == 2 ) id p7.mncq1?!{p7} = p5.mncq1-p6.mncq1; id p3.mncq1?!{p3} = p2.mncq1-Q.mncq1; #call ACCU(moms1) id p4.mncq1?!{p4} = p1.mncq1-Q.mncq1; id p2.mncq1?!{p2} = p1.mncq1-p5.mncq1; #call ACCU2(AB P Q p1 p5 p6,moms2) #endif #endif *#call ACCU(moms2) * #break *--#] o1 : *--#[ o2 : #case o2 * id p7.mncq1?!{p7} = p4.mncq1-p6.mncq1; id p2.mncq1?!{p2} = p3.mncq1+Q.mncq1; #call ACCU(moms1) id p1.mncq1?!{p1} = p4.mncq1+Q.mncq1; id p5.mncq1?!{p5} = p4.mncq1-p3.mncq1; #call ACCU2(AB P Q p3 p4 p6,moms2) * #break *--#] o2 : *--#[ o3 : #case o3 * id p7.mncq1?!{p7} = Q.mncq1-p6.mncq1; id p4.mncq1?!{p4} = p1.mncq1-Q.mncq1; #call ACCU(moms1) id p5.mncq1?!{p5} = p1.mncq1-p2.mncq1; id p3.mncq1?!{p3} = p2.mncq1-Q.mncq1; #call ACCU2(AB P Q p1 p2 p6,moms2) * #break *--#] o3 : *--#[ o4 : #case o4 * id p7.mncq1?!{p7} = Q.mncq1-p6.mncq1; id p5.mncq1?!{p5} = p1.mncq1-p2.mncq1; #call ACCU(moms1) id p4.mncq1?!{p4} = p1.mncq1-p6.mncq1; id p3.mncq1?!{p3} = p2.mncq1-p6.mncq1; #call ACCU2(AB P Q p1 p2 p6,moms2) * #break *--#] o4 : *--#[ y1 : #case y1 * id p4.mncq1?!{p4} = p1.mncq1-p3.mncq1; id p6.mncq1?!{p6} = p2.mncq1-p5.mncq1; id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; #call ACCU2(AB P Q p1 p3 p5,moms2) * #break *--#] y1 : *--#[ y2 : #case y2 * id p4.mncq1?!{p4} = p1.mncq1-p3.mncq1; id p6.mncq1?!{p6} = p1.mncq1-p5.mncq1; id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; #call ACCU2(AB P Q p1 p3 p5,moms2) * #break *--#] y2 : *--#[ y3 : #case y3 * id p4.mncq1?!{p4} = p1.mncq1-p3.mncq1; id p6.mncq1?!{p6} = p3.mncq1-p5.mncq1; id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; #call ACCU2(AB P Q p1 p3 p5,moms2) * #break *--#] y3 : *--#[ y4 : #case y4 * id p4.mncq1?!{p4} = p1.mncq1-p3.mncq1; id p6.mncq1?!{p6} = Q.mncq1-p5.mncq1; id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; #call ACCU2(AB P Q p1 p3 p5,moms2) * #break *--#] y4 : *--#[ y5 : #case y5 * id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; id p4.mncq1?!{p4} = Q.mncq1-p3.mncq1; id p6.mncq1?!{p6} = Q.mncq1-p5.mncq1; #call ACCU2(AB P Q p1 p3 p5,moms2) * #break *--#] y5 : *--#[ t1 : #case t1 * id p4.mncq1?!{p4} = p1.mncq1-Q.mncq1; #call ACCU(moms1) id p3.mncq1?!{p3} = p2.mncq1-Q.mncq1; #call ACCU(moms2) id p5.mncq1?!{p5} = p1.mncq1-p2.mncq1; #call ACCU2(AB P Q p1 p2,moms3) * #break *--#] t1 : *--#[ t2 : #case t2 * id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; #call ACCU(moms1) id p4.mncq1?!{p4} = p1.mncq1-p3.mncq1; #call ACCU2(AB P Q p1 p3,moms2) * #break *--#] t2 : *--#[ t3 : #case t3 * id p2.mncq1?!{p2} = Q.mncq1-p1.mncq1; #call ACCU{moms1} id p4.mncq1?!{p4} = Q.mncq1-p3.mncq1; #call ACCU2(AB P Q p1 p3,moms2) * #break *--#] t3 : *--#[ l1 : #case l1 * * #break *--#] l1 : *--#[ l2 : #case l2 * * #break *--#] l2 : *--#[ l3 : #case l3 * * #break *--#] l3 : *--#[ tr : #case tr * * #break *--#] tr : #default #message Unknown case `TOPO' in momsubs.prc #break #endswitch #endprocedure *--#] momsubs : *--#[ newplane : #procedure newplane(P1,P2,P3,P4,P5,P6,P7,P8,Q,INTS) * * Reduction procedure for three loop graphs of the NO or nonplanar type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * For the first part we use the algorithms from Chetyrkin & Tkachov * (Nuclear physics B192(1981)159. * To reduce powers in the numerator. These algorithms work faster. * * /-<------<-----<-\ * P1 / \ P2 / \ P3 * / v / \ * / P7 \ / \ * / \ / \ * Q --<-- / --<-- Q * \ / \ / * \ P8 / \ / * \ ^ \ / * P6 \ / P5 \ / P4 * \->------>----->-/ * * Express everything in powers of pi.pi, Q.Q and Q.p2 or p2.p5; * We need p2.p5 only when there are enough denominators. * The only difficult relation here is the one for p7.p8 * * Note that the system here is optimized for the big and difficult * expressions. * Note also that the final stages can be improved. * At the moment the goto statements are not so good * #ifndef `NOSPEC' if ( count(`P7'.`P7',1) < count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU2(AB `P1'.`Q' `P1'.`P1' `Q'.`Q' `P6'.`P6',dots 0) id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P6'.`P6'/2; #call ACCU2(AB `P3'.`Q' `P3'.`P3' `Q'.`Q' `P4'.`P4',dots 1) id `P3'.`Q' = `P3'.`P3'/2+`Q'.`Q'/2-`P4'.`P4'/2; #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P7'.`P7',dots 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P3' `P3'.`P3' `P2'.`P2' `P8'.`P8',dots 3) id `P3'.`P2' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; if ( count(`P7'.`P7',1) < count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU(dots 4) id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; * repeat id `P1'.`P3'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' * /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = * (`P2'.`P5'+`P2'.`P2'/2+`P5'.`P5'/2+`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2) * /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' * /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'; #call ACCU(dots 5) repeat id `Q'.`P2'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = (`P1'.`P1'/2+`P3'.`P3'/2-`P7'.`P7'/2-`P8'.`P8'/2-`P2'.`P5') /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'; #call ACCU(dots 6) * if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' * /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') == 0 ); * id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 * +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; * endif; *#call ACCU(dots 7) #else #if ( `NOSPEC' == 0 ) if ( count(`P7'.`P7',1) < count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU2(AB `P1'.`Q' `P1'.`P1' `Q'.`Q' `P6'.`P6',dots 0) id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P6'.`P6'/2; #call ACCU2(AB `P3'.`Q' `P3'.`P3' `Q'.`Q' `P4'.`P4',dots 1) id `P3'.`Q' = `P3'.`P3'/2+`Q'.`Q'/2-`P4'.`P4'/2; #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P7'.`P7',dots 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P3' `P3'.`P3' `P2'.`P2' `P8'.`P8',dots 3) id `P3'.`P2' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; if ( count(`P7'.`P7',1) < count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; #call ACCU(dots 4) id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; * repeat id `P1'.`P3'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' * /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = * (`P2'.`P5'+`P2'.`P2'/2+`P5'.`P5'/2+`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2) * /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' * /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'; #call ACCU(dots 5) repeat id `Q'.`P2'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = (`P1'.`P1'/2+`P3'.`P3'/2-`P7'.`P7'/2-`P8'.`P8'/2-`P2'.`P5') /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'; #call ACCU(dots 6) * if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' * /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') == 0 ); * id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 * +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; * endif; *#call ACCU(dots 7) #endif #if ( `NOSPEC' == 1 ) id `P2'.`P7' = `P2'.`P2'/2+`P7'.`P7'/2-`P1'.`P1'/2; #call ACCU2(AB `P2'.`P8' `P3'.`P3' `P2'.`P2' `P8'.`P8',dots 0) id `P2'.`P8' = -`P3'.`P3'/2+`P2'.`P2'/2+`P8'.`P8'/2; #call ACCU2(AB `P7'.`P8' `P7'.`P7' `P8'.`P8' `P1'.`P1' `P3'.`P3' `P1'.`P3',dots 1) id `P7'.`P8' = `P7'.`P7'/2+`P8'.`P8'/2-`P1'.`P1'/2-`P3'.`P3'/2+`P1'.`P3'; #call ACCU2(AB `P7'.`Q' `Q'.`P2' `P1'.`P1' `Q'.`Q' `P6'.`P6',dots 2) id `P7'.`Q' = `Q'.`P2'-`P1'.`P1'/2-`Q'.`Q'/2+`P6'.`P6'/2; #call ACCU2(AB `P8'.`Q' `P3'.`P3' `Q'.`Q' `P4'.`P4' `Q'.`P2',dots 3) id `P8'.`Q' = `Q'.`P2'-`P3'.`P3'/2-`Q'.`Q'/2+`P4'.`P4'/2; #call ACCU2(AB `P1'.`P3' `P2'.`P5' `P2'.`P2' `P5'.`P5' `Q'.`Q' `P4'.`P4' `P6'.`P6',dots 4) repeat id `P1'.`P3'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = (`P2'.`P5'+`P2'.`P2'/2+`P5'.`P5'/2+`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2) /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'; #call ACCU2(AB `Q'.`P2' `P1'.`P1' `P3'.`P3' `P7'.`P7' `P8'.`P8' `P2'.`P5',dots 5) #do ii6 = 1,1 id `Q'.`P2'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = (`P1'.`P1'/2+`P3'.`P3'/2-`P7'.`P7'/2-`P8'.`P8'/2-`P2'.`P5') /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'; if ( match(`Q'.`P2'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') ) redefine ii6 "0"; #call ACCU2(AB `Q'.`P2' `P1'.`P1' `P3'.`P3' `P7'.`P7' `P8'.`P8' `P2'.`P5',dots 6) #enddo if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') == 0 ); id,once,`P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; endif; #call ACCU(dots 7) if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') == 0 ); id,`P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; endif; #call ACCU(dots 8) #endif #if ( `NOSPEC' == 2 ) #call ACCU2(AB `P1'.`Q' `P1'.`P1' `Q'.`Q' `P6'.`P6',dots 0) id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P6'.`P6'/2; #call ACCU2(AB `P8'.`Q' `P2'.`Q' `P3'.`P3' `Q'.`Q' `P4'.`P4',dots 1) id `P8'.`Q' = `P2'.`Q'-`P3'.`P3'/2-`Q'.`Q'/2+`P4'.`P4'/2; #call ACCU2(AB `P1'.`P2' `P1'.`P1' `P2'.`P2' `P7'.`P7',dots 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU2(AB `P2'.`P8' `P3'.`P3' `P2'.`P2' `P8'.`P8',dots 3) id `P2'.`P8' = `P8'.`P8'/2+`P2'.`P2'/2-`P3'.`P3'/2; #call ACCU2(AB `P1'.`P8' `P2'.`Q' `P3'.`P3' `P5'.`P5' `Q'.`Q' `P4'.`P4' `P6'.`P6' `P8'.`P8',dots 4) id `P1'.`P8' = +`P2'.`Q'-`P3'.`P3'/2-`P5'.`P5'/2 -`Q'.`Q'/2+`P4'.`P4'/2+`P6'.`P6'/2+`P8'.`P8'/2; #call ACCU(dots 5) repeat id `Q'.`P2'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = (`P1'.`P1'/2+`P3'.`P3'/2-`P7'.`P7'/2-`P8'.`P8'/2-`P2'.`P5') /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'; #call ACCU(dots 6) * if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' * /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') == 0 ); * id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 * +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; * endif; *#call ACCU(dots 7) #endif #endif if ( count(`P7'.`P7',1) < count(`P8'.`P8',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P7'.`P7',1) == count(`P8'.`P8',1) ); if ( count(`P1'.`P1',1) < count(`P3'.`P3',1) ); multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); elseif ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ); if ( count(`P6'.`P6',1) < count(`P4'.`P4',1) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4' ,`P7',`P8',`P8',`P7'); endif; endif; * * Now we start a set of iterations to make either * 1: the power of `P2'.`P5' equal to zero * 2: the power of `P2'.`P2',`P5'.`P5',`P7'.`P7',`P8'.`P8' >= 0 * 3: the power of `P1'.`P1',`P3'.`P3',`P4'.`P4',`P6'.`P6' >= -1 * repeat; if ( match(`P2'.`P5'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5' /`P6'.`P6'/`P7'.`P7'/`P8'.`P8') ); if ( count(`P6'.`P6',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4? /`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6?/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3/`P4'.`P4'^mncx4 /`P5'.`P5'^mncx5/`P6'.`P6'^mncx6/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx6-1)*(`P3'.`P3'-`P2'.`P2'-`P8'.`P8') +acc(3-2*ep+mncx9-mncx1-mncx8-2*mncx2)*`P6'.`P6' +mncx1*`P6'.`P6'/`P1'.`P1'*(`P7'.`P7'-`P2'.`P2') +mncx8*`P6'.`P6'/`P8'.`P8'*(`P3'.`P3'-`P2'.`P2') )/(mncx6-1)/2/`P2'.`P5'; elseif ( count(`P1'.`P1',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4? /`P5'.`P5'^mncx5?/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3/`P4'.`P4'^mncx4 /`P5'.`P5'^mncx5/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx1-1)*(`P4'.`P4'-`P5'.`P5'-`P7'.`P7') +acc(2-2*ep+mncx9-mncx7-2*mncx5)*`P1'.`P1' +`P1'.`P1'/`P6'.`P6'*(`P8'.`P8'-`P5'.`P5') +mncx7*`P1'.`P1'/`P7'.`P7'*(`P4'.`P4'-`P5'.`P5') )/(mncx1-1)/2/`P2'.`P5'; elseif ( count(`P4'.`P4',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4? /`P5'.`P5'^mncx5?/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3/`P4'.`P4'^mncx4 /`P5'.`P5'^mncx5/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx4-1)*(`P1'.`P1'-`P2'.`P2'-`P7'.`P7') +acc(3-2*ep+mncx9-mncx3-mncx7-2*mncx2)*`P4'.`P4' +mncx3*`P4'.`P4'/`P3'.`P3'*(`P8'.`P8'-`P2'.`P2') +mncx7*`P4'.`P4'/`P7'.`P7'*(`P1'.`P1'-`P2'.`P2') )/(mncx4-1)/2/`P2'.`P5'; elseif ( count(`P3'.`P3',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?/`P4'.`P4' /`P5'.`P5'^mncx5?/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3/`P4'.`P4' /`P5'.`P5'^mncx5/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx3-1)*(`P6'.`P6'-`P5'.`P5'-`P8'.`P8') +acc(2-2*ep+mncx9-mncx8-2*mncx5)*`P3'.`P3' +`P3'.`P3'/`P4'.`P4'*(`P7'.`P7'-`P5'.`P5') +mncx8*`P3'.`P3'/`P8'.`P8'*(`P6'.`P6'-`P5'.`P5') )/(mncx3-1)/2/`P2'.`P5'; endif; endif; endrepeat; #call ACCU(nonplanar pass 1) * * The next set of iterations has two phases. * The first phase stops when either * 1: the power of `P2'.`P5' equal to zero * 2: the power of `P1'.`P1',`P3'.`P3',`P4'.`P4',`P6'.`P6',`P7'.`P7',`P8'.`P8' >= 0 * 3: the power of `P2'.`P2',`P5'.`P5' >= -1 * The second phase stops when * 1: the power of `P2'.`P5' equal to zero * 2: the power of all others is >= -1 * #ifdef `LONGINT' #do i = 1,`LONGINT' if ( match(`P2'.`P5'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5' /`P6'.`P6'/`P7'.`P7'/`P8'.`P8') ); if ( count(`P5'.`P5',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^mncx5?/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'^mncx2/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^mncx5/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(2*mncx2+mncx7+mncx8-mncx9-3+2*ep) +acc(mncx9-1)*`P2'.`P2'/`P2'.`P5' +mncx7*(`P2'.`P2'-`P1'.`P1')/`P7'.`P7' +mncx8*(`P2'.`P2'-`P3'.`P3')/`P8'.`P8' )/(mncx5-1)/2/`P2'.`P5'*`P5'.`P5'; elseif ( count(`P2'.`P2',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'^mncx2/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx7+mncx8-mncx9-1+2*ep) +acc(mncx9-1)*`P5'.`P5'/`P2'.`P5' +mncx7*(`P5'.`P5'-`P4'.`P4')/`P7'.`P7' +mncx8*(`P5'.`P5'-`P6'.`P6')/`P8'.`P8' )/(mncx2-1)/2/`P2'.`P5'*`P2'.`P2'; elseif ( count(`P8'.`P8',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx8-1)*(2*`P1'.`P1'+2*`P3'.`P3'-2*`P2'.`P2'-`P7'.`P7'-`Q'.`Q') +acc(mncx9-1)*`P8'.`P8'*(`P1'.`P1'-`P2'.`P2'-`P7'.`P7')/`P2'.`P5' +acc(3-2*ep-2*mncx7-mncx8)*`P8'.`P8' +2*`P8'.`P8'/`P2'.`P2'*(`P1'.`P1'-`P7'.`P7') )/(mncx8-1)/2/`P2'.`P5'; elseif ( count(`P7'.`P7',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8' = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8' * ( +acc(mncx7-1)*(2*`P6'.`P6'+2*`P4'.`P4'-2*`P5'.`P5'-`P8'.`P8'-`Q'.`Q') +acc(mncx9-1)*`P7'.`P7'*(`P6'.`P6'-`P5'.`P5'-`P8'.`P8')/`P2'.`P5' +acc(1-2*ep-mncx7)*`P7'.`P7' +2*`P7'.`P7'/`P5'.`P5'*(`P6'.`P6'-`P8'.`P8') )/(mncx7-1)/2/`P2'.`P5'; endif; * id acc(0) = 0; endif; #call ACCU(nonplanar pass 2\,`i') #enddo #endif repeat; if ( match(`P2'.`P5'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5' /`P6'.`P6'/`P7'.`P7'/`P8'.`P8') ); if ( count(`P5'.`P5',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^mncx5?/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'^mncx2/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^mncx5/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(2*mncx2+mncx7+mncx8-mncx9-3+2*ep) +acc(mncx9-1)*`P2'.`P2'/`P2'.`P5' +mncx7*(`P2'.`P2'-`P1'.`P1')/`P7'.`P7' +mncx8*(`P2'.`P2'-`P3'.`P3')/`P8'.`P8' )/(mncx5-1)/2/`P2'.`P5'*`P5'.`P5'; elseif ( count(`P2'.`P2',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'^mncx2/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx7+mncx8-mncx9-1+2*ep) +acc(mncx9-1)*`P5'.`P5'/`P2'.`P5' +mncx7*(`P5'.`P5'-`P4'.`P4')/`P7'.`P7' +mncx8*(`P5'.`P5'-`P6'.`P6')/`P8'.`P8' )/(mncx2-1)/2/`P2'.`P5'*`P2'.`P2'; elseif ( count(`P8'.`P8',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8 * ( +acc(mncx8-1)*(2*`P1'.`P1'+2*`P3'.`P3'-2*`P2'.`P2'-`P7'.`P7'-`Q'.`Q') +acc(mncx9-1)*`P8'.`P8'*(`P1'.`P1'-`P2'.`P2'-`P7'.`P7')/`P2'.`P5' +acc(3-2*ep-2*mncx7-mncx8)*`P8'.`P8' +2*`P8'.`P8'/`P2'.`P2'*(`P1'.`P1'-`P7'.`P7') )/(mncx8-1)/2/`P2'.`P5'; elseif ( count(`P7'.`P7',1) < -1 ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8' = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^mncx7/`P8'.`P8' * ( +acc(mncx7-1)*(2*`P6'.`P6'+2*`P4'.`P4'-2*`P5'.`P5'-`P8'.`P8'-`Q'.`Q') +acc(mncx9-1)*`P7'.`P7'*(`P6'.`P6'-`P5'.`P5'-`P8'.`P8')/`P2'.`P5' +acc(1-2*ep-mncx7)*`P7'.`P7' +2*`P7'.`P7'/`P5'.`P5'*(`P6'.`P6'-`P8'.`P8') )/(mncx7-1)/2/`P2'.`P5'; endif; * id acc(0) = 0; endif; endrepeat; #call ACCU(nonplanar pass 2) * * Note: equation 6.14 is wrong!!! 6.13 is confusing. Use d/dk instead * multiply acc(1/ep); while ( match(`P2'.`P5'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5' /`P6'.`P6'/`P7'.`P7'/`P8'.`P8') ); id `P2'.`P5'^mncx9?/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' = `P2'.`P5'^mncx9/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' * ( +2*`P3'.`P3'-2*`P8'.`P8' +acc(1+2*ep-mncx9)*mncdeno(mncx9-1,-4)*`Q'.`Q' +2*`Q'.`Q'*mncdeno(mncx9-1,-4)*(`P2'.`P2'-`P8'.`P8')/`P3'.`P3' )/2/`P2'.`P5'; * id acc(0) = 0; * id acc(2*ep)*mncdeno(0,-4) = -1/2; id 1/`P2'.`P5' = 0; id mncdeno(0,-4) = acc(-1/4/ep); id mncdeno(mncx1?,-4)=acc(1+4/mncx1*ep+16/mncx1^2*ep^2+64/mncx1^3*ep^3 +256/mncx1^4*ep^4+1024/mncx1^5*ep^5+4096/mncx1^6*ep^6)/mncx1; endwhile; multiply ep; #call ACCU(nonplanar pass 3) * * Next are four recursions that reduce the powers of the propagators * that connect to `Q' to 1. * #ifdef `LONGINT' label 6; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'^2/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx1+2*mncx2+mncx5+mncx6+2*mncx7+mncx8-9+4*ep)*`P6'.`P6' +acc(mncx6-1)*`P1'.`P1' +mncx8*`P2'.`P2'*`P6'.`P6'/`P8'.`P8' -mncx8*`P3'.`P3'*`P6'.`P6'/`P8'.`P8' +mncx5*`P6'.`P6'*`P7'.`P7'/`P5'.`P5' -mncx5*`P4'.`P4'*`P6'.`P6'/`P5'.`P5' )/(mncx6-1); label 1; while ( match(1/`P1'.`P1'^2/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx6+2*mncx5+mncx2+mncx1+2*mncx8+mncx7-9+4*ep)*`P1'.`P1' +acc(mncx1-1)*`P6'.`P6' +mncx7*`P5'.`P5'*`P1'.`P1'/`P7'.`P7' -mncx7*`P4'.`P4'*`P1'.`P1'/`P7'.`P7' +mncx2*`P1'.`P1'*`P8'.`P8'/`P2'.`P2' -mncx2*`P3'.`P3'*`P1'.`P1'/`P2'.`P2' )/(mncx1-1); label 3; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'^2/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx4+2*mncx5+mncx2+mncx3+2*mncx7+mncx8-9+4*ep)*`P3'.`P3' +acc(mncx3-1)*`P4'.`P4' +mncx8*`P5'.`P5'*`P3'.`P3'/`P8'.`P8' -mncx8*`P6'.`P6'*`P3'.`P3'/`P8'.`P8' +mncx2*`P3'.`P3'*`P7'.`P7'/`P2'.`P2' -mncx2*`P1'.`P1'*`P3'.`P3'/`P2'.`P2' )/(mncx3-1); label 4; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'^2 /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx3+2*mncx2+mncx5+mncx4+2*mncx8+mncx7-9+4*ep)*`P4'.`P4' +acc(mncx4-1)*`P3'.`P3' +mncx7*`P2'.`P2'*`P4'.`P4'/`P7'.`P7' -mncx7*`P1'.`P1'*`P4'.`P4'/`P7'.`P7' +mncx5*`P4'.`P4'*`P8'.`P8'/`P5'.`P5' -mncx5*`P6'.`P6'*`P4'.`P4'/`P5'.`P5' )/(mncx4-1); id mncdeno(0,mncx1?) = 1/mncx1/ep; id mncdeno(mncx1?,mncx2?) = mncaccm(1+ep*mncx2/mncx1)/mncx1; repeat id mncaccm(mncx1?)*mncaccm(mncx2?) = mncaccm(mncx1*mncx2); id mncaccm(mncx1?) = mncaccm(mncx1-1); id mncaccm(mncx1?) = mncaccm(mncx1-mncx1^2,mncx1^3); id mncaccm(mncx1?,mncx2?) = acc(1-mncx1-mncx2+mncx2*mncx1+mncx2^2); #call ACCU(Preparation) #endif label 6; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'^2/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx1+2*mncx2+mncx5+mncx6+2*mncx7+mncx8-9+4*ep)*`P6'.`P6' +acc(mncx6-1)*`P1'.`P1' +mncx8*`P2'.`P2'*`P6'.`P6'/`P8'.`P8' -mncx8*`P3'.`P3'*`P6'.`P6'/`P8'.`P8' +mncx5*`P6'.`P6'*`P7'.`P7'/`P5'.`P5' -mncx5*`P4'.`P4'*`P6'.`P6'/`P5'.`P5' )/(mncx6-1); label 1; while ( match(1/`P1'.`P1'^2/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx6+2*mncx5+mncx2+mncx1+2*mncx8+mncx7-9+4*ep)*`P1'.`P1' +acc(mncx1-1)*`P6'.`P6' +mncx7*`P5'.`P5'*`P1'.`P1'/`P7'.`P7' -mncx7*`P4'.`P4'*`P1'.`P1'/`P7'.`P7' +mncx2*`P1'.`P1'*`P8'.`P8'/`P2'.`P2' -mncx2*`P3'.`P3'*`P1'.`P1'/`P2'.`P2' )/(mncx1-1); label 3; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'^2/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx4+2*mncx5+mncx2+mncx3+2*mncx7+mncx8-9+4*ep)*`P3'.`P3' +acc(mncx3-1)*`P4'.`P4' +mncx8*`P5'.`P5'*`P3'.`P3'/`P8'.`P8' -mncx8*`P6'.`P6'*`P3'.`P3'/`P8'.`P8' +mncx2*`P3'.`P3'*`P7'.`P7'/`P2'.`P2' -mncx2*`P1'.`P1'*`P3'.`P3'/`P2'.`P2' )/(mncx3-1); label 4; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'^2 /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx3+2*mncx2+mncx5+mncx4+2*mncx8+mncx7-9+4*ep)*`P4'.`P4' +acc(mncx4-1)*`P3'.`P3' +mncx7*`P2'.`P2'*`P4'.`P4'/`P7'.`P7' -mncx7*`P1'.`P1'*`P4'.`P4'/`P7'.`P7' +mncx5*`P4'.`P4'*`P8'.`P8'/`P5'.`P5' -mncx5*`P6'.`P6'*`P4'.`P4'/`P5'.`P5' )/(mncx4-1); * * Now we have that in the 'active terms' the powers of `P1'.`P1', `P3'.`P3', * `P4'.`P4' and `P6'.`P6' is 1 and the power of `Q'.`P2' is zero. * The final recursion is for lines that don't touch the outside. * * Remark: it seems better to combine this recursion more directly * with the above recursions.This can give: * 1: 5 a: mncx7=mncx8=1 b: mncx7>1,mncx8=1 c: mncx7=1,mncx8>1 d: mncx7>1,mncx8>1 * 2: 2 mncx5=1 ( a: mncx7=mncx8=1 b: mncx7>1,mncx8=1 c: mncx7=1,mncx8>1 d: mncx7>1,mncx8>1 ) * 3: 8 mncx2=mncx5=1 * 4: 7 mncx2=mncx5=mncx8=1 * if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) > `INNOTABL' ); while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^2/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx1+2*mncx2+2*mncx3+mncx4+2*mncx5+mncx6+2*mncx7+2*mncx8-14+6*ep) +mncx4*`P3'.`P3'/`P4'.`P4'+mncx6*`P1'.`P1'/`P6'.`P6' )*`P5'.`P5'/`Q'.`Q' +acc(mncx5-1)*mncx4*`P7'.`P7'/`P4'.`P4' +acc(mncx5-1)*mncx6*`P8'.`P8'/`P6'.`P6' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx5+mncx6+mncx7+mncx8-9+4*ep)*mncx4*`P5'.`P5'/`P4'.`P4' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx5+mncx6+mncx7+mncx8-9+4*ep)*mncx6*`P5'.`P5'/`P6'.`P6' )/(mncx5-1)*mncdeno(mncx4+mncx6+2*mncx5-4,2); if ( count(`P4'.`P4',1) < -1 ) goto 4; if ( count(`P6'.`P6',1) < -1 ) goto 6; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; while ( match(1/`P1'.`P1'/`P2'.`P2'^2/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx6+2*mncx2+2*mncx4+mncx3+2*mncx5+mncx1+2*mncx7+2*mncx8-14+6*ep) +mncx3*`P4'.`P4'/`P3'.`P3'+mncx1*`P6'.`P6'/`P1'.`P1' )*`P2'.`P2'/`Q'.`Q' +acc(mncx2-1)*mncx3*`P8'.`P8'/`P3'.`P3' +acc(mncx2-1)*mncx1*`P7'.`P7'/`P1'.`P1' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx2+mncx6+mncx7+mncx8-9+4*ep)*mncx3*`P2'.`P2'/`P3'.`P3' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx2+mncx6+mncx7+mncx8-9+4*ep)*mncx1*`P2'.`P2'/`P1'.`P1' )/(mncx2-1)*mncdeno(mncx3+mncx1+2*mncx2-4,2); if ( count(`P3'.`P3',1) < -1 ) goto 3; if ( count(`P1'.`P1',1) < -1 ) goto 1; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'^2) > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx1+2*mncx2+2*mncx4+mncx3+2*mncx5+mncx6+2*mncx7+2*mncx8-14+6*ep) +mncx3*`P4'.`P4'/`P3'.`P3'+mncx6*`P1'.`P1'/`P6'.`P6' )*`P8'.`P8'/`Q'.`Q' +acc(mncx8-1)*mncx3*`P2'.`P2'/`P3'.`P3' +acc(mncx8-1)*mncx6*`P5'.`P5'/`P6'.`P6' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx8+mncx6+mncx7+mncx5-9+4*ep)*mncx3*`P8'.`P8'/`P3'.`P3' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx8+mncx6+mncx7+mncx5-9+4*ep)*mncx6*`P8'.`P8'/`P6'.`P6' )/(mncx8-1)*mncdeno(mncx3+mncx6+2*mncx8-4,2); if ( count(`P3'.`P3',1) < -1 ) goto 3; if ( count(`P6'.`P6',1) < -1 ) goto 6; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^2/`P8'.`P8') > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx6+2*mncx2+2*mncx3+mncx4+2*mncx5+mncx1+2*mncx7+2*mncx8-14+6*ep) +mncx4*`P3'.`P3'/`P4'.`P4'+mncx1*`P6'.`P6'/`P1'.`P1' )*`P7'.`P7'/`Q'.`Q' +acc(mncx7-1)*mncx4*`P5'.`P5'/`P4'.`P4' +acc(mncx7-1)*mncx1*`P2'.`P2'/`P1'.`P1' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx7+mncx6+mncx2+mncx8-9+4*ep)*mncx4*`P7'.`P7'/`P4'.`P4' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx7+mncx6+mncx2+mncx8-9+4*ep)*mncx1*`P7'.`P7'/`P1'.`P1' )/(mncx7-1)*mncdeno(mncx4+mncx1+2*mncx7-4,2); if ( count(`P4'.`P4',1) < -1 ) goto 4; if ( count(`P1'.`P1',1) < -1 ) goto 1; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; endif; label 9; * * Here we take those integrals that have been tabulated * if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') ); if ( count(`P2'.`P2',1) > count(`P5'.`P5',1) ) multiply replace_(`P2',`P5',`P5',`P2'); if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ) multiply replace_(`P7',`P8',`P8',`P7'); if ( ( count(`P2'.`P2',1) > count(`P7'.`P7',1) ) || ( ( count(`P2'.`P2',1) == count(`P7'.`P7',1) ) && ( count(`P8'.`P8',1) > count(`P5'.`P5',1) ) ) ) multiply replace_(`P2',`P7',`P7',`P2',`P8',`P5',`P5',`P8'); if ( ( count(`P2'.`P2',1) > count(`P8'.`P8',1) ) || ( ( count(`P2'.`P2',1) == count(`P8'.`P8',1) ) && ( count(`P7'.`P7',1) > count(`P5'.`P5',1) ) ) ) multiply replace_(`P2',`P8',`P8',`P2',`P7',`P5',`P5',`P7'); if ( count(`P2'.`P2',1) > count(`P5'.`P5',1) ) multiply replace_(`P2',`P5',`P5',`P2'); if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ) multiply replace_(`P7',`P8',`P8',`P7'); id `INTS'/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^mncx5?/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = mncnoptab(mncx2,mncx7,mncx8,mncx5)*mnceq^3/`Q'.`Q'^(mncx2+mncx5+mncx7+mncx8-2); endif; * * The value will only be substituted when the routine subint is * invoked. This way we can keep an eye on the accuracy of the calculation. * id mncdeno(0,mncx1?) = 1/mncx1/ep; id mncdeno(mncx1?,mncx2?) = mncaccm(1+ep*mncx2/mncx1)/mncx1; repeat id mncaccm(mncx1?)*mncaccm(mncx2?) = mncaccm(mncx1*mncx2); id mncaccm(mncx1?) = mncaccm(mncx1-1); id mncaccm(mncx1?) = mncaccm(mncx1-mncx1^2,mncx1^3); id mncaccm(mncx1?,mncx2?) = acc(1-mncx1-mncx2+mncx2*mncx1+mncx2^2); * #endprocedure *--#] newplane : *--#[ newtwo : #procedure newtwo(P1,E1,P2,E2,P3,E3,P4,E4,P5,E5,Q,EQ,REDUCTION,INTS) * * Newer way to do two loop integrals. * The case with the ep power on the outside can be done * with the resolved triangle and the part with the ep on the * inside and all other powers one is done with a table. * This leaves only one type of explicit recursion. We deal * with them by making powers equal to 1 as quickly as possible * so that in the next recursion they may get killed. It isn't * clear whether this is the best strategy. * #if ( `REDUCTION' > 0 ) id `P4'.mncp?!{`P4'} = `P1'.mncp-`Q'.mncp; id `P3'.mncp?!{`P3'} = `P2'.mncp-`Q'.mncp; id `P5'.mncp?!{`P5'} = `P1'.mncp-`P2'.mncp; #call ACCU(Two loop momenta) id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P4'.`P4'/2; id `P2'.`Q' = `P2'.`P2'/2+`Q'.`Q'/2-`P3'.`P3'/2; id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P5'.`P5'/2; #call ACCU(Two loop scalars) #endif if ( count(`E5',1) == 1 ); repeat; if ( match(`E5'/`P1'.`P1'^2/`P4'.`P4'^2/`P2'.`P2'/`P3'.`P3') ); id 1/`P1'.`P1'^mncx1?/`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?*`E5' = 1/`P1'.`P1'^mncx1/`P4'.`P4'^mncx4/`P5'.`P5'^mncx5*`E5' * ( +acc(ep+mncx5)*acc(1-2*ep-mncx5)/(mncx1-1)/(mncx4-1)* `P1'.`P1'*`P4'.`P4'/`P5'.`P5'/`Q'.`Q' +acc(mncx1+mncx4-3+ep)/(mncx1-1)*`P1'.`P1'/`Q'.`Q' +acc(mncx1+mncx4-3+ep)/(mncx4-1)*`P4'.`P4'/`Q'.`Q' ); endif; endrepeat; repeat; if ( match(`E5'/`P1'.`P1'/`P4'.`P4'/`P2'.`P2'^2/`P3'.`P3'^2) ); id 1/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?/`P5'.`P5'^mncx5?*`E5' = 1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3/`P5'.`P5'^mncx5*`E5' * ( +acc(ep+mncx5)*acc(1-2*ep-mncx5)/(mncx2-1)/(mncx3-1)* `P2'.`P2'*`P3'.`P3'/`P5'.`P5'/`Q'.`Q' +acc(mncx2+mncx3-3+ep)/(mncx2-1)*`P2'.`P2'/`Q'.`Q' +acc(mncx2+mncx3-3+ep)/(mncx3-1)*`P3'.`P3'/`Q'.`Q' ); endif; endrepeat; endif; #call ACCU(Reduction 2 loops) if ( count(`E5',1) == 0 ); if ( count(`E2',1,`E3',1) == 0 ); if ( ( match(1/`P2'.`P2'/`P3'.`P3'/`P5'.`P5') > 0 ) && ( ( count(`E1',1) > 0 ) || ( count(`P1'.`P1',1) < 0 ) ) && ( ( count(`E4',1) > 0 ) || ( count(`P4'.`P4',1) < 0 ) ) ); #call triangl2(`P5',`P1',`P4',`P2',`P3',`E1',`E4') endif; else; if ( ( match(1/`P1'.`P1'/`P4'.`P4'/`P5'.`P5') > 0 ) && ( ( count(`E2',1) > 0 ) || ( count(`P2'.`P2',1) < 0 ) ) && ( ( count(`E3',1) > 0 ) || ( count(`P3'.`P3',1) < 0 ) ) ); #call triangl2(`P5',`P2',`P3',`P1',`P4',`E2',`E3') endif; endif; else; repeat; if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4') > 0 ); if ( count(`P1'.`P1',1) < count(`P4'.`P4',1) ); multiply replace_(`P1',`P4',`P4',`P1',`P2',`P3',`P3',`P2'); endif; if ( count(`P3'.`P3',1) < count(`P4'.`P4',1) ); multiply replace_(`P3',`P4',`P4',`P3',`P2',`P1',`P1',`P2'); if ( count(`P1'.`P1',1) < count(`P4'.`P4',1) ); multiply replace_(`P1',`P4',`P4',`P1',`P2',`P3',`P3',`P2'); endif; else; if ( count(`P2'.`P2',1) < count(`P4'.`P4',1) ); multiply replace_(`P2',`P4',`P4',`P2',`P3',`P1',`P1',`P3'); endif; endif; if ( count(`P4'.`P4',1) < -1 ); id 1/`P1'.`P1'^mncx1?/`P4'.`P4'^mncx4?*`E5'^mncy5?/`P5'.`P5'^mncx5? = 1/`P1'.`P1'^mncx1/`P4'.`P4'^mncx4*`E5'^mncy5/`P5'.`P5'^mncx5*( +acc((2*mncx1+mncx4+mncx5+mncy5*ep-5+2*ep)/(mncx4-1))*`P4'.`P4' +`P1'.`P1' +acc((mncx5+mncy5*ep)/(mncx4-1))*`P1'.`P1'*`P4'.`P4'/`P5'.`P5' -acc((mncx5+mncy5*ep)/(mncx4-1))*`P2'.`P2'*`P4'.`P4'/`P5'.`P5' )/`Q'.`Q'; endif; endif; endrepeat; if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4') > 0 ); * * Here we substitute from the table * id `INTS'/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'*`E5'/`P5'.`P5'^mncx5? = mncTabTwo(mncx5)*`EQ'^3/`Q'.`Q'^mncx5; endif; endif; #endprocedure *--#] newtwo : *--#[ noplane : #procedure noplane(P1,P2,P3,P4,P5,P6,P7,P8,Q,INTS) * * Reduction procedure for three loop graphs of the NO or nonplanar type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<-----<-\ * P1 / \ P2 / \ P3 * / v / \ * / P7 \ / \ * / \ / \ * Q --<-- / --<-- Q * \ / \ / * \ P8 / \ / * \ ^ \ / * P6 \ / P5 \ / P4 * \->------>----->-/ * * Express everything in powers of pi.pi, Q.Q and p2.Q; * The only difficult relation here is the one for p1.p3 * It is derived by squaring: * p1-p3 = p6-p4 = p5+p8-p4 * and p2-Q = p4+p8 * * id `P5'.P?!{`P5'} = `P6'.P-`P8'.P; * id `P4'.P?!{`P4'} = `P3'.P-Q.P; *#call ACCU(moms 1) * id `P6'.P?!{`P6'} = `P1'.P-Q.P; *#call ACCU(moms 2) * id `P7'.P?!{`P7'} = `P2'.P-`P1'.P; *#call ACCU(moms 3) * id `P8'.P?!{`P8'} = `P2'.P-`P3'.P; *#call ACCU(moms 4) id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P6'.`P6'/2; #call ACCU(dots 1) id `P3'.`Q' = `P3'.`P3'/2+`Q'.`Q'/2-`P4'.`P4'/2; #call ACCU(dots 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU(dots 3) id `P3'.`P2' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; #call ACCU(dots 4) id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; #call ACCU(dots 5) * * First step: eliminate the powers of `Q'.`P2' * Equation 3.18 hasn't been checked yet. * Note how common factors are kept together in acc till the end. * This trick allows us to do an 'intermediate sort' in the argument * of acc, thereby making in the end only the terms that are necessary. * while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'*`Q'.`P2') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8?*`Q'.`P2'^mncx9? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*`Q'.`P2'^mncx9*`Q'.`Q'/`Q'.`P2'/2*( +acc(3-2*mncx2-mncx1-mncx3+mncx9-2*ep) +mncx1*`P7'.`P7'/`P1'.`P1'-mncx1*`P2'.`P2'/`P1'.`P1' +mncx3*`P8'.`P8'/`P3'.`P3'-mncx3*`P2'.`P2'/`P3'.`P3' +2*acc(mncx9-1)*`P2'.`P2'/`Q'.`P2'/2 )*mncdeno(7-mncx1-mncx2-mncx3-mncx4-mncx5-mncx6-mncx7-mncx8+mncx9,-4); #ifdef `LONGINT' id mncdeno(0,-4) = -1/4/ep; id mncdeno(mncx1?,-4) = mncaccm(1-4*ep/mncx1)/mncx1; repeat id mncaccm(mncx1?)*mncaccm(mncx2?) = mncaccm(mncx1*mncx2); id mncaccm(mncx1?) = mncaccm(mncx1-1); id mncaccm(mncx1?) = mncaccm(mncx1-mncx1^2,mncx1^3); id mncaccm(mncx1?,mncx2?) = acc(1-mncx1-mncx2+mncx2*mncx1+mncx2^2); repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); #endif #call ACCU(Eliminate `Q'.`P2') * * Next are four recursions that reduce the powers of the propagators * that connect to `Q' to 1. * #ifdef `LONGINT' label 6; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'^2/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx1+2*mncx2+mncx5+mncx6+2*mncx7+mncx8-9+4*ep)*`P6'.`P6' +acc(mncx6-1)*`P1'.`P1' +mncx8*`P2'.`P2'*`P6'.`P6'/`P8'.`P8' -mncx8*`P3'.`P3'*`P6'.`P6'/`P8'.`P8' +mncx5*`P6'.`P6'*`P7'.`P7'/`P5'.`P5' -mncx5*`P4'.`P4'*`P6'.`P6'/`P5'.`P5' )/(mncx6-1); label 1; while ( match(1/`P1'.`P1'^2/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx6+2*mncx5+mncx2+mncx1+2*mncx8+mncx7-9+4*ep)*`P1'.`P1' +acc(mncx1-1)*`P6'.`P6' +mncx7*`P5'.`P5'*`P1'.`P1'/`P7'.`P7' -mncx7*`P4'.`P4'*`P1'.`P1'/`P7'.`P7' +mncx2*`P1'.`P1'*`P8'.`P8'/`P2'.`P2' -mncx2*`P3'.`P3'*`P1'.`P1'/`P2'.`P2' )/(mncx1-1); label 3; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'^2/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx4+2*mncx5+mncx2+mncx3+2*mncx7+mncx8-9+4*ep)*`P3'.`P3' +acc(mncx3-1)*`P4'.`P4' +mncx8*`P5'.`P5'*`P3'.`P3'/`P8'.`P8' -mncx8*`P6'.`P6'*`P3'.`P3'/`P8'.`P8' +mncx2*`P3'.`P3'*`P7'.`P7'/`P2'.`P2' -mncx2*`P1'.`P1'*`P3'.`P3'/`P2'.`P2' )/(mncx3-1); label 4; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'^2 /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx3+2*mncx2+mncx5+mncx4+2*mncx8+mncx7-9+4*ep)*`P4'.`P4' +acc(mncx4-1)*`P3'.`P3' +mncx7*`P2'.`P2'*`P4'.`P4'/`P7'.`P7' -mncx7*`P1'.`P1'*`P4'.`P4'/`P7'.`P7' +mncx5*`P4'.`P4'*`P8'.`P8'/`P5'.`P5' -mncx5*`P6'.`P6'*`P4'.`P4'/`P5'.`P5' )/(mncx4-1); id mncdeno(0,mncx1?) = 1/mncx1/ep; id mncdeno(mncx1?,mncx2?) = mncaccm(1+ep*mncx2/mncx1)/mncx1; repeat id mncaccm(mncx1?)*mncaccm(mncx2?) = mncaccm(mncx1*mncx2); id mncaccm(mncx1?) = mncaccm(mncx1-1); id mncaccm(mncx1?) = mncaccm(mncx1-mncx1^2,mncx1^3); id mncaccm(mncx1?,mncx2?) = acc(1-mncx1-mncx2+mncx2*mncx1+mncx2^2); repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); #call ACCU(Preparation) #endif label 6; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'^2/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx1+2*mncx2+mncx5+mncx6+2*mncx7+mncx8-9+4*ep)*`P6'.`P6' +acc(mncx6-1)*`P1'.`P1' +mncx8*`P2'.`P2'*`P6'.`P6'/`P8'.`P8' -mncx8*`P3'.`P3'*`P6'.`P6'/`P8'.`P8' +mncx5*`P6'.`P6'*`P7'.`P7'/`P5'.`P5' -mncx5*`P4'.`P4'*`P6'.`P6'/`P5'.`P5' )/(mncx6-1); label 1; while ( match(1/`P1'.`P1'^2/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx6+2*mncx5+mncx2+mncx1+2*mncx8+mncx7-9+4*ep)*`P1'.`P1' +acc(mncx1-1)*`P6'.`P6' +mncx7*`P5'.`P5'*`P1'.`P1'/`P7'.`P7' -mncx7*`P4'.`P4'*`P1'.`P1'/`P7'.`P7' +mncx2*`P1'.`P1'*`P8'.`P8'/`P2'.`P2' -mncx2*`P3'.`P3'*`P1'.`P1'/`P2'.`P2' )/(mncx1-1); label 3; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'^2/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx4+2*mncx5+mncx2+mncx3+2*mncx7+mncx8-9+4*ep)*`P3'.`P3' +acc(mncx3-1)*`P4'.`P4' +mncx8*`P5'.`P5'*`P3'.`P3'/`P8'.`P8' -mncx8*`P6'.`P6'*`P3'.`P3'/`P8'.`P8' +mncx2*`P3'.`P3'*`P7'.`P7'/`P2'.`P2' -mncx2*`P1'.`P1'*`P3'.`P3'/`P2'.`P2' )/(mncx3-1); label 4; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'^2 /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8/`Q'.`Q'*( +acc(2*mncx3+2*mncx2+mncx5+mncx4+2*mncx8+mncx7-9+4*ep)*`P4'.`P4' +acc(mncx4-1)*`P3'.`P3' +mncx7*`P2'.`P2'*`P4'.`P4'/`P7'.`P7' -mncx7*`P1'.`P1'*`P4'.`P4'/`P7'.`P7' +mncx5*`P4'.`P4'*`P8'.`P8'/`P5'.`P5' -mncx5*`P6'.`P6'*`P4'.`P4'/`P5'.`P5' )/(mncx4-1); * * Now we have that in the 'active terms' the powers of `P1'.`P1', `P3'.`P3', * `P4'.`P4' and `P6'.`P6' is 1 and the power of `Q'.`P2' is zero. * The final recursion is for lines that don't touch the outside. * * Remark: it seems better to combine this recursion more directly * with the above recursions.This can give: * 1: 5 a: mncx7=mncx8=1 b: mncx7>1,mncx8=1 c: mncx7=1,mncx8>1 d: mncx7>1,mncx8>1 * 2: 2 mncx5=1 ( a: mncx7=mncx8=1 b: mncx7>1,mncx8=1 c: mncx7=1,mncx8>1 d: mncx7>1,mncx8>1 ) * 3: 8 mncx2=mncx5=1 * 4: 7 mncx2=mncx5=mncx8=1 * if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) > `INNOTABL' ); while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^2/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx1+2*mncx2+2*mncx3+mncx4+2*mncx5+mncx6+2*mncx7+2*mncx8-14+6*ep) +mncx4*`P3'.`P3'/`P4'.`P4'+mncx6*`P1'.`P1'/`P6'.`P6' )*`P5'.`P5'/`Q'.`Q' +acc(mncx5-1)*mncx4*`P7'.`P7'/`P4'.`P4' +acc(mncx5-1)*mncx6*`P8'.`P8'/`P6'.`P6' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx5+mncx6+mncx7+mncx8-9+4*ep)*mncx4*`P5'.`P5'/`P4'.`P4' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx5+mncx6+mncx7+mncx8-9+4*ep)*mncx6*`P5'.`P5'/`P6'.`P6' )/(mncx5-1)*mncdeno(mncx4+mncx6+2*mncx5-4,2); if ( count(`P4'.`P4',1) < -1 ) goto 4; if ( count(`P6'.`P6',1) < -1 ) goto 6; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; while ( match(1/`P1'.`P1'/`P2'.`P2'^2/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx6+2*mncx2+2*mncx4+mncx3+2*mncx5+mncx1+2*mncx7+2*mncx8-14+6*ep) +mncx3*`P4'.`P4'/`P3'.`P3'+mncx1*`P6'.`P6'/`P1'.`P1' )*`P2'.`P2'/`Q'.`Q' +acc(mncx2-1)*mncx3*`P8'.`P8'/`P3'.`P3' +acc(mncx2-1)*mncx1*`P7'.`P7'/`P1'.`P1' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx2+mncx6+mncx7+mncx8-9+4*ep)*mncx3*`P2'.`P2'/`P3'.`P3' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx2+mncx6+mncx7+mncx8-9+4*ep)*mncx1*`P2'.`P2'/`P1'.`P1' )/(mncx2-1)*mncdeno(mncx3+mncx1+2*mncx2-4,2); if ( count(`P3'.`P3',1) < -1 ) goto 3; if ( count(`P1'.`P1',1) < -1 ) goto 1; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'^2) > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx1+2*mncx2+2*mncx4+mncx3+2*mncx5+mncx6+2*mncx7+2*mncx8-14+6*ep) +mncx3*`P4'.`P4'/`P3'.`P3'+mncx6*`P1'.`P1'/`P6'.`P6' )*`P8'.`P8'/`Q'.`Q' +acc(mncx8-1)*mncx3*`P2'.`P2'/`P3'.`P3' +acc(mncx8-1)*mncx6*`P5'.`P5'/`P6'.`P6' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx8+mncx6+mncx7+mncx5-9+4*ep)*mncx3*`P8'.`P8'/`P3'.`P3' -acc(mncx1+mncx2+mncx3+mncx4+2*mncx8+mncx6+mncx7+mncx5-9+4*ep)*mncx6*`P8'.`P8'/`P6'.`P6' )/(mncx8-1)*mncdeno(mncx3+mncx6+2*mncx8-4,2); if ( count(`P3'.`P3',1) < -1 ) goto 3; if ( count(`P6'.`P6',1) < -1 ) goto 6; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'^2/`P8'.`P8') > 0 ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( +acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8-8+4*ep)*( +acc(2*mncx6+2*mncx2+2*mncx3+mncx4+2*mncx5+mncx1+2*mncx7+2*mncx8-14+6*ep) +mncx4*`P3'.`P3'/`P4'.`P4'+mncx1*`P6'.`P6'/`P1'.`P1' )*`P7'.`P7'/`Q'.`Q' +acc(mncx7-1)*mncx4*`P5'.`P5'/`P4'.`P4' +acc(mncx7-1)*mncx1*`P2'.`P2'/`P1'.`P1' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx7+mncx6+mncx2+mncx8-9+4*ep)*mncx4*`P7'.`P7'/`P4'.`P4' -acc(mncx1+mncx5+mncx3+mncx4+2*mncx7+mncx6+mncx2+mncx8-9+4*ep)*mncx1*`P7'.`P7'/`P1'.`P1' )/(mncx7-1)*mncdeno(mncx4+mncx1+2*mncx7-4,2); if ( count(`P4'.`P4',1) < -1 ) goto 4; if ( count(`P1'.`P1',1) < -1 ) goto 1; if ( count(`P2'.`P2',-1,`P5'.`P5',-1,`P7'.`P7',-1,`P8'.`P8',-1) <= `INNOTABL' ) goto 9; endwhile; * * If we ever get here (luckily we have to do this only at the beginning * of the program and for rather few terms), the only interesting integral * left is the fundamental integral below: * endif; label 9; * * Here we take those integrals that have been tabulated * if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') ); if ( count(`P2'.`P2',1) > count(`P5'.`P5',1) ) multiply replace_(`P2',`P5',`P5',`P2'); if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ) multiply replace_(`P7',`P8',`P8',`P7'); if ( ( count(`P2'.`P2',1) > count(`P7'.`P7',1) ) || ( ( count(`P2'.`P2',1) == count(`P7'.`P7',1) ) && ( count(`P8'.`P8',1) > count(`P5'.`P5',1) ) ) ) multiply replace_(`P2',`P7',`P7',`P2',`P8',`P5',`P5',`P8'); if ( ( count(`P2'.`P2',1) > count(`P8'.`P8',1) ) || ( ( count(`P2'.`P2',1) == count(`P8'.`P8',1) ) && ( count(`P7'.`P7',1) > count(`P5'.`P5',1) ) ) ) multiply replace_(`P2',`P8',`P8',`P2',`P7',`P5',`P5',`P7'); if ( count(`P2'.`P2',1) > count(`P5'.`P5',1) ) multiply replace_(`P2',`P5',`P5',`P2'); if ( count(`P7'.`P7',1) > count(`P8'.`P8',1) ) multiply replace_(`P7',`P8',`P8',`P7'); id `INTS'/`P1'.`P1'/`P2'.`P2'^mncx2?/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'^mncx5?/`P6'.`P6'/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = mncnoptab(mncx2,mncx7,mncx8,mncx5)*mnceq^3/`Q'.`Q'^(mncx2+mncx5+mncx7+mncx8-2); endif; * * The value will only be substituted when the routine subint is * invoked. This way we can keep an eye on the accuracy of the calculation. * id mncdeno(0,mncx1?) = 1/mncx1/ep; id mncdeno(mncx1?,mncx2?) = mncaccm(1+ep*mncx2/mncx1)/mncx1; repeat id mncaccm(mncx1?)*mncaccm(mncx2?) = mncaccm(mncx1*mncx2); id mncaccm(mncx1?) = mncaccm(mncx1-1); id mncaccm(mncx1?) = mncaccm(mncx1-mncx1^2,mncx1^3); id mncaccm(mncx1?,mncx2?) = acc(1-mncx1-mncx2+mncx2*mncx1+mncx2^2); repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); * #endprocedure *--#] noplane : *--#[ noplred : #procedure noplred(P1,P2,P3,P4,P5,P6,P7,P8,Q) * * /-<------<-----<-\ * P1 / \ P2 / \ P3 * / v / \ * / P7 \ / \ * / \ / \ * Q --<-- / --<-- Q * \ / \ / * \ P8 / \ / * \ ^ \ / * P6 \ / P5 \ / P4 * \->------>----->-/ * * Express everything in powers of pi.pi, Q.Q and p2.Q; * The only difficult relation here is the one for p1.p3 * It is derived by squaring: * p1-p3 = p6-p4 = p5+p8-p4 * and p2-Q = p4+p8 * id `P5'.P?!{`P5'} = `P6'.P-`P8'.P; id `P4'.P?!{`P4'} = `P3'.P-Q.P; #call ACCU(moms 1) id `P6'.P?!{`P6'} = `P1'.P-Q.P; #call ACCU(moms 2) id `P7'.P?!{`P7'} = `P2'.P-`P1'.P; #call ACCU(moms 3) id `P8'.P?!{`P8'} = `P2'.P-`P3'.P; #call ACCU(moms 4) id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P6'.`P6'/2; #call ACCU(dots 1) id `P3'.`Q' = `P3'.`P3'/2+`Q'.`Q'/2-`P4'.`P4'/2; #call ACCU(dots 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU(dots 3) id `P3'.`P2' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; #call ACCU(dots 4) id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; #call ACCU(dots 5) #endprocedure *--#] noplred : *--#[ one : #procedure one(P,PQ,Q,EP,EPQ,EQ,INT) * * Routine for the reduction of one loop integrals. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * Method involves a reduction to a standard function mncG. * One problem is the presence of loopmomenta in the numerator. * The two propagators are P and P-Q (=PQ) in which Q is the external * momentum. * * The formula we use is (3.1) * This means that we have to find a way to take the d'Alembertian (dal) * of a polynomial in dotproducts. Such is done with the help of the * noncommuting(!) function mncFQ. * The use of the function distrib_ avoids the generation of double * terms. They can speed things up very much over the conventional * differentiation by commutation. Example: * 8 FQ, 3 d'Alembertians: commutation: 229.7 sec, distrib_: 13.6 sec * The simple cases have dedicated code. * * Recoded by J.A.M.Vermaseren 4-nov-1990 * * We start with some trivialities * id `P'.`PQ' = `P'.`P'/2+`PQ'.`PQ'/2-`Q'.`Q'/2; id `PQ'.mncp?!{`PQ'} = `P'.mncp-`Q'.mncp; id `P'.`Q' = `P'.`P'/2+`Q'.`Q'/2-`PQ'.`PQ'/2; if ( ( count(`EP',1) == 0 ) && ( count(`P'.`P',1) >= 0 ) ) discard; if ( ( count(`EPQ',1) == 0 ) && ( count(`PQ'.`PQ',1) >= 0 ) ) discard; totensor,nosquare,mncFQ,`P'; * * Now relation (3.1) after which we don't need mncx anymore * if ( count(mncFQ,1) == 0 ); id `INT'/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2? = `Q'.`Q'^2/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`EQ'^mncy1*`EQ'^mncy2*`EQ' *mncG(mncx1,mncy1,mncx2,mncy2,0,0); else; if ( match(mncFQ(mnci1?)) ); id `INT'/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2?*mncFQ(mnci1?) = `Q'.`Q'^2/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`EQ'^mncy1*`EQ'^mncy2*`EQ' *mncG(mncx1,mncy1,mncx2,mncy2,1,0)*`Q'(mnci1); else; if ( match(mncFQ(mnci1?,mnci2?)) ); id `INT'/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2?*mncFQ(mnci1?,mnci2?) = `Q'.`Q'^2/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`EQ'^mncy1*`EQ'^mncy2*`EQ'*( +mncG(mncx1,mncy1,mncx2,mncy2,2,0)*`Q'(mnci1)*`Q'(mnci2) +mncG(mncx1,mncy1,mncx2,mncy2,2,1)*`Q'.`Q'*d_(mnci1,mnci2)/2 ); else; id `INT'/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2?*mncFQ(?a) = `Q'.`Q'^2/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`EQ'^mncy1*`EQ'^mncy2*`EQ' *sum_(mncj,0,integer_(nargs_(?a)/2),mncG(mncx1,mncy1,mncx2,mncy2,nargs_(?a),mncj) *`Q'.`Q'^mncj/2^mncj*distrib_(1,2*mncj,mncdel,mncFQ,?a)); tovector,mncFQ,`Q'; id mncdel(?a) = dd_(?a); endif; endif; endif; * id mncG(mncx1?,mncy1?,0,0,?a) = 0; id mncG(0,0,?a) = 0; id mncG(2,0,1,0,0,0) = mncG(1,0,2,0,0,0); * #endprocedure *--#] one : *--#[ one4 : #procedure one4(P,PQ,Q,EP,EPQ,EQ,P1,P2,P3,P4,P5,INT) * * The procedure one4 does an integral of type one4 in which * P1-P5 are the 5 momenta in the sub two loop part, P is its * momentum flow, Q is the overall momentum flow and PQ = P-Q * * Note that the central formula (B6 in ref 9b) is wrong * This can be tested by trying A16 on P.p1^2*P.p2^2. This shows * that it isn't an identity operator. Also the first two arguments * of the mncG function in B6 should be exchanged. * * Recoded from the old one4 by J.A.M.Vermaseren, 25-mar-1993 * id,many,mncq1?{`P1',`P2',`P3',`P4',`P5'}.mncq2?{`P1',`P2',`P3',`P4',`P5'}^mncx1? = mncq1.mncq2^mncx1*`P'.`P'^mncx1/`Q'.`Q'^mncx1; multiply `EP'^2/`EQ'^2*`P'.`P'^4/`Q'.`Q'^4; id `Q'.`P' = `P'.`P'/2+`Q'.`Q'/2-`PQ'.`PQ'/2; id `Q'.`PQ' = `P'.`P'/2-`Q'.`Q'/2-`PQ'.`PQ'/2; if ( ( count(`EPQ',1) == 0 ) && ( count(`PQ'.`PQ',1) >= 0 ) ) discard; totensor,nosquare,mncFQ,`Q'; if ( count(mncFQ,1) == 0 ); id `INT'/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2? = 1/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`Q'.`Q'^2*`EQ'*`EQ'^mncy1*`EQ'^mncy2* mncG(mncx1,mncy1,mncx2,mncy2,0,0); elseif ( match(mncFQ(mnci1?)) ); id `INT'*mncFQ(mnci1?)/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2? = 1/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`Q'.`Q'^2*`EQ'*`EQ'^mncy1*`EQ'^mncy2*`Q'(mnci1)* mncG(mncx1,mncy1,mncx2,mncy2,1,0); elseif ( match(mncFQ(mnci1?,mnci2?)) ); id `INT'*mncFQ(mnci1?,mnci2?)/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2? = 1/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`Q'.`Q'^2*`EQ'*`EQ'^mncy1*`EQ'^mncy2* (mncG(mncx1,mncy1,mncx2,mncy2,2,0)*`Q'(mnci1)*`Q'(mnci2) -mncG(mncx1,mncy1,mncx2,mncy2,2,0)*d_(mnci1,mnci2)*`Q'.`Q'/2*acc(mncpoch(3,1)) +mncG(mncx1-1,mncy1,mncx2,mncy2,0,0)*acc(mncpoch(3,1))*d_(mnci1,mnci2)*`Q'.`Q'/2); else; id `INT'*mncFQ(?a)/`P'.`P'^mncx1?/`PQ'.`PQ'^mncx2?*`EP'^mncy1?*`EPQ'^mncy2? = mncFQ(?a)/`Q'.`Q'^mncx1/`Q'.`Q'^mncx2*`Q'.`Q'^2*`EQ'*`EQ'^mncy1*`EQ'^mncy2* sum_(mncs,0,integer_(nargs_(?a)/2),mncG(mncx1-mncs,mncy1,mncx2,mncy2,nargs_(?a)-2*mncs,0) *acc(mncpoch(nargs_(?a)+2-mncs,mncs))*`Q'.`Q'^mncs *sum_(mncj,0,integer_(nargs_(?a)/2)-mncs,sign_(mncj)*`Q'.`Q'^mncj * the original mncy/4 becomes mncy/2 when we consider the normalization of * the distrib_ to expand the mncFQ. *mncy^mncj*mncy^mncs/2^mncj/2^mncs*acc(mncpoch(nargs_(?a)+1-2*mncs,mncj)) )); id mncy^mncs?*mncFQ(?a) = fac_(mncs)*distrib_(1,2*mncs,mncdel,mncFQ,?a); tovector,mncFQ,`Q'; id mncdel(?a) = dd_(?a); endif; #endprocedure *--#] one4 : *--#[ pochtabl : #procedure pochtabl(NN) * #[ Declarations : The tables and their variables. Commentary. * * The variable ep should be declared in the rest of the program. * It has a power limitation of 6. * Note the funny convention: * When the argument of mncPO or mncPOINV is 0 or less we have * taken out an overal factor of 1/mncx/ep, cq. x*ep. This is to * avoid a temporary anomalous number of powers of ep which could * destroy the accuracy. * * The parameter NN was to be friendly to older versions of FORM * At the moment it has been disabled. * * Values are generated with the program potabl.frm in lib/progs * CTable,check,strict,mncPO(-40:40,mncx?); CTable,check,strict,mncPOINV(-40:40,mncx?); * * #] Declarations : *--#[ mncPO-neg : mncPO negative values * Fill mncPO(0) = +1 ; Fill mncPO(-1) = -1 -mncx*ep -mncx^2*ep^2 -mncx^3*ep^3 -mncx^4*ep^4 -mncx^5*ep^5 -mncx^6*ep^6 ; Fill mncPO(-2) = +1/2 +3/4*mncx*ep +7/8*mncx^2*ep^2 +15/16*mncx^3*ep^3 +31/32*mncx^4*ep^4 +63/64*mncx^5*ep^5 +127/128*mncx^6*ep^6 ; Fill mncPO(-3) = -1/6 -11/36*mncx*ep -85/216*mncx^2*ep^2 -575/1296*mncx^3*ep^3 -3661/7776*mncx^4*ep^4 -22631/46656*mncx^5*ep^5 -137845/279936*mncx^6*ep^6 ; Fill mncPO(-4) = +1/24 +25/288*mncx*ep +415/3456*mncx^2*ep^2 +5845/41472*mncx^3*ep^3 +76111/497664*mncx^4*ep^4 +952525/5971968*mncx^5*ep^5 +11679655/71663616*mncx^6*ep^6 ; Fill mncPO(-5) = -1/120 -137/7200*mncx*ep -12019/432000*mncx^2*ep^2 -874853/25920000*mncx^3*ep^3 -58067611/1555200000*mncx^4*ep^4 -3673451957/93312000000*mncx^5*ep^5 -226576032859/5598720000000*mncx^6*ep^6 ; Fill mncPO(-6) = +1/720 +49/14400*mncx*ep +13489/2592000*mncx^2*ep^2 +336581/51840000*mncx^3*ep^3 +68165041/9331200000*mncx^4*ep^4 +483900263/62208000000*mncx^5*ep^5 +270127056529/33592320000000*mncx^6*ep^6 ; Fill mncPO(-7) = -1/5040 -121/235200*mncx*ep -726301/889056000*mncx^2*ep^2 -129973303/124467840000*mncx^3*ep^3 -187059457981/156829478400000*mncx^4*ep^4 -28139924320343/21956126976000000*mncx^5*ep^5 -36845364451242061/27664719989760000000*mncx^6*ep^6 ; Fill mncPO(-8) = +1/40320 +761/11289600*mncx*ep +3144919/28449792000*mncx^2*ep^2 +1149858589/7965941760000*mncx^3*ep^3 +3355156783231/20074173235200000*mncx^4*ep^4 +339302688554687/1873589501952000000*mncx^5*ep^5 +2678744365563671119/14164336634757120000000*mncx^6*ep^6 ; Fill mncPO(-9) = -1/362880 -7129/914457600*mncx*ep -30300391/2304433152000*mncx^2*ep^2 -101622655189/5807171543040000*mncx^3*ep^3 -300222042894631/14634072288460800000*mncx^4*ep^4 -826117151879597149/36877862166921216000000*mncx^5*ep^5 -2184117445022203447471/92932212660641464320000000*mncx^6*ep^6 ; Fill mncPO(-10) = +1/3628800 +7381/9144576000*mncx*ep +32160403/23044331520000*mncx^2*ep^2 +21945415349/11614343086080000*mncx^3*ep^3 +327873266234371/146340722884608000000*mncx^4*ep^4 +908741214970658641/368778621669212160000000*mncx^5*ep^5 +2413120231194809425003/929322126606414643200000000*mncx^6*ep^6 ; Fill mncPO(-11) = -1/39916800 -83711/1106493696000*mncx*ep -4102360483/30672005253120000*mncx^2*ep^2 -31276937512951/170045597123297280000*mncx^3*ep^3 -5194481903600608411/23568319761289003008000000*mncx^4*ep^4 -159443775809313077987411/653313823782931163381760000000*mncx^5*ep^5 -4676788004935176736296015403/18109859195262851848942387200000000*mncx^6* ep^6 ; Fill mncPO(-12) = +1/479001600 +86021/13277924352000*mncx*ep +4301068993/368064063037440000*mncx^2*ep^2 +33264031387717/2040547165479567360000*mncx^3*ep^3 +5578681466128739761/282819837135468036096000000*mncx^4*ep^4 +172330529996070466835321/7839765885395173960581120000000*mncx^5*ep^5 +5074871529226099514685606913/217318310343154222187308646400000000*mncx^6 *ep^6 ; Fill mncPO(-13) = -1/6227020800 -1145993/2243969215488000*mncx*ep -758647585777/808636746493255680000*mncx^2*ep^2 -77287019174361937/58280067593261923368960000*mncx^3*ep^3 -170044702211669500782121/105009025789539333526192128000000*mncx^4*ep^4 -68698758619138470404367234173/37841052533518394229498595246080000000* mncx^5*ep^5 -26399765160034818571989179349406177/136364016909786885445421137828773888\ 00000000*mncx^6*ep^6 ; Fill mncPO(-14) = +1/87178291200 +1171733/31415569016832000*mncx*ep +112686856171/1617273492986511360000*mncx^2*ep^2 +81347802723340093/815920946305666927165440000*mncx^3*ep^3 +180514164422163370751221/1470126361053550669366689792000000*mncx^4*ep^4 +10477884744480707938214808959/75682105067036788458997190492160000000* mncx^5*ep^5 +28287670433295352528296723627638797/190909623673701639623589592960283443\ 200000000*mncx^6*ep^6 ; Fill mncPO(-15) = -1/1307674368000 -1195757/471233535252480000*mncx*ep -476696711/99016744468561920000*mncx^2*ep^2 -17055178843123409/2447762838917000781496320000*mncx^3*ep^3 -190757504835343290196621/22051895415803260040500346880000000*mncx^4*ep^4 -11132564501075606110169612231/1135231576005551826884957857382400000000* mncx^5*ep^5 -6031962308062447011326345395460321/5727288710211049188707687788808503296\ 00000000*mncx^6*ep^6 ; Fill mncPO(-16) = +1/20922789888000 +2436559/15079473128079360000*mncx*ep +96568406789/310516510653410181120000*mncx^2*ep^2 +142531324182321979/313313643381376100031528960000*mncx^3*ep^3 +3212628164810309981747311/5645285226445634570368088801280000000*mncx^4* ep^4 +376915326274973740257971537677/581238566914842535365098422979788800000000 *mncx^5*ep^5 +81962999787375055541354912877997039/117294872785122287384733445914798147\ 502080000000*mncx^6*ep^6 ; Fill mncPO(-17) = -1/355687428096000 -42142223/4357967734014935040000*mncx*ep -28776062218037/1525567616840204219842560000*mncx^2*ep^2 -729291672694244960123/26168268808855913250733330268160000*mncx^3*ep^3 -281462294311726805677013376031/80154977457654193641791234611190169600000\ 00*mncx^4*ep^4 -564145222241140781833967990767603949/14029686014368128821510003376465837\ 765427200000000*mncx^5*ep^5 -10461164856476842638038161189836649078663547/240653112241754467740880813\ 276977714544308859699200000000*mncx^6*ep^6 ; Fill mncPO(-18) = +1/6402373705728000 +14274301/26147806404089610240000*mncx*ep +29608882035581/27460217103123675957166080000*mncx^2*ep^2 +50500501069854396349/31401922570627095900879996321792000*mncx^3*ep^3 +294352799712312489617077371031/14427895942377754855522422230014230528000\ 0000*mncx^4*ep^4 +65863120942796227591592510480739821/280593720287362576430200067529316755\ 30854400000000*mncx^5*ep^5 +88208355135479668752967444674123414750223/346540481628126433546868371118\ 84790894380475796684800000*mncx^6*ep^6 ; Fill mncPO(-19) = -1/121645100408832000 -275295799/9439358111876349296640000*mncx*ep -1568274265798307/26907089872903613341457448960000*mncx^2*ep^2 -1794683268312579709384043/20461649756633468824492910003261276160000* mncx^3*ep^3 -40009517970859535080774906095604951/357248987150256164200042141613160061\ 961502720000000*mncx^4*ep^4 -170864658958309558725823727346322640908759/13200778773986545574588597183\ 17620008155187930726400000000*mncx^5*ep^5 -545107754958038941477256969841397265941063458146891/38720342868353865808\ 30089611201274450551405153503756576358400000000*mncx^6*ep^6 ; Fill mncPO(-20) = +1/2432902008176640000 +11167027/7551486489501079437312000*mncx*ep +11256448518043769/3766992582206505867804042854400000*mncx^2*ep^2 +9279131712715653650968723/2046164975663346882449291000326127616000000* mncx^3*ep^3 +41629602590344731254886672725930611/714497974300512328400084283226320123\ 9230054400000000*mncx^4*ep^4 +7142239112579651595742062778098987074987/1056062301918923645967087774654\ 096006524150344581120000000*mncx^5*ep^5 +571294651960644279934630828168658674310905345370231/77440685736707731616\ 601792224025489011028103070075131527168000000000*mncx^6*ep^6 ; Fill mncPO(-21) = -1/51090942171709440000 -18858053/264302027132537780305920000*mncx*ep -80676574383943103/553747909584356362567194299596800000*mncx^2*ep^2 -9577241336253249489726083/42969464488930284531435111006848679936000000* mncx^3*ep^3 -6174587158661922297334017385371973/2143493922901536985200252849678960371\ 7690163200000000*mncx^4*ep^4 -111696754789037742399995916535691943099157/33265962510446094847963264901\ 6040242055107358543052800000000*mncx^5*ep^5 -597296825451676635924546421568548733116332437242151/16262544004708623639\ 48637636704535269231590164471577762070528000000000*mncx^6*ep^6 ; Fill mncPO(-22) = +1/1124000727777607680000 +6364399/1938214865638610388910080000*mncx*ep +82494882923667143/12182454010855839976478274591129600000*mncx^2*ep^2 +9868213987506291289829963/945328218756466259691572442150670958592000000* mncx^3*ep^3 +6398344963543032449814395864411773/4715686630383381367440556269293712817\ 89183590400000000*mncx^4*ep^4 +116210352073359830867133385439115668950093/73185117522981408665519182783\ 52885325212361887947161600000000*mncx^5*ep^5 +623120053293078163170149467651030900158655068872591/35777596810358972006\ 870028007499775923094983618374710765551616000000000*mncx^6*ep^6 ; Fill mncPO(-23) = -1/25852016738884976640000 -444316699/3075946991768474687200296960000*mncx*ep -44570695662918553607/148223917950083004993811166950273843200000*mncx^2* ep^2 -123525135034106281845251414461/26454159406502827457834932378388591172334\ 3872000000*mncx^3*ep^3 -264591239933345908907390540426325365899/43359680905230948543794931799963\ 8620563548468255129600000000*mncx^4*ep^4 -776713959740478684849561077289313689586845388571/10834023934084030762272\ 43586991318834832866105871976452482662400000000*mncx^5*ep^5 -96041208895558385773482948005826382154738052851832630885359/ 1218164720524162610937517301815379439097517152218903519958149931487723520\ 00000000*mncx^6*ep^6 ; Fill mncPO(-24) = +1/620448401733239439360000 +269564591/44293636681466035495684276224000*mncx*ep +45472764736767046157/3557374030801992119851468006806572236800000*mncx^2* ep^2 +126906684898093000128113947991/63489982575606785898803837708132618813602\ 52928000000*mncx^3*ep^3 +1912807200725066844334929443722155255943/7284426392078799355357548542393\ 9288254676142666861772800000000*mncx^4*ep^4 +53677524641216006737724172489720819744162618911/173344382945344492196358\ 9739186110135732585769395162323972259840000000*mncx^5*ep^5 +99813356898970334531896288222195044055013592737697579224909/ 2923595329257990266250041524356910653834041165325368447899559835570536448\ 000000000*mncx^6*ep^6 ; Fill mncPO(-25) = -1/15511210043330985984000000 -34052522467/138417614629581360924013363200000000*mncx*ep -5793490591633676917801/11116793846256225374535837521270538240000000000* mncx^2*ep^2 -81384656370757013035663184180567/992030977743856029668809964189572168962\ 53952000000000000*mncx^3*ep^3 -176122096932442395019595242667343669886849/16259880339461605703923099424\ 9864482711330675595673600000000000000*mncx^4*ep^4 -1446748397713984600368618807470929295440186517370209/1128544159800419871\ 070045403115957119617568860283308804669440000000000000000*mncx^5*ep^5 -8090725701340520405271382597523589771894308313467672735828693401/ 5710147127457012238769612352259591120769611651026110249803827803848704000\ 000000000000000*mncx^6*ep^6 ; Fill mncPO(-26) = +1/403291461126605635584000000 +34395742267/3598857980369115384024347443200000000*mncx*ep +5899738289669258497201/289036640002661859737931775553033994240000000000* mncx^2*ep^2 +83409563366589638003220811960367/257928054213402567713890590689288763930\ 2602752000000000000*mncx^3*ep^3 +1269661867514370193728286786947387535922143/2959298221782012238114004095\ 3475335853462182958412595200000000000000*mncx^4*ep^4 +4485502890553923346111651037532362873187789797454427/8802644446443274994\ 3463541443044655330170371102098086764216320000000000000000*mncx^5*ep^5 +8381693734884639563224191438763431636799403704468574686255012801/ 1484638253138823182080099211587493691400099029266788664948995229000663040\ 00000000000000000*mncx^6*ep^6 ; Fill mncPO(-27) = -1/10888869450418352160768000000 -312536252003/874522489229695038317916428697600000000*mncx*ep -54027306066201893389609/702359035206468319163174214593872606003200000000\ 00*mncx^2*ep^2 -6916882722942792550203844435294127/5640886545647114155902787218374745267\ 154792218624000000000000*mncx^3*ep^3 -105781863112692028426923791152458954384121183/64719852110372607647553269\ 565250559511521794130048345702400000000000000*mncx^4*ep^4 -10124450547451531665251301003609713279538398648943034649/ 5197873519180289451411578658670343852591230243207789925340209479680000000\ 000000000*mncx^5*ep^5 -6321066054179278690866136146657264317464969772671961192473023910729/ 2922213473653145669288259278167663832782814919305820129219107309242005061\ 632000000000000000000*mncx^6*ep^6 ; Fill mncPO(-28) = +1/304888344611713860501504000000 +315404588903/24486629698431461072901660003532800000000*mncx*ep +54931992686981698810309/196660529857811129365688780086284329680896000000\ 0000*mncx^2*ep^2 +1010635169222484615218019977199461/2256354618258845662361114887349898106\ 8619168874496000000000000*mncx^3*ep^3 +108680705261010625358435939397997327030532083/18121558590904330141314915\ 47827015666322610235641353679667200000000000000*mncx^4*ep^4 +10436183424669712573258978534871152798761441249245797349/ 1455404585370481046395242024427696278725544468098181179095258654310400000\ 00000000000*mncx^5*ep^5 +6530607484264318239070044916372416367692549786298717916415436057429/ 8182197726228807874007125978869458731791881774056296361813500465877614172\ 5696000000000000000000*mncx^6*ep^6 ; Fill mncPO(-29) = -1/8841761993739701954543616000000 -9227046511387/20593255576380858762310296062971084800000000*mncx*ep -46938861633377181563318269/479635366270215563409978365752438851658737254\ 40000000000*mncx^2*ep^2 -25186927017635217446536551133584958729/159587675075673461892043169863972\ 32829194034380722405376000000000000*mncx^3*ep^3 -78890646478256977372499817524180507318888060599123/371693988370268760273\ 70128729720544557277340612164915885352209612800000000000000*mncx^4*ep^4 -220394091880767057381928499928284371416460564271231904088227601/ 8657085888686975513843729395688454248908700080473386830091375281109030928\ 3840000000000000000*mncx^5*ep^5 -400846187516914154875914463903897327820615883520726692055932081171823277\ 4109/14114189871322798085914817932007871078118996653282259744392959396270\ 27196088509806936064000000000000000000*mncx^6*ep^6 ; Fill mncPO(-30) = +1/265252859812191058636308480000000 +9304682830147/617797667291425762869308881889132544000000000*mncx*ep +47661242955539172992975989/143890609881064669022993509725731655497621176\ 3200000000000*mncx^2*ep^2 +25715533224862937981129332151160709249/478763025227020385676129509591916\ 984875821031421672161280000000000000*mncx^3*ep^3 +80887105812785807182912885219853936646131104810363/111508196511080628082\ 1103861891616336718320218364947476560566288384000000000000000*mncx^4*ep^4 +226673869011222345191985022310524244322560444045040215307537481/ 2597125766606092654153118818706536274672610024142016049027412584332709278\ 515200000000000000000*mncx^5*ep^5 +413164874841296575681906255716369228175069979546000212222776589085717687\ 9029/42342569613968394257744453796023613234356989959846779233178878188810\ 815882655294208081920000000000000000000*mncx^6*ep^6 ; Fill mncPO(-31) = -1/8222838654177922817725562880000000 -290774257297357/593703558267060158117405835495456374784000000000*mncx*ep -46479693768075341170975445029/428664515896679755486399964823927174892963\ 24637491200000000000*mncx^2*ep^2 -781556503107229568390876511159818552568559/44214770782068309360000480082\ 7836765789503114759574096057466880000000000000*mncx^3*ep^3 -76521255941455275592333629944010738538900877943907253323/ 3192384995653400474537578644877822973797563399792305441352141291565508198\ 4000000000000000*mncx^4*ep^4 -6667705282222096185300565038664400439373549415795418232677816898893031/ 2304958677882854107587952889232422602531968466303538110272905138501002413\ 385094214451200000000000000000*mncx^5*ep^5 -377556125228009940562091755613952065421188786959973299420548922518209727\ 5036627133349/11649547782572666665636314305404667771607764719807658217286\ 58963444626575362564967578131202435973120000000000000000000*mncx^6*ep^6 ; Fill mncPO(-32) = +1/263130836933693530167218012160000000 +586061125622639/37997027729091850119513973471709207986176000000000*mncx* ep +188563440970824224217342974191/54869058034775008702259195497462678386299\ 29553598873600000000000*mncx^2*ep^2 +6374011091027611713181285626046594885588997/1131898132020948719616012290\ 11926212042112797378450968590711521280000000000000*mncx^3*ep^3 +1253103527804771871114914850704998968323017858623755794393/ 1634501117774541042963240266177445362584352460693660385972296341281540197\ 5808000000000000000*mncx^4*ep^4 +219021337829810613341650082757499547365333779437895662406850111446001517/ 2360277686152042606170063758574000744992735709494823024919454861825026471\ 306336475598028800000000000000000*mncx^5*ep^5 +248554426877018194483796891687105191326133831297962684645980033038470417\ 598667492069911/238582738587088213312231716974687595962527021461660840290\ 0293557134595226342533053600012702588872949760000000000000000000*mncx^6* ep^6 ; Fill mncPO(-33) = -1/8683317618811886495518194401280000000 -53676090078349/113991083187275550358541920415127623958528000000000*mncx* ep -191147113675074393547229862991/18106789151475752871745534514162683867478\ 7675268762828800000000000*mncx^2*ep^2 -6493501663928207284923763331891522805938597/3735263835669130774732840557\ 393564997389722313488881963493480202240000000000000*mncx^3*ep^3 -1281518216016642673897384956891070655754678612565673196793/ 5393853688655985441778692878385569696528363120289079273708577926229082652\ 01664000000000000000*mncx^4*ep^4 -224629088844679436707044990778140173948721827021389476075843741063887117/ 7788916364301740600361210403294202458476027841332915982234201044022587355\ 3109103694734950400000000000000000*mncx^5*ep^5 -255435053228138403128470654509381028350984604020895179028694925583796862\ 430658515774711/787323037337391103930364666016469066676339170823480772957\ 09687385441642469303590768800419185432807342080000000000000000000*mncx^6* ep^6 ; Fill mncPO(-34) = +1/295232799039604140847618609643520000000 +54062195834749/3875696828367368712190425294114339214589952000000000*mncx *ep +193672834401940297285176238591/61563083115017559763934817348153125149427\ 80959137936179200000000000*mncx^2*ep^2 +6611010257989610727955230791776284831303797/1269989704127504463409165789\ 51381209911250558658621986758778326876160000000000000*mncx^3*ep^3 +1309596256295164289625430756003219542652775000893320755593/ 1833910254143035050204755578651093696819643460898286953060916494917888101\ 6856576000000000000000*mncx^4*ep^4 +230191158028949416073834042540087090094585156318457665222350343814884317/ 2648231563862591804122811537120028835881849466053191433959628354967679700\ 805709525620988313600000000000000000*mncx^5*ep^5 +262278669329565080577541157375092806300683649718885554909323049217499202\ 181779758942311/267689832694712975336323986445599482669955318079983462805\ 4129371105015843956322086139214252304715449630720000000000000000000* mncx^6*ep^6 ; Fill mncPO(-35) = -1/10333147966386144929666651337523200000000 -54437269998109/135649388992857904926664885294001872510648320000000000* mncx*ep -28020487719351088554569096233/307815415575087798819674086740765625747139\ 04795689680896000000000000*mncx^2*ep^2 -6726617628860633132194043822000226660155477/4444963964446265621932080263\ 298342346893769553051769536557241440665600000000000000*mncx^3*ep^3 -1337349041568427108208504105948050572191945009309584705513/ 6418685889500622675716644525278827938868752113144004335713207732212608355\ 89980160000000000000000*mncx^4*ep^4 -235708813830701748331660980065818578642451649931134784063493088815524797/ 9268810473519071314429840379920100925586473131186170018858699242386878952\ 8199833396734590976000000000000000000*mncx^5*ep^5 -269086107362662971607704557753188335966759017341527797426919736935809337\ 701066139462151/936914414431495413677133952559598189344843613279942119818\ 94527988675554538471273014872498830665040737075200000000000000000000* mncx^6*ep^6 ; Fill mncPO(-36) = +1/371993326789901217467999448150835200000000 +54801925434709/4883378003742884577359935870584067410383339520000000000* mncx*ep +28365922323001895565692364433/110813549607031607575082671226675625268970\ 0572644828512256000000000000*mncx^2*ep^2 +6840399294542448499145530506469847851081277/1600187027200655623895548894\ 78740324488175703909863703316060691863961600000000000000*mncx^3*ep^3 +1364787318272393902310082315639579768613532772621310625713/ 2310726920220224163257992029100378057992750760731841560856754783596539008\ 1239285760000000000000000*mncx^4*ep^4 +241183262100220140849575649035124968298858892399689742143012614029778597/ 3336771770466865673194742536771236333211130327227021206789131727259276423\ 015194002282445275136000000000000000000*mncx^5*ep^5 +275858164018779108255860951501407989498653796590642496343098766635251225\ 077224664127551/337289189195338348923768222921455348164143700780779163134\ 8203007592319963384965828535409957903941466534707200000000000000000000* mncx^6*ep^6 ; Fill mncPO(-37) = -1/13763753091226345046315979581580902400000000 -2040798836801833/6685344487124008986405752206829588284814791802880000000\ 000*mncx*ep -39296045464550797787239457431177/561303872824497201850066254564480044674\ 91403106178498631303168000000000000*mncx^2*ep^2 -352161234046208215339252267574509136702023691081/29990081190854079447357\ 0581220365445283083865415414068070531622324454136217600000000000000* mncx^3*ep^3 -2608684498588375105517626756450359829025314345805903633658883393/ 1602349481944936549073231791722793647371928150639061097268636868732627063\ 281683538452152320000000000000000*mncx^4*ep^4 -171013050661720159566906093714710194318958438162996619791883595630791538\ 85873129/8561243452292523517171314326549614651700120853307180048661925366\ 808910708761138659914476119513706266624000000000000000000*mncx^5*ep^5 -725063001035943052469479181619316097777903710198896844188251120449343750\ 417133885707805597715159/320194958669810512763942477217493534214642269186\ 7684368272132390570951849184846348139270834635216735174966551905304576000\ 00000000000000000*mncx^6*ep^6 ; Fill mncPO(-38) = +1/523022617466601111760007224100074291200000000 +2053580969474233/2540430905107123414834185838595243548229620885094400000\ 00000*mncx*ep +39749780674985882178980437798777/213295471673308936703025176734502416976\ 4673318034782947989520384000000000000*mncx^2*ep^2 +357750190719359398209347777918099374415101893881/11396230852524550189995\ 682086373886920757186885785734586680201648329257176268800000000000000* mncx^3*ep^3 +2658985413003238910771173525609793878940548365941169558772311793/ 6088928031390758886478280808546615860013326972428432169620820101183982840\ 4703974461181788160000000000000000*mncx^4*ep^4 +174751676137248367434629126308906747211036344655198215819163300076987902\ 67618329/3253272511871158936525099444088853567646045924256728418491531639\ 38738606932923269076750092541520838131712000000000000000000*mncx^5*ep^5 +742262484176094563006431126693903121562516373538281131135537536308520808\ 714695198186793014024359/121674084294527994850298141342647543001564062290\ 9720059943410308416961702690241612292922917161382359366487289724015738880\ 0000000000000000000*mncx^6*ep^6 ; Fill mncPO(-39) = -1/20397882081197443358640281739902897356800000000 -2066035355155033/9907680529917781317853324770521449838095521451868160000\ 000000*mncx*ep -40194562866176681556204641717977/831852339525904853141798189264559426208\ 22259403356534971591294976000000000000*mncx^2*ep^2 -363256775189631187172928799970374912083283051481/44445300324845745740983\ 1601368581589909530288545643648880527864284841029874483200000000000000* mncx^3*ep^3 -2708750952776367511754929445487032491402381958608770810738224593/ 2374681932242395965726529515333180185405197519247088546152119839461753307\ 783455003986089738240000000000000000*mncx^4*ep^4 -178462617335950615774363407395022425191767023902592242501363486714297999\ 54676729/1268776279629751985244788783194652891381957910460124083211697339\ 3610805670384007493993253609119312687136768000000000000000000*mncx^5*ep^5 -759376829623578102586033668224832815298091263145655117559915634200781766\ 870276142570887835970759/474528928748659179916162751236325417706099842934\ 7908233779300202826150640491942287942399376929391201529300429923661381632\ 00000000000000000000*mncx^6*ep^6 ; Fill mncPO(-40) = +1/815915283247897734345611269596115894272000000000 +2078178381193813/3963072211967112527141329908208579935238208580747264000\ 00000000*mncx*ep +40630774334422967689121916324397/332740935810361941256719275705823770483\ 2890376134261398863651799040000000000000*mncx^2*ep^2 +368683961247536801596614790345267288407486323741/17778120129938298296393\ 264054743263596381211541825745955221114571393641194979328000000000000000* mncx^3*ep^3 +2757997281132970865939093578334734854928763733759781509645660373/ 9498727728969583862906118061332720741620790076988354184608479357847013231\ 1338200159443589529600000000000000000*mncx^4*ep^4 +182146564943915647791277936566142100003343018525106594345690078194760414\ 34591069/5075105118519007940979155132778611565527831641840496332846789357\ 44432226815360299759730144364772507485470720000000000000000000*mncx^5* ep^5 +776407770327188012905286289437702564472631687637943515864539604489420665\ 928534152925141981468899/189811571499463671966465100494530167082439937173\ 9163293511720081130460256196776915176959750771756480611720171969464552652\ 8000000000000000000000*mncx^6*ep^6 ; *--#] mncPO-neg : mncPO negative values *--#[ mncPO-pos : mncPO positive values * Fill mncPO(1) = +1 ; Fill mncPO(2) = +1 +mncx*ep ; Fill mncPO(3) = +2 +3*mncx*ep +mncx^2*ep^2 ; Fill mncPO(4) = +6 +11*mncx*ep +6*mncx^2*ep^2 +mncx^3*ep^3 ; Fill mncPO(5) = +24 +50*mncx*ep +35*mncx^2*ep^2 +10*mncx^3*ep^3 +mncx^4*ep^4 ; Fill mncPO(6) = +120 +274*mncx*ep +225*mncx^2*ep^2 +85*mncx^3*ep^3 +15*mncx^4*ep^4 +mncx^5*ep^5 ; Fill mncPO(7) = +720 +1764*mncx*ep +1624*mncx^2*ep^2 +735*mncx^3*ep^3 +175*mncx^4*ep^4 +21*mncx^5*ep^5 +mncx^6*ep^6 ; Fill mncPO(8) = +5040 +13068*mncx*ep +13132*mncx^2*ep^2 +6769*mncx^3*ep^3 +1960*mncx^4*ep^4 +322*mncx^5*ep^5 +28*mncx^6*ep^6 ; Fill mncPO(9) = +40320 +109584*mncx*ep +118124*mncx^2*ep^2 +67284*mncx^3*ep^3 +22449*mncx^4*ep^4 +4536*mncx^5*ep^5 +546*mncx^6*ep^6 ; Fill mncPO(10) = +362880 +1026576*mncx*ep +1172700*mncx^2*ep^2 +723680*mncx^3*ep^3 +269325*mncx^4*ep^4 +63273*mncx^5*ep^5 +9450*mncx^6*ep^6 ; Fill mncPO(11) = +3628800 +10628640*mncx*ep +12753576*mncx^2*ep^2 +8409500*mncx^3*ep^3 +3416930*mncx^4*ep^4 +902055*mncx^5*ep^5 +157773*mncx^6*ep^6 ; Fill mncPO(12) = +39916800 +120543840*mncx*ep +150917976*mncx^2*ep^2 +105258076*mncx^3*ep^3 +45995730*mncx^4*ep^4 +13339535*mncx^5*ep^5 +2637558*mncx^6*ep^6 ; Fill mncPO(13) = +479001600 +1486442880*mncx*ep +1931559552*mncx^2*ep^2 +1414014888*mncx^3*ep^3 +657206836*mncx^4*ep^4 +206070150*mncx^5*ep^5 +44990231*mncx^6*ep^6 ; Fill mncPO(14) = +6227020800 +19802759040*mncx*ep +26596717056*mncx^2*ep^2 +20313753096*mncx^3*ep^3 +9957703756*mncx^4*ep^4 +3336118786*mncx^5*ep^5 +790943153*mncx^6*ep^6 ; Fill mncPO(15) = +87178291200 +283465647360*mncx*ep +392156797824*mncx^2*ep^2 +310989260400*mncx^3*ep^3 +159721605680*mncx^4*ep^4 +56663366760*mncx^5*ep^5 +14409322928*mncx^6*ep^6 ; Fill mncPO(16) = +1307674368000 +4339163001600*mncx*ep +6165817614720*mncx^2*ep^2 +5056995703824*mncx^3*ep^3 +2706813345600*mncx^4*ep^4 +1009672107080*mncx^5*ep^5 +272803210680*mncx^6*ep^6 ; Fill mncPO(17) = +20922789888000 +70734282393600*mncx*ep +102992244837120*mncx^2*ep^2 +87077748875904*mncx^3*ep^3 +48366009233424*mncx^4*ep^4 +18861567058880*mncx^5*ep^5 +5374523477960*mncx^6*ep^6 ; Fill mncPO(18) = +355687428096000 +1223405590579200*mncx*ep +1821602444624640*mncx^2*ep^2 +1583313975727488*mncx^3*ep^3 +909299905844112*mncx^4*ep^4 +369012649234384*mncx^5*ep^5 +110228466184200*mncx^6*ep^6 ; Fill mncPO(19) = +6402373705728000 +22376988058521600*mncx*ep +34012249593822720*mncx^2*ep^2 +30321254007719424*mncx^3*ep^3 +17950712280921504*mncx^4*ep^4 +7551527592063024*mncx^5*ep^5 +2353125040549984*mncx^6*ep^6 ; Fill mncPO(20) = +121645100408832000 +431565146817638400*mncx*ep +668609730341153280*mncx^2*ep^2 +610116075740491776*mncx^3*ep^3 +371384787345228000*mncx^4*ep^4 +161429736530118960*mncx^5*ep^5 +52260903362512720*mncx^6*ep^6 ; Fill mncPO(21) = +2432902008176640000 +8752948036761600000*mncx*ep +13803759753640704000*mncx^2*ep^2 +12870931245150988800*mncx^3*ep^3 +8037811822645051776*mncx^4*ep^4 +3599979517947607200*mncx^5*ep^5 +1206647803780373360*mncx^6*ep^6 ; Fill mncPO(22) = +51090942171709440000 +186244810780170240000*mncx*ep +298631902863216384000*mncx^2*ep^2 +284093315901811468800*mncx^3*ep^3 +181664979520697076096*mncx^4*ep^4 +83637381699544802976*mncx^5*ep^5 +28939583397335447760*mncx^6*ep^6 ; Fill mncPO(23) = +1124000727777607680000 +4148476779335454720000*mncx*ep +6756146673770930688000*mncx^2*ep^2 +6548684852703068697600*mncx^3*ep^3 +4280722865357147142912*mncx^4*ep^4 +2021687376910682741568*mncx^5*ep^5 +720308216440924653696*mncx^6*ep^6 ; Fill mncPO(24) = +25852016738884976640000 +96538966652493066240000*mncx*ep +159539850276066860544000*mncx^2*ep^2 +157375898285941510732800*mncx^3*ep^3 +105005310755917452984576*mncx^4*ep^4 +50779532534302850198976*mncx^5*ep^5 +18588776355051949776576*mncx^6*ep^6 ; Fill mncPO(25) = +620448401733239439360000 +2342787216398718566400000*mncx*ep +3925495373278097719296000*mncx^2*ep^2 +3936561409138663118131200*mncx^3*ep^3 +2677503356427960382362624*mncx^4*ep^4 +1323714091579185857760000*mncx^5*ep^5 +496910165055549644836800*mncx^6*ep^6 ; Fill mncPO(26) = +15511210043330985984000000 +59190128811701203599360000*mncx*ep +100480171548351161548800000*mncx^2*ep^2 +102339530601744675672576000*mncx^3*ep^3 +70874145319837672677196800*mncx^4*ep^4 +35770355645907606826362624*mncx^5*ep^5 +13746468217967926978680000*mncx^6*ep^6 ; Fill mncPO(27) = +403291461126605635584000000 +1554454559147562279567360000*mncx*ep +2671674589068831403868160000*mncx^2*ep^2 +2761307967193712729035776000*mncx^3*ep^3 +1945067308917524165279692800*mncx^4*ep^4 +1000903392113435450162625024*mncx^5*ep^5 +393178529313073708272042624*mncx^6*ep^6 ; Fill mncPO(28) = +10888869450418352160768000000 +42373564558110787183902720000*mncx*ep +73689668464006010184007680000*mncx^2*ep^2 +77226989703299075087834112000*mncx^3*ep^3 +55278125307966865191587481600*mncx^4*ep^4 +28969458895980281319670568448*mncx^5*ep^5 +11616723683566425573507775872*mncx^6*ep^6 ; Fill mncPO(29) = +304888344611713860501504000000 +1197348677077520393310044160000*mncx*ep +2105684281550279072336117760000*mncx^2*ep^2 +2236045380156380112643362816000*mncx^3*ep^3 +1625014498326371300452283596800*mncx^4*ep^4 +866422974395414742142363398144*mncx^5*ep^5 +354237722035840197377888292864*mncx^6*ep^6 ; Fill mncPO(30) = +8841761993739701954543616000000 +35027999979859805266492784640000*mncx*ep +62262192842035613491057459200000*mncx^2*ep^2 +66951000306085302338993639424000*mncx^3*ep^3 +49361465831621147825759587123200*mncx^4*ep^4 +26751280755793398822580822142976*mncx^5*ep^5 +11139316913434780466101123891200*mncx^6*ep^6 ; Fill mncPO(31) = +265252859812191058636308480000000 +1059681761389533859949327155200000*mncx*ep +1902893785240928209998216560640000*mncx^2*ep^2 +2070792202024594683660866641920000*mncx^3*ep^3 +1547794975254719737111781253120000*mncx^4*ep^4 +851899888505423112503184251412480*mncx^5*ep^5 +360930788158836812805614538878976*mncx^6*ep^6 ; Fill mncPO(32) = +8222838654177922817725562880000000 +33115387462887740717065450291200000*mncx*ep +60049389103858308369894040535040000*mncx^2*ep^2 +66097452048003363403485082460160000*mncx^3*ep^3 +50052436434920906534126085488640000*mncx^4*ep^4 +27956691518922836224710493046906880*mncx^5*ep^5 +12040754321429364309477234956660736*mncx^6*ep^6 ; Fill mncPO(33) = +263130836933693530167218012160000000 +1067915237466585625763819972198400000*mncx*ep +1954695838786353608553674747412480000*mncx^2*ep^2 +2175167854639965937281416679260160000*mncx^3*ep^3 +1667775417965472372495519818096640000*mncx^4*ep^4 +944666565040451665724861862989660160*mncx^5*ep^5 +413260829804662494127982011660050432*mncx^6*ep^6 ; Fill mncPO(34) = +8683317618811886495518194401280000000 +35504333673331019180373277094707200000*mncx*ep +65572877917416254708035086636810240000*mncx^2*ep^2 +73735235041905229538840425162997760000*mncx^3*ep^3 +57211756647500554229633570676449280000*mncx^4*ep^4 +32841772064300377341415961296755425280*mncx^5*ep^5 +14582273948594313971948268247771324416*mncx^6*ep^6 ; Fill mncPO(35) = +295232799039604140847618609643520000000 +1215830662512066538628209615621324800000*mncx*ep +2264982182865483679253566222746255360000*mncx^2*ep^2 +2572570869342194059028609542178734080000*mncx^3*ep^3 +2018934961056924073346381828162273280000*mncx^4*ep^4 +1173832006833713383837776254766133739520*mncx^5*ep^5 +528639086316507052387657081720980455424*mncx^6*ep^6 ; Fill mncPO(36) = +10333147966386144929666651337523200000000 +42849305986961932992834955156389888000000*mncx*ep +80490207062803995312503027411740262400000*mncx^2*ep^2 +92304962609842275745254900199001948160000*mncx^3*ep^3 +73235294506334536626151973527858298880000*mncx^4*ep^4 +43103055200236892507668550744976954163200*mncx^5*ep^5 +19676200027911460217405774115000449679360*mncx^6*ep^6 ; Fill mncPO(37) = +371993326789901217467999448150835200000000 +1552908163497015732671725036967559168000000*mncx*ep +2940496760247905764242943941979039334400000*mncx^2*ep^2 +3403468861017125922141679434575810396160000*mncx^3*ep^3 +2728775564837885594286725947201900707840000*mncx^4*ep^4 +1624945281714862666902219800347028648755200*mncx^5*ep^5 +751446256205049460334276418884993142620160*mncx^6*ep^6 ; Fill mncPO(38) = +13763753091226345046315979581580902400000000 +57829595376179483326321825815950524416000000*mncx*ep +110351288292669529009660650890192014540800000*mncx^2*ep^2 +128868844617881564883485083021284023992320000*mncx^3*ep^3 +104368164760018892910750539481046136586240000*mncx^4*ep^4 +62851750988287804269668858560041960711782400*mncx^5*ep^5 +29428456761301692699270447299091774925701120*mncx^6*ep^6 ; Fill mncPO(39) = +523022617466601111760007224100074291200000000 +2211288377386046711446545360587700830208000000*mncx*ep +4251178550497621585693426559643247076966400000*mncx^2*ep^2 +5007367383772168994582093805698984926248960000*mncx^3*ep^3 +4094859105498599495492005583301037214269440000*mncx^4*ep^4 +2492734702314955455158167164762640643633971200*mncx^5*ep^5 +1181133107917752126841945855925529407888424960*mncx^6*ep^6 ; Fill mncPO(40) = +20397882081197443358640281739902897356800000000 +86763269335522422858175276287020406669312000000*mncx*ep +168007251846793288553490181186674336831897600000*mncx^2*ep^2 +199538506517612212374395084981903659200675840000*mncx^3*ep^3 +164706872498217549318770311554439436282757120000*mncx^4*ep^4 +101311512495781862246660525009044022315994316800*mncx^5*ep^5 +48556925911107288401994055545858287551282544640*mncx^6*ep^6 ; *--#] mncPO-pos : mncPO positivevalues *--#[ mncPOINV-pos : mncPOINV positive values * Fill mncPOINV(1) = +1 ; Fill mncPOINV(2) = +1 -mncx*ep +mncx^2*ep^2 -mncx^3*ep^3 +mncx^4*ep^4 -mncx^5*ep^5 +mncx^6*ep^6 ; Fill mncPOINV(3) = +1/2 -3/4*mncx*ep +7/8*mncx^2*ep^2 -15/16*mncx^3*ep^3 +31/32*mncx^4*ep^4 -63/64*mncx^5*ep^5 +127/128*mncx^6*ep^6 ; Fill mncPOINV(4) = +1/6 -11/36*mncx*ep +85/216*mncx^2*ep^2 -575/1296*mncx^3*ep^3 +3661/7776*mncx^4*ep^4 -22631/46656*mncx^5*ep^5 +137845/279936*mncx^6*ep^6 ; Fill mncPOINV(5) = +1/24 -25/288*mncx*ep +415/3456*mncx^2*ep^2 -5845/41472*mncx^3*ep^3 +76111/497664*mncx^4*ep^4 -952525/5971968*mncx^5*ep^5 +11679655/71663616*mncx^6*ep^6 ; Fill mncPOINV(6) = +1/120 -137/7200*mncx*ep +12019/432000*mncx^2*ep^2 -874853/25920000*mncx^3*ep^3 +58067611/1555200000*mncx^4*ep^4 -3673451957/93312000000*mncx^5*ep^5 +226576032859/5598720000000*mncx^6*ep^6 ; Fill mncPOINV(7) = +1/720 -49/14400*mncx*ep +13489/2592000*mncx^2*ep^2 -336581/51840000*mncx^3*ep^3 +68165041/9331200000*mncx^4*ep^4 -483900263/62208000000*mncx^5*ep^5 +270127056529/33592320000000*mncx^6*ep^6 ; Fill mncPOINV(8) = +1/5040 -121/235200*mncx*ep +726301/889056000*mncx^2*ep^2 -129973303/124467840000*mncx^3*ep^3 +187059457981/156829478400000*mncx^4*ep^4 -28139924320343/21956126976000000*mncx^5*ep^5 +36845364451242061/27664719989760000000*mncx^6*ep^6 ; Fill mncPOINV(9) = +1/40320 -761/11289600*mncx*ep +3144919/28449792000*mncx^2*ep^2 -1149858589/7965941760000*mncx^3*ep^3 +3355156783231/20074173235200000*mncx^4*ep^4 -339302688554687/1873589501952000000*mncx^5*ep^5 +2678744365563671119/14164336634757120000000*mncx^6*ep^6 ; Fill mncPOINV(10) = +1/362880 -7129/914457600*mncx*ep +30300391/2304433152000*mncx^2*ep^2 -101622655189/5807171543040000*mncx^3*ep^3 +300222042894631/14634072288460800000*mncx^4*ep^4 -826117151879597149/36877862166921216000000*mncx^5*ep^5 +2184117445022203447471/92932212660641464320000000*mncx^6*ep^6 ; Fill mncPOINV(11) = +1/3628800 -7381/9144576000*mncx*ep +32160403/23044331520000*mncx^2*ep^2 -21945415349/11614343086080000*mncx^3*ep^3 +327873266234371/146340722884608000000*mncx^4*ep^4 -908741214970658641/368778621669212160000000*mncx^5*ep^5 +2413120231194809425003/929322126606414643200000000*mncx^6*ep^6 ; Fill mncPOINV(12) = +1/39916800 -83711/1106493696000*mncx*ep +4102360483/30672005253120000*mncx^2*ep^2 -31276937512951/170045597123297280000*mncx^3*ep^3 +5194481903600608411/23568319761289003008000000*mncx^4*ep^4 -159443775809313077987411/653313823782931163381760000000*mncx^5*ep^5 +4676788004935176736296015403/18109859195262851848942387200000000*mncx^6* ep^6 ; Fill mncPOINV(13) = +1/479001600 -86021/13277924352000*mncx*ep +4301068993/368064063037440000*mncx^2*ep^2 -33264031387717/2040547165479567360000*mncx^3*ep^3 +5578681466128739761/282819837135468036096000000*mncx^4*ep^4 -172330529996070466835321/7839765885395173960581120000000*mncx^5*ep^5 +5074871529226099514685606913/217318310343154222187308646400000000*mncx^6 *ep^6 ; Fill mncPOINV(14) = +1/6227020800 -1145993/2243969215488000*mncx*ep +758647585777/808636746493255680000*mncx^2*ep^2 -77287019174361937/58280067593261923368960000*mncx^3*ep^3 +170044702211669500782121/105009025789539333526192128000000*mncx^4*ep^4 -68698758619138470404367234173/37841052533518394229498595246080000000* mncx^5*ep^5 +26399765160034818571989179349406177/136364016909786885445421137828773888\ 00000000*mncx^6*ep^6 ; Fill mncPOINV(15) = +1/87178291200 -1171733/31415569016832000*mncx*ep +112686856171/1617273492986511360000*mncx^2*ep^2 -81347802723340093/815920946305666927165440000*mncx^3*ep^3 +180514164422163370751221/1470126361053550669366689792000000*mncx^4*ep^4 -10477884744480707938214808959/75682105067036788458997190492160000000* mncx^5*ep^5 +28287670433295352528296723627638797/190909623673701639623589592960283443\ 200000000*mncx^6*ep^6 ; Fill mncPOINV(16) = +1/1307674368000 -1195757/471233535252480000*mncx*ep +476696711/99016744468561920000*mncx^2*ep^2 -17055178843123409/2447762838917000781496320000*mncx^3*ep^3 +190757504835343290196621/22051895415803260040500346880000000*mncx^4*ep^4 -11132564501075606110169612231/1135231576005551826884957857382400000000* mncx^5*ep^5 +6031962308062447011326345395460321/5727288710211049188707687788808503296\ 00000000*mncx^6*ep^6 ; Fill mncPOINV(17) = +1/20922789888000 -2436559/15079473128079360000*mncx*ep +96568406789/310516510653410181120000*mncx^2*ep^2 -142531324182321979/313313643381376100031528960000*mncx^3*ep^3 +3212628164810309981747311/5645285226445634570368088801280000000*mncx^4* ep^4 -376915326274973740257971537677/581238566914842535365098422979788800000000 *mncx^5*ep^5 +81962999787375055541354912877997039/117294872785122287384733445914798147\ 502080000000*mncx^6*ep^6 ; Fill mncPOINV(18) = +1/355687428096000 -42142223/4357967734014935040000*mncx*ep +28776062218037/1525567616840204219842560000*mncx^2*ep^2 -729291672694244960123/26168268808855913250733330268160000*mncx^3*ep^3 +281462294311726805677013376031/80154977457654193641791234611190169600000\ 00*mncx^4*ep^4 -564145222241140781833967990767603949/14029686014368128821510003376465837\ 765427200000000*mncx^5*ep^5 +10461164856476842638038161189836649078663547/240653112241754467740880813\ 276977714544308859699200000000*mncx^6*ep^6 ; Fill mncPOINV(19) = +1/6402373705728000 -14274301/26147806404089610240000*mncx*ep +29608882035581/27460217103123675957166080000*mncx^2*ep^2 -50500501069854396349/31401922570627095900879996321792000*mncx^3*ep^3 +294352799712312489617077371031/14427895942377754855522422230014230528000\ 0000*mncx^4*ep^4 -65863120942796227591592510480739821/280593720287362576430200067529316755\ 30854400000000*mncx^5*ep^5 +88208355135479668752967444674123414750223/346540481628126433546868371118\ 84790894380475796684800000*mncx^6*ep^6 ; Fill mncPOINV(20) = +1/121645100408832000 -275295799/9439358111876349296640000*mncx*ep +1568274265798307/26907089872903613341457448960000*mncx^2*ep^2 -1794683268312579709384043/20461649756633468824492910003261276160000* mncx^3*ep^3 +40009517970859535080774906095604951/357248987150256164200042141613160061\ 961502720000000*mncx^4*ep^4 -170864658958309558725823727346322640908759/13200778773986545574588597183\ 17620008155187930726400000000*mncx^5*ep^5 +545107754958038941477256969841397265941063458146891/38720342868353865808\ 30089611201274450551405153503756576358400000000*mncx^6*ep^6 ; Fill mncPOINV(21) = +1/2432902008176640000 -11167027/7551486489501079437312000*mncx*ep +11256448518043769/3766992582206505867804042854400000*mncx^2*ep^2 -9279131712715653650968723/2046164975663346882449291000326127616000000* mncx^3*ep^3 +41629602590344731254886672725930611/714497974300512328400084283226320123\ 9230054400000000*mncx^4*ep^4 -7142239112579651595742062778098987074987/1056062301918923645967087774654\ 096006524150344581120000000*mncx^5*ep^5 +571294651960644279934630828168658674310905345370231/77440685736707731616\ 601792224025489011028103070075131527168000000000*mncx^6*ep^6 ; Fill mncPOINV(22) = +1/51090942171709440000 -18858053/264302027132537780305920000*mncx*ep +80676574383943103/553747909584356362567194299596800000*mncx^2*ep^2 -9577241336253249489726083/42969464488930284531435111006848679936000000* mncx^3*ep^3 +6174587158661922297334017385371973/2143493922901536985200252849678960371\ 7690163200000000*mncx^4*ep^4 -111696754789037742399995916535691943099157/33265962510446094847963264901\ 6040242055107358543052800000000*mncx^5*ep^5 +597296825451676635924546421568548733116332437242151/16262544004708623639\ 48637636704535269231590164471577762070528000000000*mncx^6*ep^6 ; Fill mncPOINV(23) = +1/1124000727777607680000 -6364399/1938214865638610388910080000*mncx*ep +82494882923667143/12182454010855839976478274591129600000*mncx^2*ep^2 -9868213987506291289829963/945328218756466259691572442150670958592000000* mncx^3*ep^3 +6398344963543032449814395864411773/4715686630383381367440556269293712817\ 89183590400000000*mncx^4*ep^4 -116210352073359830867133385439115668950093/73185117522981408665519182783\ 52885325212361887947161600000000*mncx^5*ep^5 +623120053293078163170149467651030900158655068872591/35777596810358972006\ 870028007499775923094983618374710765551616000000000*mncx^6*ep^6 ; Fill mncPOINV(24) = +1/25852016738884976640000 -444316699/3075946991768474687200296960000*mncx*ep +44570695662918553607/148223917950083004993811166950273843200000*mncx^2* ep^2 -123525135034106281845251414461/26454159406502827457834932378388591172334\ 3872000000*mncx^3*ep^3 +264591239933345908907390540426325365899/43359680905230948543794931799963\ 8620563548468255129600000000*mncx^4*ep^4 -776713959740478684849561077289313689586845388571/10834023934084030762272\ 43586991318834832866105871976452482662400000000*mncx^5*ep^5 +96041208895558385773482948005826382154738052851832630885359/ 1218164720524162610937517301815379439097517152218903519958149931487723520\ 00000000*mncx^6*ep^6 ; Fill mncPOINV(25) = +1/620448401733239439360000 -269564591/44293636681466035495684276224000*mncx*ep +45472764736767046157/3557374030801992119851468006806572236800000*mncx^2* ep^2 -126906684898093000128113947991/63489982575606785898803837708132618813602\ 52928000000*mncx^3*ep^3 +1912807200725066844334929443722155255943/7284426392078799355357548542393\ 9288254676142666861772800000000*mncx^4*ep^4 -53677524641216006737724172489720819744162618911/173344382945344492196358\ 9739186110135732585769395162323972259840000000*mncx^5*ep^5 +99813356898970334531896288222195044055013592737697579224909/ 2923595329257990266250041524356910653834041165325368447899559835570536448\ 000000000*mncx^6*ep^6 ; Fill mncPOINV(26) = +1/15511210043330985984000000 -34052522467/138417614629581360924013363200000000*mncx*ep +5793490591633676917801/11116793846256225374535837521270538240000000000* mncx^2*ep^2 -81384656370757013035663184180567/992030977743856029668809964189572168962\ 53952000000000000*mncx^3*ep^3 +176122096932442395019595242667343669886849/16259880339461605703923099424\ 9864482711330675595673600000000000000*mncx^4*ep^4 -1446748397713984600368618807470929295440186517370209/1128544159800419871\ 070045403115957119617568860283308804669440000000000000000*mncx^5*ep^5 +8090725701340520405271382597523589771894308313467672735828693401/ 5710147127457012238769612352259591120769611651026110249803827803848704000\ 000000000000000*mncx^6*ep^6 ; Fill mncPOINV(27) = +1/403291461126605635584000000 -34395742267/3598857980369115384024347443200000000*mncx*ep +5899738289669258497201/289036640002661859737931775553033994240000000000* mncx^2*ep^2 -83409563366589638003220811960367/257928054213402567713890590689288763930\ 2602752000000000000*mncx^3*ep^3 +1269661867514370193728286786947387535922143/2959298221782012238114004095\ 3475335853462182958412595200000000000000*mncx^4*ep^4 -4485502890553923346111651037532362873187789797454427/8802644446443274994\ 3463541443044655330170371102098086764216320000000000000000*mncx^5*ep^5 +8381693734884639563224191438763431636799403704468574686255012801/ 1484638253138823182080099211587493691400099029266788664948995229000663040\ 00000000000000000*mncx^6*ep^6 ; Fill mncPOINV(28) = +1/10888869450418352160768000000 -312536252003/874522489229695038317916428697600000000*mncx*ep +54027306066201893389609/702359035206468319163174214593872606003200000000\ 00*mncx^2*ep^2 -6916882722942792550203844435294127/5640886545647114155902787218374745267\ 154792218624000000000000*mncx^3*ep^3 +105781863112692028426923791152458954384121183/64719852110372607647553269\ 565250559511521794130048345702400000000000000*mncx^4*ep^4 -10124450547451531665251301003609713279538398648943034649/ 5197873519180289451411578658670343852591230243207789925340209479680000000\ 000000000*mncx^5*ep^5 +6321066054179278690866136146657264317464969772671961192473023910729/ 2922213473653145669288259278167663832782814919305820129219107309242005061\ 632000000000000000000*mncx^6*ep^6 ; Fill mncPOINV(29) = +1/304888344611713860501504000000 -315404588903/24486629698431461072901660003532800000000*mncx*ep +54931992686981698810309/196660529857811129365688780086284329680896000000\ 0000*mncx^2*ep^2 -1010635169222484615218019977199461/2256354618258845662361114887349898106\ 8619168874496000000000000*mncx^3*ep^3 +108680705261010625358435939397997327030532083/18121558590904330141314915\ 47827015666322610235641353679667200000000000000*mncx^4*ep^4 -10436183424669712573258978534871152798761441249245797349/ 1455404585370481046395242024427696278725544468098181179095258654310400000\ 00000000000*mncx^5*ep^5 +6530607484264318239070044916372416367692549786298717916415436057429/ 8182197726228807874007125978869458731791881774056296361813500465877614172\ 5696000000000000000000*mncx^6*ep^6 ; Fill mncPOINV(30) = +1/8841761993739701954543616000000 -9227046511387/20593255576380858762310296062971084800000000*mncx*ep +46938861633377181563318269/479635366270215563409978365752438851658737254\ 40000000000*mncx^2*ep^2 -25186927017635217446536551133584958729/159587675075673461892043169863972\ 32829194034380722405376000000000000*mncx^3*ep^3 +78890646478256977372499817524180507318888060599123/371693988370268760273\ 70128729720544557277340612164915885352209612800000000000000*mncx^4*ep^4 -220394091880767057381928499928284371416460564271231904088227601/ 8657085888686975513843729395688454248908700080473386830091375281109030928\ 3840000000000000000*mncx^5*ep^5 +400846187516914154875914463903897327820615883520726692055932081171823277\ 4109/14114189871322798085914817932007871078118996653282259744392959396270\ 27196088509806936064000000000000000000*mncx^6*ep^6 ; Fill mncPOINV(31) = +1/265252859812191058636308480000000 -9304682830147/617797667291425762869308881889132544000000000*mncx*ep +47661242955539172992975989/143890609881064669022993509725731655497621176\ 3200000000000*mncx^2*ep^2 -25715533224862937981129332151160709249/478763025227020385676129509591916\ 984875821031421672161280000000000000*mncx^3*ep^3 +80887105812785807182912885219853936646131104810363/111508196511080628082\ 1103861891616336718320218364947476560566288384000000000000000*mncx^4*ep^4 -226673869011222345191985022310524244322560444045040215307537481/ 2597125766606092654153118818706536274672610024142016049027412584332709278\ 515200000000000000000*mncx^5*ep^5 +413164874841296575681906255716369228175069979546000212222776589085717687\ 9029/42342569613968394257744453796023613234356989959846779233178878188810\ 815882655294208081920000000000000000000*mncx^6*ep^6 ; Fill mncPOINV(32) = +1/8222838654177922817725562880000000 -290774257297357/593703558267060158117405835495456374784000000000*mncx*ep +46479693768075341170975445029/428664515896679755486399964823927174892963\ 24637491200000000000*mncx^2*ep^2 -781556503107229568390876511159818552568559/44214770782068309360000480082\ 7836765789503114759574096057466880000000000000*mncx^3*ep^3 +76521255941455275592333629944010738538900877943907253323/ 3192384995653400474537578644877822973797563399792305441352141291565508198\ 4000000000000000*mncx^4*ep^4 -6667705282222096185300565038664400439373549415795418232677816898893031/ 2304958677882854107587952889232422602531968466303538110272905138501002413\ 385094214451200000000000000000*mncx^5*ep^5 +377556125228009940562091755613952065421188786959973299420548922518209727\ 5036627133349/11649547782572666665636314305404667771607764719807658217286\ 58963444626575362564967578131202435973120000000000000000000*mncx^6*ep^6 ; Fill mncPOINV(33) = +1/263130836933693530167218012160000000 -586061125622639/37997027729091850119513973471709207986176000000000*mncx* ep +188563440970824224217342974191/54869058034775008702259195497462678386299\ 29553598873600000000000*mncx^2*ep^2 -6374011091027611713181285626046594885588997/1131898132020948719616012290\ 11926212042112797378450968590711521280000000000000*mncx^3*ep^3 +1253103527804771871114914850704998968323017858623755794393/ 1634501117774541042963240266177445362584352460693660385972296341281540197\ 5808000000000000000*mncx^4*ep^4 -219021337829810613341650082757499547365333779437895662406850111446001517/ 2360277686152042606170063758574000744992735709494823024919454861825026471\ 306336475598028800000000000000000*mncx^5*ep^5 +248554426877018194483796891687105191326133831297962684645980033038470417\ 598667492069911/238582738587088213312231716974687595962527021461660840290\ 0293557134595226342533053600012702588872949760000000000000000000*mncx^6* ep^6 ; Fill mncPOINV(34) = +1/8683317618811886495518194401280000000 -53676090078349/113991083187275550358541920415127623958528000000000*mncx* ep +191147113675074393547229862991/18106789151475752871745534514162683867478\ 7675268762828800000000000*mncx^2*ep^2 -6493501663928207284923763331891522805938597/3735263835669130774732840557\ 393564997389722313488881963493480202240000000000000*mncx^3*ep^3 +1281518216016642673897384956891070655754678612565673196793/ 5393853688655985441778692878385569696528363120289079273708577926229082652\ 01664000000000000000*mncx^4*ep^4 -224629088844679436707044990778140173948721827021389476075843741063887117/ 7788916364301740600361210403294202458476027841332915982234201044022587355\ 3109103694734950400000000000000000*mncx^5*ep^5 +255435053228138403128470654509381028350984604020895179028694925583796862\ 430658515774711/787323037337391103930364666016469066676339170823480772957\ 09687385441642469303590768800419185432807342080000000000000000000*mncx^6* ep^6 ; Fill mncPOINV(35) = +1/295232799039604140847618609643520000000 -54062195834749/3875696828367368712190425294114339214589952000000000*mncx *ep +193672834401940297285176238591/61563083115017559763934817348153125149427\ 80959137936179200000000000*mncx^2*ep^2 -6611010257989610727955230791776284831303797/1269989704127504463409165789\ 51381209911250558658621986758778326876160000000000000*mncx^3*ep^3 +1309596256295164289625430756003219542652775000893320755593/ 1833910254143035050204755578651093696819643460898286953060916494917888101\ 6856576000000000000000*mncx^4*ep^4 -230191158028949416073834042540087090094585156318457665222350343814884317/ 2648231563862591804122811537120028835881849466053191433959628354967679700\ 805709525620988313600000000000000000*mncx^5*ep^5 +262278669329565080577541157375092806300683649718885554909323049217499202\ 181779758942311/267689832694712975336323986445599482669955318079983462805\ 4129371105015843956322086139214252304715449630720000000000000000000* mncx^6*ep^6 ; Fill mncPOINV(36) = +1/10333147966386144929666651337523200000000 -54437269998109/135649388992857904926664885294001872510648320000000000* mncx*ep +28020487719351088554569096233/307815415575087798819674086740765625747139\ 04795689680896000000000000*mncx^2*ep^2 -6726617628860633132194043822000226660155477/4444963964446265621932080263\ 298342346893769553051769536557241440665600000000000000*mncx^3*ep^3 +1337349041568427108208504105948050572191945009309584705513/ 6418685889500622675716644525278827938868752113144004335713207732212608355\ 89980160000000000000000*mncx^4*ep^4 -235708813830701748331660980065818578642451649931134784063493088815524797/ 9268810473519071314429840379920100925586473131186170018858699242386878952\ 8199833396734590976000000000000000000*mncx^5*ep^5 +269086107362662971607704557753188335966759017341527797426919736935809337\ 701066139462151/936914414431495413677133952559598189344843613279942119818\ 94527988675554538471273014872498830665040737075200000000000000000000* mncx^6*ep^6 ; Fill mncPOINV(37) = +1/371993326789901217467999448150835200000000 -54801925434709/4883378003742884577359935870584067410383339520000000000* mncx*ep +28365922323001895565692364433/110813549607031607575082671226675625268970\ 0572644828512256000000000000*mncx^2*ep^2 -6840399294542448499145530506469847851081277/1600187027200655623895548894\ 78740324488175703909863703316060691863961600000000000000*mncx^3*ep^3 +1364787318272393902310082315639579768613532772621310625713/ 2310726920220224163257992029100378057992750760731841560856754783596539008\ 1239285760000000000000000*mncx^4*ep^4 -241183262100220140849575649035124968298858892399689742143012614029778597/ 3336771770466865673194742536771236333211130327227021206789131727259276423\ 015194002282445275136000000000000000000*mncx^5*ep^5 +275858164018779108255860951501407989498653796590642496343098766635251225\ 077224664127551/337289189195338348923768222921455348164143700780779163134\ 8203007592319963384965828535409957903941466534707200000000000000000000* mncx^6*ep^6 ; Fill mncPOINV(38) = +1/13763753091226345046315979581580902400000000 -2040798836801833/6685344487124008986405752206829588284814791802880000000\ 000*mncx*ep +39296045464550797787239457431177/561303872824497201850066254564480044674\ 91403106178498631303168000000000000*mncx^2*ep^2 -352161234046208215339252267574509136702023691081/29990081190854079447357\ 0581220365445283083865415414068070531622324454136217600000000000000* mncx^3*ep^3 +2608684498588375105517626756450359829025314345805903633658883393/ 1602349481944936549073231791722793647371928150639061097268636868732627063\ 281683538452152320000000000000000*mncx^4*ep^4 -171013050661720159566906093714710194318958438162996619791883595630791538\ 85873129/8561243452292523517171314326549614651700120853307180048661925366\ 808910708761138659914476119513706266624000000000000000000*mncx^5*ep^5 +725063001035943052469479181619316097777903710198896844188251120449343750\ 417133885707805597715159/320194958669810512763942477217493534214642269186\ 7684368272132390570951849184846348139270834635216735174966551905304576000\ 00000000000000000*mncx^6*ep^6 ; Fill mncPOINV(39) = +1/523022617466601111760007224100074291200000000 -2053580969474233/2540430905107123414834185838595243548229620885094400000\ 00000*mncx*ep +39749780674985882178980437798777/213295471673308936703025176734502416976\ 4673318034782947989520384000000000000*mncx^2*ep^2 -357750190719359398209347777918099374415101893881/11396230852524550189995\ 682086373886920757186885785734586680201648329257176268800000000000000* mncx^3*ep^3 +2658985413003238910771173525609793878940548365941169558772311793/ 6088928031390758886478280808546615860013326972428432169620820101183982840\ 4703974461181788160000000000000000*mncx^4*ep^4 -174751676137248367434629126308906747211036344655198215819163300076987902\ 67618329/3253272511871158936525099444088853567646045924256728418491531639\ 38738606932923269076750092541520838131712000000000000000000*mncx^5*ep^5 +742262484176094563006431126693903121562516373538281131135537536308520808\ 714695198186793014024359/121674084294527994850298141342647543001564062290\ 9720059943410308416961702690241612292922917161382359366487289724015738880\ 0000000000000000000*mncx^6*ep^6 ; Fill mncPOINV(40) = +1/20397882081197443358640281739902897356800000000 -2066035355155033/9907680529917781317853324770521449838095521451868160000\ 000000*mncx*ep +40194562866176681556204641717977/831852339525904853141798189264559426208\ 22259403356534971591294976000000000000*mncx^2*ep^2 -363256775189631187172928799970374912083283051481/44445300324845745740983\ 1601368581589909530288545643648880527864284841029874483200000000000000* mncx^3*ep^3 +2708750952776367511754929445487032491402381958608770810738224593/ 2374681932242395965726529515333180185405197519247088546152119839461753307\ 783455003986089738240000000000000000*mncx^4*ep^4 -178462617335950615774363407395022425191767023902592242501363486714297999\ 54676729/1268776279629751985244788783194652891381957910460124083211697339\ 3610805670384007493993253609119312687136768000000000000000000*mncx^5*ep^5 +759376829623578102586033668224832815298091263145655117559915634200781766\ 870276142570887835970759/474528928748659179916162751236325417706099842934\ 7908233779300202826150640491942287942399376929391201529300429923661381632\ 00000000000000000000*mncx^6*ep^6 ; *--#] mncPOINV-pos : mncPOINV positive values *--#[ mncPOINV-neg : mncPOINV negative values * Fill mncPOINV(0) = +1 ; Fill mncPOINV(-1) = -1 +mncx*ep ; Fill mncPOINV(-2) = +2 -3*mncx*ep +mncx^2*ep^2 ; Fill mncPOINV(-3) = -6 +11*mncx*ep -6*mncx^2*ep^2 +mncx^3*ep^3 ; Fill mncPOINV(-4) = +24 -50*mncx*ep +35*mncx^2*ep^2 -10*mncx^3*ep^3 +mncx^4*ep^4 ; Fill mncPOINV(-5) = -120 +274*mncx*ep -225*mncx^2*ep^2 +85*mncx^3*ep^3 -15*mncx^4*ep^4 +mncx^5*ep^5 ; Fill mncPOINV(-6) = +720 -1764*mncx*ep +1624*mncx^2*ep^2 -735*mncx^3*ep^3 +175*mncx^4*ep^4 -21*mncx^5*ep^5 +mncx^6*ep^6 ; Fill mncPOINV(-7) = -5040 +13068*mncx*ep -13132*mncx^2*ep^2 +6769*mncx^3*ep^3 -1960*mncx^4*ep^4 +322*mncx^5*ep^5 -28*mncx^6*ep^6 ; Fill mncPOINV(-8) = +40320 -109584*mncx*ep +118124*mncx^2*ep^2 -67284*mncx^3*ep^3 +22449*mncx^4*ep^4 -4536*mncx^5*ep^5 +546*mncx^6*ep^6 ; Fill mncPOINV(-9) = -362880 +1026576*mncx*ep -1172700*mncx^2*ep^2 +723680*mncx^3*ep^3 -269325*mncx^4*ep^4 +63273*mncx^5*ep^5 -9450*mncx^6*ep^6 ; Fill mncPOINV(-10) = +3628800 -10628640*mncx*ep +12753576*mncx^2*ep^2 -8409500*mncx^3*ep^3 +3416930*mncx^4*ep^4 -902055*mncx^5*ep^5 +157773*mncx^6*ep^6 ; Fill mncPOINV(-11) = -39916800 +120543840*mncx*ep -150917976*mncx^2*ep^2 +105258076*mncx^3*ep^3 -45995730*mncx^4*ep^4 +13339535*mncx^5*ep^5 -2637558*mncx^6*ep^6 ; Fill mncPOINV(-12) = +479001600 -1486442880*mncx*ep +1931559552*mncx^2*ep^2 -1414014888*mncx^3*ep^3 +657206836*mncx^4*ep^4 -206070150*mncx^5*ep^5 +44990231*mncx^6*ep^6 ; Fill mncPOINV(-13) = -6227020800 +19802759040*mncx*ep -26596717056*mncx^2*ep^2 +20313753096*mncx^3*ep^3 -9957703756*mncx^4*ep^4 +3336118786*mncx^5*ep^5 -790943153*mncx^6*ep^6 ; Fill mncPOINV(-14) = +87178291200 -283465647360*mncx*ep +392156797824*mncx^2*ep^2 -310989260400*mncx^3*ep^3 +159721605680*mncx^4*ep^4 -56663366760*mncx^5*ep^5 +14409322928*mncx^6*ep^6 ; Fill mncPOINV(-15) = -1307674368000 +4339163001600*mncx*ep -6165817614720*mncx^2*ep^2 +5056995703824*mncx^3*ep^3 -2706813345600*mncx^4*ep^4 +1009672107080*mncx^5*ep^5 -272803210680*mncx^6*ep^6 ; Fill mncPOINV(-16) = +20922789888000 -70734282393600*mncx*ep +102992244837120*mncx^2*ep^2 -87077748875904*mncx^3*ep^3 +48366009233424*mncx^4*ep^4 -18861567058880*mncx^5*ep^5 +5374523477960*mncx^6*ep^6 ; Fill mncPOINV(-17) = -355687428096000 +1223405590579200*mncx*ep -1821602444624640*mncx^2*ep^2 +1583313975727488*mncx^3*ep^3 -909299905844112*mncx^4*ep^4 +369012649234384*mncx^5*ep^5 -110228466184200*mncx^6*ep^6 ; Fill mncPOINV(-18) = +6402373705728000 -22376988058521600*mncx*ep +34012249593822720*mncx^2*ep^2 -30321254007719424*mncx^3*ep^3 +17950712280921504*mncx^4*ep^4 -7551527592063024*mncx^5*ep^5 +2353125040549984*mncx^6*ep^6 ; Fill mncPOINV(-19) = -121645100408832000 +431565146817638400*mncx*ep -668609730341153280*mncx^2*ep^2 +610116075740491776*mncx^3*ep^3 -371384787345228000*mncx^4*ep^4 +161429736530118960*mncx^5*ep^5 -52260903362512720*mncx^6*ep^6 ; Fill mncPOINV(-20) = +2432902008176640000 -8752948036761600000*mncx*ep +13803759753640704000*mncx^2*ep^2 -12870931245150988800*mncx^3*ep^3 +8037811822645051776*mncx^4*ep^4 -3599979517947607200*mncx^5*ep^5 +1206647803780373360*mncx^6*ep^6 ; Fill mncPOINV(-21) = -51090942171709440000 +186244810780170240000*mncx*ep -298631902863216384000*mncx^2*ep^2 +284093315901811468800*mncx^3*ep^3 -181664979520697076096*mncx^4*ep^4 +83637381699544802976*mncx^5*ep^5 -28939583397335447760*mncx^6*ep^6 ; Fill mncPOINV(-22) = +1124000727777607680000 -4148476779335454720000*mncx*ep +6756146673770930688000*mncx^2*ep^2 -6548684852703068697600*mncx^3*ep^3 +4280722865357147142912*mncx^4*ep^4 -2021687376910682741568*mncx^5*ep^5 +720308216440924653696*mncx^6*ep^6 ; Fill mncPOINV(-23) = -25852016738884976640000 +96538966652493066240000*mncx*ep -159539850276066860544000*mncx^2*ep^2 +157375898285941510732800*mncx^3*ep^3 -105005310755917452984576*mncx^4*ep^4 +50779532534302850198976*mncx^5*ep^5 -18588776355051949776576*mncx^6*ep^6 ; Fill mncPOINV(-24) = +620448401733239439360000 -2342787216398718566400000*mncx*ep +3925495373278097719296000*mncx^2*ep^2 -3936561409138663118131200*mncx^3*ep^3 +2677503356427960382362624*mncx^4*ep^4 -1323714091579185857760000*mncx^5*ep^5 +496910165055549644836800*mncx^6*ep^6 ; Fill mncPOINV(-25) = -15511210043330985984000000 +59190128811701203599360000*mncx*ep -100480171548351161548800000*mncx^2*ep^2 +102339530601744675672576000*mncx^3*ep^3 -70874145319837672677196800*mncx^4*ep^4 +35770355645907606826362624*mncx^5*ep^5 -13746468217967926978680000*mncx^6*ep^6 ; Fill mncPOINV(-26) = +403291461126605635584000000 -1554454559147562279567360000*mncx*ep +2671674589068831403868160000*mncx^2*ep^2 -2761307967193712729035776000*mncx^3*ep^3 +1945067308917524165279692800*mncx^4*ep^4 -1000903392113435450162625024*mncx^5*ep^5 +393178529313073708272042624*mncx^6*ep^6 ; Fill mncPOINV(-27) = -10888869450418352160768000000 +42373564558110787183902720000*mncx*ep -73689668464006010184007680000*mncx^2*ep^2 +77226989703299075087834112000*mncx^3*ep^3 -55278125307966865191587481600*mncx^4*ep^4 +28969458895980281319670568448*mncx^5*ep^5 -11616723683566425573507775872*mncx^6*ep^6 ; Fill mncPOINV(-28) = +304888344611713860501504000000 -1197348677077520393310044160000*mncx*ep +2105684281550279072336117760000*mncx^2*ep^2 -2236045380156380112643362816000*mncx^3*ep^3 +1625014498326371300452283596800*mncx^4*ep^4 -866422974395414742142363398144*mncx^5*ep^5 +354237722035840197377888292864*mncx^6*ep^6 ; Fill mncPOINV(-29) = -8841761993739701954543616000000 +35027999979859805266492784640000*mncx*ep -62262192842035613491057459200000*mncx^2*ep^2 +66951000306085302338993639424000*mncx^3*ep^3 -49361465831621147825759587123200*mncx^4*ep^4 +26751280755793398822580822142976*mncx^5*ep^5 -11139316913434780466101123891200*mncx^6*ep^6 ; Fill mncPOINV(-30) = +265252859812191058636308480000000 -1059681761389533859949327155200000*mncx*ep +1902893785240928209998216560640000*mncx^2*ep^2 -2070792202024594683660866641920000*mncx^3*ep^3 +1547794975254719737111781253120000*mncx^4*ep^4 -851899888505423112503184251412480*mncx^5*ep^5 +360930788158836812805614538878976*mncx^6*ep^6 ; Fill mncPOINV(-31) = -8222838654177922817725562880000000 +33115387462887740717065450291200000*mncx*ep -60049389103858308369894040535040000*mncx^2*ep^2 +66097452048003363403485082460160000*mncx^3*ep^3 -50052436434920906534126085488640000*mncx^4*ep^4 +27956691518922836224710493046906880*mncx^5*ep^5 -12040754321429364309477234956660736*mncx^6*ep^6 ; Fill mncPOINV(-32) = +263130836933693530167218012160000000 -1067915237466585625763819972198400000*mncx*ep +1954695838786353608553674747412480000*mncx^2*ep^2 -2175167854639965937281416679260160000*mncx^3*ep^3 +1667775417965472372495519818096640000*mncx^4*ep^4 -944666565040451665724861862989660160*mncx^5*ep^5 +413260829804662494127982011660050432*mncx^6*ep^6 ; Fill mncPOINV(-33) = -8683317618811886495518194401280000000 +35504333673331019180373277094707200000*mncx*ep -65572877917416254708035086636810240000*mncx^2*ep^2 +73735235041905229538840425162997760000*mncx^3*ep^3 -57211756647500554229633570676449280000*mncx^4*ep^4 +32841772064300377341415961296755425280*mncx^5*ep^5 -14582273948594313971948268247771324416*mncx^6*ep^6 ; Fill mncPOINV(-34) = +295232799039604140847618609643520000000 -1215830662512066538628209615621324800000*mncx*ep +2264982182865483679253566222746255360000*mncx^2*ep^2 -2572570869342194059028609542178734080000*mncx^3*ep^3 +2018934961056924073346381828162273280000*mncx^4*ep^4 -1173832006833713383837776254766133739520*mncx^5*ep^5 +528639086316507052387657081720980455424*mncx^6*ep^6 ; Fill mncPOINV(-35) = -10333147966386144929666651337523200000000 +42849305986961932992834955156389888000000*mncx*ep -80490207062803995312503027411740262400000*mncx^2*ep^2 +92304962609842275745254900199001948160000*mncx^3*ep^3 -73235294506334536626151973527858298880000*mncx^4*ep^4 +43103055200236892507668550744976954163200*mncx^5*ep^5 -19676200027911460217405774115000449679360*mncx^6*ep^6 ; Fill mncPOINV(-36) = +371993326789901217467999448150835200000000 -1552908163497015732671725036967559168000000*mncx*ep +2940496760247905764242943941979039334400000*mncx^2*ep^2 -3403468861017125922141679434575810396160000*mncx^3*ep^3 +2728775564837885594286725947201900707840000*mncx^4*ep^4 -1624945281714862666902219800347028648755200*mncx^5*ep^5 +751446256205049460334276418884993142620160*mncx^6*ep^6 ; Fill mncPOINV(-37) = -13763753091226345046315979581580902400000000 +57829595376179483326321825815950524416000000*mncx*ep -110351288292669529009660650890192014540800000*mncx^2*ep^2 +128868844617881564883485083021284023992320000*mncx^3*ep^3 -104368164760018892910750539481046136586240000*mncx^4*ep^4 +62851750988287804269668858560041960711782400*mncx^5*ep^5 -29428456761301692699270447299091774925701120*mncx^6*ep^6 ; Fill mncPOINV(-38) = +523022617466601111760007224100074291200000000 -2211288377386046711446545360587700830208000000*mncx*ep +4251178550497621585693426559643247076966400000*mncx^2*ep^2 -5007367383772168994582093805698984926248960000*mncx^3*ep^3 +4094859105498599495492005583301037214269440000*mncx^4*ep^4 -2492734702314955455158167164762640643633971200*mncx^5*ep^5 +1181133107917752126841945855925529407888424960*mncx^6*ep^6 ; Fill mncPOINV(-39) = -20397882081197443358640281739902897356800000000 +86763269335522422858175276287020406669312000000*mncx*ep -168007251846793288553490181186674336831897600000*mncx^2*ep^2 +199538506517612212374395084981903659200675840000*mncx^3*ep^3 -164706872498217549318770311554439436282757120000*mncx^4*ep^4 +101311512495781862246660525009044022315994316800*mncx^5*ep^5 -48556925911107288401994055545858287551282544640*mncx^6*ep^6 ; Fill mncPOINV(-40) = +815915283247897734345611269596115894272000000000 -3490928655502094357685651333220719164129280000000*mncx*ep +6807053343207253964997782523753993879945216000000*mncx^2*ep^2 -8149547512551281783529293580462820704858931200000*mncx^3*ep^3 +6787813406446314185125207547159481110510960640000*mncx^4*ep^4 -4217167372329492039185191311916200328922529792000*mncx^5*ep^5 +2043588548940073398326422746843375524367296102400*mncx^6*ep^6 ; *--#] mncPOINV-neg : mncPOINV negative values #endprocedure *--#] pochtabl : *--#[ projectP : * #procedure projectP(topo,power) * * Projects out the P, using harmonic projections. * id 1/P.Q = 1/Q.Q/mncproexp; #do mnci = 1,8 id 1/P.p`mnci' = 1/P.p`mnci'/mncproexp; #enddo id P = mncproexp*P; if ( count(mncproexp,1) > `power' ) discard; id mncepexp(mncp?mncpp18[mncn],mncx?) = mncee18[mncn]^mncx/mnceq^mncx; id mncepexp(-mncp?mncpp18[mncn],mncx?) = mncee18[mncn]^mncx/mnceq^mncx; id mncepexp(-mncp?[mncPp],mncx?) = mncepexp(mncp,mncx); id mncepexp([P+Q],mncx?) = mncepexp( mncproexp*2*P.Q/Q.Q,mncx); id mncepexp([P-Q],mncx?) = mncepexp(-mncproexp*2*P.Q/Q.Q,mncx); id mncepexp(mncp?[mncpp18][D],mncx?) = mncee18[D]^mncx/mnceq^mncx *mncepexp( 2*mncproexp*P.mncpp18[D]/mncpp18[D].mncpp18[D],mncx); id mncepexp(mncp?[-mncpp18][D],mncx?) = mncee18[D]^mncx/mnceq^mncx *mncepexp(-2*mncproexp*P.mncpp18[D]/mncpp18[D].mncpp18[D],mncx); #do mnci = 1,8 if ( count([P+p`mnci'].[P+p`mnci'],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P+p`mnci'].[P+p`mnci'] = ( sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.p`mnci'^mncj/ p`mnci'.p`mnci'^mncj*sign_(mncj)))*mncproexp^mncx/p`mnci'.p`mnci'; endrepeat; endif; if ( count([P-p`mnci'].[P-p`mnci'],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P-p`mnci'].[P-p`mnci'] = ( sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.p`mnci'^mncj/ p`mnci'.p`mnci'^mncj))*mncproexp^mncx/p`mnci'.p`mnci'; endrepeat; endif; #enddo if ( count([P+Q].[P+Q],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P+Q].[P+Q] = (sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.Q^mncj/ Q.Q^mncj*sign_(mncj)))*mncproexp^mncx/Q.Q; endrepeat; endif; if ( count([P-Q].[P-Q],1) < 0 ); repeat; id,once,mncproexp^mncx?/[P-Q].[P-Q] = (sum_(mncj,0,`power'-mncx,2^mncj*mncproexp^mncj*P.Q^mncj/Q.Q^mncj)) *mncproexp^mncx/Q.Q; endrepeat; endif; repeat; id,once,mncproexp^mncx?*mncepexp(y?,D?) = sump_(mncj,0,`power'-mncx, y*acc((-D*ep-mncj+1)/mncj))*mncproexp^mncx; if ( count(P.P,1) > 0 ) discard; if ( count(mncproexp,1) > `power' ) discard; endrepeat; if ( count(mncproexp,1) != `power' ) discard; id mncproexp^`power' = 1; #call ACCU(Expand in P) #call momsubs(`topo') #call sym2(`topo') #call ACCU(moms) #call harmo1(P,Q,mncFFPP) #call ACCU(Harmonics) #endprocedure * *--#] projectP : *--#[ reduceto : #procedure reduceto(TOPO) #switch `TOPO' *--#[ reducela : #case reducela * #call dovert1(p2,p7,p1) #call dovert1(p2,p8,p3) #call dovert1(Q,p4,p3) #call dovert1(p8,p5,p4) #call dovert1(p5,p7,p6) #call dovert1(p6,Q,p1) * #break *--#] reducela : *--#[ reducebe : #case reducebe * #call dovert1(p1,p6,p2) #call dovert1(p7,p3,p2) #call dovert1(Q,p4,p3) #call dovert1(p8,p5,p4) #call dovert1(p5,Q,p1) #call dovert1(p7,p8,p6) * #break *--#] reducebe : *--#[ reduceno : #case reduceno * #call dovert1(p1,p7,p2) #call dovert1(p8,p3,p2) #call dovert1(Q,p4,p3) #call dovert1(p7,p5,p4) #call dovert1(p6,Q,p1) #call dovert1(p5,p8,p6) * #break *--#] reduceno : *--#[ reducefa : #case reducefa * #call dovert1(p1,p6,p2) #call dovert1(p7,p3,p2) #call dovert1(Q,p4,p3) #call dovert1(p5,Q,p1) * #break *--#] reducefa : *--#[ reducebu : #case reducebu * #call dovert1(p4,p6,p1) #call dovert1(p4,p5,p2) #call dovert1(p3,p5,p7) #call dovert1(p7,Q,p6) * #break *--#] reducebu : *--#[ reduceo1 : #case reduceo1 * #call dovert1(p2,p5,p1) #call dovert1(p3,p5,p4) #call dovert1(Q,p4,p1) #call dovert1(p6,p7,p5) #call dovert1(p3,Q,p2) * #break *--#] reduceo1 : *--#[ reduceo2 : #case reduceo2 * #call dovert1(p2,p5,p1) #call dovert1(p3,p5,p4) #call dovert1(Q,p3,p2) #call dovert1(p6,p7,p4) #call dovert1(p4,Q,p1) * #break *--#] reduceo2 : *--#[ reduceo3 : #case reduceo3 * #call dovert1(p3,p5,p4) #call dovert1(p2,p5,p1) #call dovert1(p7,p6,Q) #call dovert1(p3,Q,p2) #call dovert1(p4,Q,p1) * #break *--#] reduceo3 : *--#[ reduceo4 : #case reduceo4 * #call dovert1(p4,p6,p1) #call dovert1(p2,p5,p1) #call dovert1(p7,p6,Q) #call dovert1(p3,p5,p4) #call dovert1(p3,p6,p2) * #break *--#] reduceo4 : *--#[ reduceo5 : #case reduceo5 * #call dovert1(p2,p5,p1) #call dovert1(p3,p5,p4) #call dovert1(Q,p3,p2) #call dovert1(p6,p7,p3) #call dovert1(p4,Q,p1) * #break *--#] reduceo5 : *--#[ reduceo6 : #case reduceo6 * #call dovert1(p3,p5,p4) #call dovert1(p2,p5,p1) #call dovert1(p7,p6,Q) #call dovert1(p3,Q,p2) #call dovert1(p4,Q,p1) * #break *--#] reduceo6 : *--#[ reducey1 : #case reducey1 * #call dovert1(p5,p6,p2) #call dovert1(p3,p4,p1) #call dovert1(p1,p2,Q) * #break *--#] reducey1 : *--#[ reducey2 : #case reducey2 * #call dovert1(p5,p6,p1) #call dovert1(p3,p4,p1) #call dovert1(p1,p2,Q) * #break *--#] reducey2 : *--#[ reducey3 : #case reducey3 * #call dovert1(p5,p6,p3) #call dovert1(p3,p4,p1) #call dovert1(p1,p2,Q) * #break *--#] reducey3 : *--#[ reducey4 : #case reducey4 * #call dovert1(p5,p6,Q) #call dovert1(p3,p4,p1) #call dovert1(p1,p2,Q) * #break *--#] reducey4 : *--#[ reducey5 : #case reducey5 * #call dovert1(p5,p6,Q) #call dovert1(p3,p4,Q) #call dovert1(p1,p2,Q) * #break *--#] reducey5 : *--#[ reducey6 : #case reducey6 * #call dovert1(p5,p6,Q) #call dovert1(p3,p4,p1) #call dovert1(p1,p2,Q) * #break *--#] reducey6 : *--#[ reducet1 : #case reducet1 * #call dovert1(p4,Q,p1) #call dovert1(p2,p5,p1) #call dovert1(p3,p5,p4) #call dovert1(p3,Q,p2) * #break *--#] reducet1 : *--#[ reducet2 : #case reducet2 * #call dovert1(p3,p4,p1) #call dovert1(p1,p2,Q) * #break *--#] reducet2 : *--#[ reducet3 : #case reducet3 * #call dovert1(p3,p4,Q) #call dovert1(p1,p2,Q) * #break *--#] reducet3 : *--#[ reducel1 : #case reducel1 * * #break *--#] reducel1 : *--#[ reducel2 : #case reducel2 * * #break *--#] reducel2 : *--#[ reducel3 : #case reducel3 * * #break *--#] reducel3 : *--#[ reducetr : #case reducetr * * #break *--#] reducetr : #default #message Illegal case `TOPO' in reduceto.prc #break #endswitch #endprocedure *--#] reduceto : *--#[ rename : #procedure rename(TOPO) #switch `TOPO' *--#[ la : * * *--#] la : *--#[ be : * * *--#] be : *--#[ no : * * *--#] no : *--#[ fa : * * *--#] fa : *--#[ bu : * * *--#] bu : *--#[ o1 : #case o1 * Multiply replace_(p8,p5,[P+p8],[P+p5],[P-p8],[P-p5]); * #break *--#] o1 : *--#[ o2 : #case o2 * Multiply replace_(p8,p4,[P+p8],[P+p4],[P-p8],[P-p4]); * #break *--#] o2 : *--#[ o3 : #case o3 * Multiply replace_(p8,Q,[P+p8],[P+Q],[P-p8],[P-Q]); * #break *--#] o3 : *--#[ o4 : #case o4 * Multiply replace_(p8,p6,[P+p8],[P+p6],[P-p8],[P-p6]); * #break *--#] o4 : *--#[ o5 : #case o5 * Multiply replace_(p8,p3,[P+p8],[P+p3],[P-p8],[P-p3]); * #break *--#] o5 : *--#[ o6 : #case o6 * Multiply replace_(p8,Q,[P+p8],[P+Q],[P-p8],[P-Q]); * #break *--#] o6 : *--#[ y1 : #case y1 * Multiply replace_(p8,p2,[P+p8],[P+p2],[P-p8],[P-p2]); Multiply replace_(p7,p1,[P+p7],[P+p1],[P-p7],[P-p1]); * #break *--#] y1 : *--#[ y2 : #case y2 * Multiply replace_(p8,p1,[P+p8],[P+p1],[P-p8],[P-p1]); Multiply replace_(p7,p1,[P+p7],[P+p1],[P-p7],[P-p1]); * #break *--#] y2 : *--#[ y3 : #case y3 * Multiply replace_(p8,p3,[P+p8],[P+p3],[P-p8],[P-p3]); Multiply replace_(p7,p1,[P+p7],[P+p1],[P-p7],[P-p1]); * #break *--#] y3 : *--#[ y4 : #case y4 * Multiply replace_(p8,Q,[P+p8],[P+Q],[P-p8],[P-Q]); Multiply replace_(p7,p1,[P+p7],[P+p1],[P-p7],[P-p1]); * #break *--#] y4 : *--#[ y5 : #case y5 * Multiply replace_(p8,Q,[P+p8],[P+Q],[P-p8],[P-Q]); Multiply replace_(p7,Q,[P+p7],[P+Q],[P-p7],[P-Q]); * #break *--#] y5 : *--#[ y6 : #case y6 * Multiply replace_(p8,Q,[P+p8],[P+Q],[P-p8],[P-Q]); Multiply replace_(p7,p1,[P+p7],[P+p1],[P-p7],[P-p1]); * #break *--#] y6 : *--#[ t1 : * * *--#] t1 : *--#[ t2 : #case t2 * Multiply replace_(p5,p1,[P+p5],[P+p1],[P-p5],[P-p1]); * #break *--#] t2 : *--#[ t3 : #case t3 * Multiply replace_(p5,Q,[P+p5],[P+Q],[P-p5],[P-Q]); * #break *--#] t3 : *--#[ l1 : * * *--#] l1 : *--#[ l2 : * * *--#] l2 : *--#[ l3 : * * *--#] l3 : *--#[ tr : * * *--#] tr : #endswitch #endprocedure *--#] rename : *--#[ rplane : #procedure rplane(P1,P2,P3,P4,P5,P6,P7,P8,Q,INTS) * * Reduction procedure for three loop graphs of the NO or nonplanar type. * Notation is from S.G.Gorishny et.al. Comp.Phys.Comm 55(1989)381 * * /-<------<-----<-\ * p1 / \ p2 / \ p3 * / v / \ * / p7 \ / \ * / \ / \ * Q --<-- / --<-- Q * \ / \ / * \ p8 / \ / * \ ^ \ / * p6 \ / p5 \ / p4 * \->------>----->-/ * * Routine put together 26-feb-1993 by J.Vermaseren. * * First express everything in powers of pi.pi, Q.Q and p2.Q; * * id `P5'.P?!{`P5'} = `P6'.P-`P8'.P; * id `P4'.P?!{`P4'} = `P3'.P-`Q'.P; *#call ACCU(moms 1) * id `P6'.P?!{`P6'} = `P1'.P-`Q'.P; *#call ACCU(moms 2) * id `P7'.P?!{`P7'} = `P2'.P-`P1'.P; *#call ACCU(moms 3) * id `P8'.P?!{`P8'} = `P2'.P-`P3'.P; *#call ACCU(moms 4) id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P6'.`P6'/2; #call ACCU(dots 1) id `P3'.`Q' = `P3'.`P3'/2+`Q'.`Q'/2-`P4'.`P4'/2; #call ACCU(dots 2) id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P7'.`P7'/2; #call ACCU(dots 3) id `P3'.`P2' = `P3'.`P3'/2+`P2'.`P2'/2-`P8'.`P8'/2; #call ACCU(dots 4) id `P1'.`P3' = -`P2'.`Q'+`P1'.`P1'/2+`P2'.`P2'/2+`P3'.`P3'/2+`P5'.`P5'/2 +`Q'.`Q'/2-`P4'.`P4'/2-`P6'.`P6'/2-`P7'.`P7'/2-`P8'.`P8'/2; #call ACCU(dots 5) * * First step: eliminate the powers of `Q'.`P2' * Note how common factors are kept together in acc till the end. * This trick allows us to do an intermediate sort in the argument * of acc, thereby making in the end only the terms that are necessary. * while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8'*`Q'.`P2') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?/`P6'.`P6'^mncx6? /`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8?*`Q'.`P2'^mncx9? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'^mncx5/`P6'.`P6'^mncx6 /`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*`Q'.`P2'^mncx9*`Q'.`Q'/`Q'.`P2'/2*( +acc(3-2*mncx2-mncx1-mncx3+mncx9-2*ep) +mncx1*`P7'.`P7'/`P1'.`P1'-mncx1*`P2'.`P2'/`P1'.`P1' +mncx3*`P8'.`P8'/`P3'.`P3'-mncx3*`P2'.`P2'/`P3'.`P3' +2*acc(mncx9-1)*`P2'.`P2'/`Q'.`P2'/2 )*mncdeno(7-mncx1-mncx2-mncx3-mncx4-mncx5-mncx6-mncx7-mncx8+mncx9,-4); id mncdeno(0,-4) = -1/4/ep; id mncdeno(mncx1?,-4) = acc(1+4*ep/mncx1+16*ep^2/mncx1^2+64*ep^3/mncx1^3+256*ep^4/mncx1^4 +1024*ep^5/mncx1^5+4096*ep^6/mncx1^6)/mncx1; repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); #call ACCU(Eliminate `Q'.`P2') * * The essence of the strategy is now to depopulate the inner * propagators. This will leave integrals with only excess powers * in `P1',`P3',`P4',`P6'. These are tabulated. * In case an integral is not in the tables we have to use * recursions at the edge to reach the table. The paper has the * extra recursion (29) which we combine directly with the * recursions below (more general form of (30)) to reach the * table automatically. * repeat; repeat; while ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5'^2 /`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5? /`P6'.`P6'^mncx6?/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3/`P4'.`P4'^mncx4/`P5'.`P5'^mncx5 /`P6'.`P6'^mncx6/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( acc(-8+4*ep+mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8)*`P5'.`P5'/`Q'.`Q'* (acc(-14+6*ep+2*(mncx1+mncx2+mncx3+mncx5+mncx7+mncx8)+mncx4+mncx6) +mncx4*`P3'.`P3'/`P4'.`P4'+mncx6*`P1'.`P1'/`P6'.`P6')/(mncx5-1) +mncx4*`P7'.`P7'/`P4'.`P4'+mncx6*`P8'.`P8'/`P6'.`P6' -acc(mncx1+mncx2+mncx3+mncx4+mncx5+mncx6+mncx7+mncx8+mncx5-9+4*ep)*`P5'.`P5' *(mncx4/`P4'.`P4'+mncx6/`P6'.`P6')/(mncx5-1) )*mncdeno(-4+mncx4+mncx6+2*mncx5,2); while ( match(1/`P1'.`P1'/`P2'.`P2'^2/`P3'.`P3'/`P4'.`P4'/`P5'.`P5' /`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4?/`P5'.`P5' /`P6'.`P6'^mncx6?/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3/`P4'.`P4'^mncx4/`P5'.`P5' /`P6'.`P6'^mncx6/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( acc(-7+4*ep+mncx1+mncx2+mncx3+mncx4+mncx6+mncx7+mncx8)*`P2'.`P2'/`Q'.`Q'* (acc(-12+6*ep+2*(mncx6+mncx2+mncx4+mncx7+mncx8)+mncx1+mncx3) +mncx3*`P4'.`P4'/`P3'.`P3'+mncx1*`P6'.`P6'/`P1'.`P1')/(mncx2-1) +mncx3*`P8'.`P8'/`P3'.`P3'+mncx1*`P7'.`P7'/`P1'.`P1' -acc(mncx1+mncx2+mncx3+mncx4+mncx6+mncx7+mncx8+mncx2-8+4*ep)*`P2'.`P2' *(mncx3/`P3'.`P3'+mncx1/`P1'.`P1')/(mncx2-1) )*mncdeno(-4+mncx1+mncx3+2*mncx2,2); if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5' /`P6'.`P6'/`P7'.`P7'^2/`P8'.`P8') > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4?/`P5'.`P5' /`P6'.`P6'^mncx6?/`P7'.`P7'^mncx7?/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'/`P3'.`P3'^mncx3/`P4'.`P4'^mncx4/`P5'.`P5' /`P6'.`P6'^mncx6/`P7'.`P7'^mncx7/`P8'.`P8'^mncx8*( acc(-6+4*ep+mncx1+mncx3+mncx4+mncx6+mncx7+mncx8)*`P7'.`P7'/`Q'.`Q'* (acc(-10+6*ep+2*(mncx6+mncx3+mncx7+mncx8)+mncx4+mncx1) +mncx4*`P3'.`P3'/`P4'.`P4'+mncx1*`P6'.`P6'/`P1'.`P1')/(mncx7-1) +mncx4*`P5'.`P5'/`P4'.`P4'+mncx1*`P2'.`P2'/`P1'.`P1' -acc(mncx1+mncx3+mncx4+mncx6+mncx7+mncx8+mncx7-7+4*ep)*`P7'.`P7' *(mncx4/`P4'.`P4'+mncx1/`P1'.`P1')/(mncx7-1) )*mncdeno(-4+mncx4+mncx1+2*mncx7,2); endrepeat; if ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5' /`P6'.`P6'/`P7'.`P7'/`P8'.`P8'^2) > 0 ) id 1/`P1'.`P1'^mncx1?/`P2'.`P2'/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4?/`P5'.`P5' /`P6'.`P6'^mncx6?/`P7'.`P7'/`P8'.`P8'^mncx8? = 1/`P1'.`P1'^mncx1/`P2'.`P2'/`P3'.`P3'^mncx3/`P4'.`P4'^mncx4/`P5'.`P5' /`P6'.`P6'^mncx6/`P7'.`P7'/`P8'.`P8'^mncx8*( acc(-5+4*ep+mncx1+mncx3+mncx4+mncx6+mncx8)*`P8'.`P8'/`Q'.`Q'* (acc(-8+6*ep+2*(mncx1+mncx4+mncx8)+mncx6+mncx3) +mncx3*`P4'.`P4'/`P3'.`P3'+mncx6*`P1'.`P1'/`P6'.`P6')/(mncx8-1) +mncx3*`P2'.`P2'/`P3'.`P3'+mncx6*`P5'.`P5'/`P6'.`P6' -acc(mncx1+mncx3+mncx4+mncx6+mncx8+mncx8-6+4*ep)*`P8'.`P8' *(mncx3/`P3'.`P3'+mncx6/`P6'.`P6')/(mncx8-1) )*mncdeno(-4+mncx6+mncx3+2*mncx8,2); endrepeat; id mncdeno(0,2) = 1/2/ep; id mncdeno(mncx1?,2) = acc(1-2*ep/mncx1+4*ep^2/mncx1^2-8*ep^3/mncx1^3+16*ep^4/mncx1^4 -32*ep^5/mncx1^5+64*ep^6/mncx1^6)/mncx1; repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); * * We arrange the integral so that mncx1 >= mncx3,mncx4,mncx5, mncx3 >= mncx4 etc. * if ( match( 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' ) > 0 ); if ( count(`P1'.`P1',1) > count(`P6'.`P6',1) ) multiply replace_(`P1',`P6',`P6',`P1'); if ( count(`P3'.`P3',1) > count(`P4'.`P4',1) ) multiply replace_(`P3',`P4',`P4',`P3'); if ( ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ) || ( ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ) && ( count(`P4'.`P4',1) > count(`P6'.`P6',1) ) ) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4'); if ( ( count(`P1'.`P1',1) > count(`P4'.`P4',1) ) || ( ( count(`P1'.`P1',1) == count(`P4'.`P4',1) ) && ( count(`P3'.`P3',1) > count(`P6'.`P6',1) ) ) ) multiply replace_(`P1',`P4',`P4',`P1',`P3',`P6',`P6',`P3'); if ( count(`P1'.`P1',1) > count(`P6'.`P6',1) ) multiply replace_(`P1',`P6',`P6',`P1'); if ( count(`P3'.`P3',1) > count(`P4'.`P4',1) ) multiply replace_(`P3',`P4',`P4',`P3'); endif; #call ACCU(Inside Reduction) while ( ( match(1/`P1'.`P1'^2/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) && ( count(`P1'.`P1',-1,`P3'.`P3',-1,`P4'.`P4',-1,`P6'.`P6',-1) > `INRTABL' ) ); id 1/`P1'.`P1'^mncx1?/`P2'.`P2'/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'/`P6'.`P6'^mncx6? /`P7'.`P7'/`P8'.`P8' = 1/`P1'.`P1'^mncx1/`P2'.`P2'/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'/`P6'.`P6'^mncx6 /`P7'.`P7'/`P8'.`P8'/`Q'.`Q'*( +acc((2*mncx6+mncx1-3+4*ep)*(mncx3+mncx1-2+2*ep)*(mncx4+mncx1-2+2*ep) +(mncx6+mncx3+mncx4+mncx1-4+4*ep)*((mncx4-1)*(mncx3+mncx1-2+2*ep) +(mncx3-1)*(mncx4+mncx1-2+2*ep))) *`P1'.`P1'/(mncx1-1)*mncdeno(-2+mncx4+mncx1,2)*mncdeno(-2+mncx1+mncx3,2) +`P6'.`P6' +`P8'.`P8'*`P1'.`P1'/`P2'.`P2'*acc(1+2*ep/(mncx1-1))*mncdeno(-2+mncx1+mncx3,2) +`P5'.`P5'*`P1'.`P1'/`P7'.`P7'*acc(1+2*ep/(mncx1-1))*mncdeno(-2+mncx4+mncx1,2) +acc(-5+4*ep+mncx1+mncx3+mncx4+mncx6)*( -`P4'.`P4'*acc((-6+6*ep+2*(mncx6+mncx3)+mncx4+mncx1)*(mncx3+mncx1-2+2*ep) +(mncx3-1)*(mncx4+mncx1-2+2*ep)) -`P3'.`P3'*acc((-6+6*ep+2*(mncx6+mncx4)+mncx1+mncx3)*(mncx4+mncx1-2+2*ep) +(mncx4-1)*(mncx3+mncx1-2+2*ep)) )*`P1'.`P1'/`Q'.`Q'/(mncx1-1)*mncdeno(-2+mncx4+mncx1,2)*mncdeno(-2+mncx1+mncx3,2) +(-`P6'.`P6'*`P4'.`P4'*acc(-5+4*ep+mncx1+mncx3+mncx4+mncx6)/`Q'.`Q' -`P2'.`P2'*`P4'.`P4'/`P7'.`P7' +`P4'.`P4'*acc(mncx1+mncx3+mncx4+mncx6-4+4*ep) )*mncdeno(-2+mncx4+mncx1,2) +(-`P6'.`P6'*`P3'.`P3'*acc(-5+4*ep+mncx1+mncx3+mncx4+mncx6)/`Q'.`Q' -`P7'.`P7'*`P3'.`P3'/`P2'.`P2' +`P3'.`P3'*acc(mncx1+mncx3+mncx4+mncx6-4+4*ep) )*mncdeno(-2+mncx1+mncx3,2) ); #ifndef `STRATEGY2' if ( match( 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' ) > 0 ); if ( count(`P1'.`P1',1) > count(`P6'.`P6',1) ) multiply replace_(`P1',`P6',`P6',`P1'); if ( count(`P3'.`P3',1) > count(`P4'.`P4',1) ) multiply replace_(`P3',`P4',`P4',`P3'); if ( ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ) || ( ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ) && ( count(`P4'.`P4',1) > count(`P6'.`P6',1) ) ) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4'); if ( ( count(`P1'.`P1',1) > count(`P4'.`P4',1) ) || ( ( count(`P1'.`P1',1) == count(`P4'.`P4',1) ) && ( count(`P3'.`P3',1) > count(`P6'.`P6',1) ) ) ) multiply replace_(`P1',`P4',`P4',`P1',`P3',`P6',`P6',`P3'); if ( count(`P1'.`P1',1) > count(`P6'.`P6',1) ) multiply replace_(`P1',`P6',`P6',`P1'); if ( count(`P3'.`P3',1) > count(`P4'.`P4',1) ) multiply replace_(`P3',`P4',`P4',`P3'); endif; #endif endwhile; #ifdef `STRATEGY2' while ( ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'^2/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8') > 0 ) && ( count(`P1'.`P1',-1,`P3'.`P3',-1,`P4'.`P4',-1,`P6'.`P6',-1) > `INRTABL' ) ) id 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'^mncx3? /`P4'.`P4'^mncx4?/`P5'.`P5'/`P6'.`P6'^mncx6? /`P7'.`P7'/`P8'.`P8' = 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'^mncx3 /`P4'.`P4'^mncx4/`P5'.`P5'/`P6'.`P6'^mncx6 /`P7'.`P7'/`P8'.`P8'/`Q'.`Q'*( +acc((2*mncx4+mncx3-3+4*ep)*(mncx6+mncx3-2+2*ep)*(1+mncx3-2+2*ep) +(mncx4+mncx6+1+mncx3-4+4*ep)*((1-1)*(mncx6+mncx3-2+2*ep) +(mncx6-1)*(1+mncx3-2+2*ep))) *`P3'.`P3'/(mncx3-1)*mncdeno(-2+1+mncx3,2)*mncdeno(-2+mncx3+mncx6,2) +`P4'.`P4' +`P5'.`P5'*`P3'.`P3'/`P8'.`P8'*acc(1+2*ep/(mncx3-1))*mncdeno(-2+mncx3+mncx6,2) +`P7'.`P7'*`P3'.`P3'/`P2'.`P2'*acc(1+2*ep/(mncx3-1))*mncdeno(-1+mncx3,2) +acc(-4+4*ep+mncx4+mncx6+mncx3)*( -`P1'.`P1'*acc((-5+6*ep+2*(mncx4+mncx6)+mncx3)*(mncx6+mncx3-2+2*ep) +(mncx6-1)*(mncx3-1+2*ep))*mncdeno(-1+mncx3,2) -`P6'.`P6'*acc(-6+6*ep+2*(mncx4+1)+mncx3+mncx6) )*`P3'.`P3'/`Q'.`Q'/(mncx3-1)*mncdeno(-2+mncx3+mncx6,2) +(-`P4'.`P4'*`P1'.`P1'*acc(-4+4*ep+mncx4+mncx6+mncx3)/`Q'.`Q' -`P8'.`P8'*`P1'.`P1'/`P2'.`P2' +`P1'.`P1'*acc(mncx4+mncx6+mncx3-3+4*ep) )*mncdeno(-1+mncx3,2) +(-`P4'.`P4'*`P6'.`P6'*acc(-4+4*ep+mncx4+mncx6+mncx3)/`Q'.`Q' -`P2'.`P2'*`P6'.`P6'/`P8'.`P8' +`P6'.`P6'*acc(mncx4+mncx6+mncx3-3+4*ep) )*mncdeno(-2+mncx3+mncx6,2) ); while ( ( match(1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'^2/`P7'.`P7'/`P8'.`P8') > 0 ) && ( count(`P1'.`P1',-1,`P3'.`P3',-1,`P4'.`P4',-1,`P6'.`P6',-1) > `INRTABL' ) ) id 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3' /`P4'.`P4'^mncx4?/`P5'.`P5'/`P6'.`P6'^mncx6? /`P7'.`P7'/`P8'.`P8' = 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3' /`P4'.`P4'^mncx4/`P5'.`P5'/`P6'.`P6'^mncx6 /`P7'.`P7'/`P8'.`P8'/`Q'.`Q'*( +acc(mncx6-2+4*ep+mncx4)*acc(mncx4+mncx6-2+2*ep) *`P6'.`P6'/(mncx6-1)*mncdeno(-2+mncx4+mncx6,2) +`P1'.`P1' +`P2'.`P2'*`P6'.`P6'/`P8'.`P8'*acc(1+2*ep/(mncx6-1))*mncdeno(-1+mncx6,2) +`P7'.`P7'*`P6'.`P6'/`P5'.`P5'*acc(1+2*ep/(mncx6-1))*mncdeno(-2+mncx4+mncx6,2) +acc(-3+4*ep+mncx4+mncx6)*( -`P4'.`P4'*acc(-2+6*ep+mncx4+mncx6) -`P3'.`P3'*acc((-3+6*ep+2*mncx4+mncx6)*(mncx4+mncx6-2+2*ep) +(mncx4-1)*(mncx6-1+2*ep))*mncdeno(-1+mncx6,2) )*`P6'.`P6'/`Q'.`Q'/(mncx6-1)*mncdeno(-2+mncx4+mncx6,2) +(-`P1'.`P1'*`P4'.`P4'*acc(-3+4*ep+mncx4+mncx6)/`Q'.`Q' -`P8'.`P8'*`P4'.`P4'/`P5'.`P5' +`P4'.`P4'*acc(mncx4+mncx6-2+4*ep) )*mncdeno(-2+mncx4+mncx6,2) +(-`P1'.`P1'*`P3'.`P3'*acc(-3+4*ep+mncx4+mncx6)/`Q'.`Q' -`P5'.`P5'*`P3'.`P3'/`P8'.`P8' +`P3'.`P3'*acc(mncx4+mncx6-2+4*ep) )*mncdeno(-1+mncx6,2) ); while ( ( match(1/`P1'.`P1'/`P7'.`P7'/`P4'.`P4'^2/`P3'.`P3' /`P8'.`P8'/`P6'.`P6'/`P2'.`P2'/`P5'.`P5') > 0 ) && ( count(`P1'.`P1',-1,`P4'.`P4',-1,`P3'.`P3',-1,`P6'.`P6',-1) > `INRTABL' ) ) id 1/`P1'.`P1'/`P7'.`P7'/`P4'.`P4'^mncx4? /`P3'.`P3'/`P8'.`P8'/`P6'.`P6' /`P2'.`P2'/`P5'.`P5' = 1/`P1'.`P1'/`P7'.`P7'/`P4'.`P4'^mncx4 /`P3'.`P3'/`P8'.`P8'/`P6'.`P6' /`P2'.`P2'/`P5'.`P5'/`Q'.`Q'*( +acc(mncx4-1+4*ep)*`P4'.`P4'/(mncx4-1) +`P3'.`P3' +`P8'.`P8'*`P4'.`P4'/`P5'.`P5'*acc(1+2*ep/(mncx4-1))*mncdeno(-1+mncx4,2) +`P2'.`P2'*`P4'.`P4'/`P7'.`P7'*acc(1+2*ep/(mncx4-1))*mncdeno(-1+mncx4,2) +acc(-2+4*ep+mncx4)*( -`P1'.`P1'*acc(-1+6*ep+mncx4) -`P6'.`P6'*acc(-1+6*ep+mncx4) )*`P4'.`P4'/`Q'.`Q'/(mncx4-1)*mncdeno(-1+mncx4,2) +(-`P3'.`P3'*`P1'.`P1'*acc(-2+4*ep+mncx4)/`Q'.`Q' -`P5'.`P5'*`P1'.`P1'/`P7'.`P7' +`P1'.`P1'*acc(mncx4-1+4*ep) )*mncdeno(-1+mncx4,2) +(-`P3'.`P3'*`P6'.`P6'*acc(-2+4*ep+mncx4)/`Q'.`Q' -`P7'.`P7'*`P6'.`P6'/`P5'.`P5' +`P6'.`P6'*acc(mncx4-1+4*ep) )*mncdeno(-1+mncx4,2) ); #endif id mncdeno(0,2) = 1/2/ep; id mncdeno(mncx1?,2) = acc(1-2*ep/mncx1+4*ep^2/mncx1^2-8*ep^3/mncx1^3+16*ep^4/mncx1^4 -32*ep^5/mncx1^5+64*ep^6/mncx1^6)/mncx1; repeat id acc(mncx1?)*acc(mncx2?) = acc(mncx1*mncx2); * * Integrals that are left can be looked up in the table. * We may have to apply symmetries to map it to an actual * element of the table. * if ( match( 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4' /`P5'.`P5'/`P6'.`P6'/`P7'.`P7'/`P8'.`P8' ) > 0 ); if ( count(`P1'.`P1',1) > count(`P6'.`P6',1) ) multiply replace_(`P1',`P6',`P6',`P1'); if ( count(`P3'.`P3',1) > count(`P4'.`P4',1) ) multiply replace_(`P3',`P4',`P4',`P3'); if ( ( count(`P1'.`P1',1) > count(`P3'.`P3',1) ) || ( ( count(`P1'.`P1',1) == count(`P3'.`P3',1) ) && ( count(`P4'.`P4',1) > count(`P6'.`P6',1) ) ) ) multiply replace_(`P1',`P3',`P3',`P1',`P4',`P6',`P6',`P4'); if ( ( count(`P1'.`P1',1) > count(`P4'.`P4',1) ) || ( ( count(`P1'.`P1',1) == count(`P4'.`P4',1) ) && ( count(`P3'.`P3',1) > count(`P6'.`P6',1) ) ) ) multiply replace_(`P1',`P4',`P4',`P1',`P3',`P6',`P6',`P3'); if ( count(`P1'.`P1',1) > count(`P6'.`P6',1) ) multiply replace_(`P1',`P6',`P6',`P1'); if ( count(`P3'.`P3',1) > count(`P4'.`P4',1) ) multiply replace_(`P3',`P4',`P4',`P3'); id `INTS'/`P1'.`P1'^mncx1?/`P2'.`P2'/`P3'.`P3'^mncx3?/`P4'.`P4'^mncx4? /`P5'.`P5'/`P6'.`P6'^mncx6?/`P7'.`P7'/`P8'.`P8' = mncrtab(mncx1,mncx3,mncx4,mncx6)*mnceq^3/`Q'.`Q'^(mncx1+mncx3+mncx4+mncx6-2); endif; #endprocedure; *--#] rplane : *--#[ scalars : #procedure scalars(TOPO) #switch `TOPO' *--#[ la : #case la * #ifdef `LATRANS' #if ( `LATRANS' == 1 ) #call ACCU2(AB Q.p3 p3.p3 Q.Q p4.p4,Ladder rewrite 0) id Q.p3 = p3.p3/2-p4.p4/2+Q.Q/2; #call ACCU2(AB Q.p2 p2.p2 Q.Q p5.p5,Ladder rewrite 1) id Q.p2 = p2.p2/2+Q.Q/2-p5.p5/2; #call ACCU2(AB p2.p7 p1.p1 p2.p2 p7.p7,Ladder rewrite 2) id p2.p7 = p1.p1/2-p2.p2/2-p7.p7/2; #call ACCU2(AB p2.p3 p3.p3 p2.p2 p8.p8,Ladder rewrite 3) id p2.p3 = p3.p3/2+p2.p2/2-p8.p8/2; #call ACCU2(AB Q.p7 p1.p1 p2.p2 p5.p5 p6.p6,Ladder rewrite 4) id Q.p7 = p1.p1/2-p2.p2/2+p5.p5/2-p6.p6/2; #call ACCU(Ladder rewrite 5) #else #if ( `LATRANS' == 2 ) #call ACCU2(AB p3.p7 p1.p7 p7.p8 p7.p7,Ladder rewrite 0) id p3.p7 = p1.p7-p7.p7+p7.p8; #call ACCU2(AB Q.p3 p3.p3 Q.Q p4.p4,Ladder rewrite 1) id Q.p3 = p3.p3/2-p4.p4/2+Q.Q/2; #call ACCU2(AB Q.p1 p1.p1 Q.Q p6.p6,Ladder rewrite 2) id Q.p1 = p1.p1/2+Q.Q/2-p6.p6/2; #call ACCU2(AB p1.p7 p1.p1 p2.p2 p7.p7,Ladder rewrite 3) id p1.p7 = p1.p1/2-p2.p2/2+p7.p7/2; #call ACCU2(AB Q.p7 p1.p1 p2.p2 p5.p5 p6.p6,Ladder rewrite 4) id Q.p7 = p1.p1/2-p2.p2/2+p5.p5/2-p6.p6/2; #call ACCU(Ladder rewrite 5) #else #if ( `LATRANS' == 3 ) #call ACCU2(AB Q.p2 p2.p2 Q.Q p5.p5,Ladder rewrite 0) id Q.p2 = p2.p2/2+Q.Q/2-p5.p5/2; #call ACCU2(AB p2.p7 p1.p1 p2.p2 p7.p7,Ladder rewrite 1) id p2.p7 = p1.p1/2-p2.p2/2-p7.p7/2; #call ACCU2(AB p2.p8 p3.p3 p2.p2 p8.p8,Ladder rewrite 2) id p2.p8 = p3.p3/2-p2.p2/2-p8.p8/2; #call ACCU2(AB Q.p7 p1.p1 p2.p2 p5.p5 p6.p6,Ladder rewrite 3) id Q.p7 = p1.p1/2-p2.p2/2+p5.p5/2-p6.p6/2; #call ACCU2(AB Q.p8 p3.p3 p2.p2 p5.p5 p4.p4,Ladder rewrite 4) id Q.p8 = p3.p3/2-p2.p2/2+p5.p5/2-p4.p4/2; #call ACCU(Ladder rewrite 5) #else #call ACCU2(AB Q.p1 p1.p1 p6.p6 Q.Q,Ladder rewrite 0) id Q.p1 = p1.p1/2-p6.p6/2+Q.Q/2; #call ACCU2(AB Q.p3 p3.p3 p4.p4 Q.Q,Ladder rewrite 1) id Q.p3 = p3.p3/2-p4.p4/2+Q.Q/2; #call ACCU2(AB Q.p2 p2.p2 Q.Q p5.p5,Ladder rewrite 2) id Q.p2 = p2.p2/2+Q.Q/2-p5.p5/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p7.p7,Ladder rewrite 3) id p1.p2 = p1.p1/2+p2.p2/2-p7.p7/2; #call ACCU2(AB p2.p3 p3.p3 p2.p2 p8.p8,Ladder rewrite 4) id p2.p3 = p3.p3/2+p2.p2/2-p8.p8/2; #call ACCU(Ladder rewrite 5) #endif #endif #endif #else #call ACCU2(AB Q.p1 p1.p1 p6.p6 Q.Q,Ladder rewrite 0) id Q.p1 = p1.p1/2-p6.p6/2+Q.Q/2; #call ACCU2(AB Q.p3 p3.p3 p4.p4 Q.Q,Ladder rewrite 1) id Q.p3 = p3.p3/2-p4.p4/2+Q.Q/2; #call ACCU2(AB Q.p2 p2.p2 Q.Q p5.p5,Ladder rewrite 2) id Q.p2 = p2.p2/2+Q.Q/2-p5.p5/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p7.p7,Ladder rewrite 3) id p1.p2 = p1.p1/2+p2.p2/2-p7.p7/2; #call ACCU2(AB p2.p3 p3.p3 p2.p2 p8.p8,Ladder rewrite 4) id p2.p3 = p3.p3/2+p2.p2/2-p8.p8/2; #call ACCU(Ladder rewrite 5) #endif * #break *--#] la : *--#[ be : #case be * #ifndef `BEPATH' #call ACCU2(AB p1.p3 p1.p1 p3.p3 p8.p8,Benz rewrite 0) id p1.p3 = p1.p1/2+p3.p3/2-p8.p8/2; #call ACCU2(AB p2.p3 p2.p2 p3.p3 p7.p7,Benz rewrite 1) id p2.p3 = p2.p2/2+p3.p3/2-p7.p7/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p6.p6,Benz rewrite 2) id p1.p2 = p1.p1/2+p2.p2/2-p6.p6/2; #call ACCU2(AB Q.p1 p1.p1 Q.Q p5.p5,Benz rewrite 3) id Q.p1 = p1.p1/2+Q.Q/2-p5.p5/2; #call ACCU2(AB Q.p3 p3.p3 Q.Q p4.p4,Benz rewrite 4) id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU(Benz rewrite 5) #else #if ( `BEPATH' == 0 ) #call ACCU2(AB p1.p3 p1.p1 p3.p3 p8.p8,Benz rewrite 0 \(0\)) id p1.p3 = p1.p1/2+p3.p3/2-p8.p8/2; #call ACCU2(AB p2.p3 p2.p2 p3.p3 p7.p7,Benz rewrite 1 \(0\)) id p2.p3 = p2.p2/2+p3.p3/2-p7.p7/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p6.p6,Benz rewrite 2 \(0\)) id p1.p2 = p1.p1/2+p2.p2/2-p6.p6/2; #call ACCU2(AB Q.p1 p1.p1 Q.Q p5.p5,Benz rewrite 3 \(0\)) id Q.p1 = p1.p1/2+Q.Q/2-p5.p5/2; #call ACCU2(AB Q.p3 p3.p3 Q.Q p4.p4,Benz rewrite 4 \(0\)) id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU(Benz rewrite 5 \(0\)) #endif #if ( `BEPATH' == 1 ) #call ACCU2(AB Q.p1 p1.p1 Q.Q p5.p5,Benz rewrite 0 \(1\)) id Q.p1 = p1.p1/2+Q.Q/2-p5.p5/2; #call ACCU2(AB p1.p6 p2.p2 p1.p1 p6.p6,Benz rewrite 1 \(1\)) id p1.p6 = p2.p2/2-p1.p1/2-p6.p6/2; #call ACCU2(AB p6.p8 p6.p6 p8.p8 p7.p7,Benz rewrite 2 \(1\)) id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; #call ACCU2(AB p1.p8 p3.p3 p1.p1 p8.p8,Benz rewrite 3 \(1\)) id p1.p8 = p3.p3/2-p1.p1/2-p8.p8/2; #call ACCU2(AB Q.p8 p3.p3 p4.p4 p1.p1 p5.p5,Benz rewrite 4 \(1\)) id Q.p8 = p3.p3/2-p4.p4/2-p1.p1/2+p5.p5/2; #call ACCU2(AB Q.p6 Q.p2 Q.Q p1.p1 p5.p5,Benz rewrite 5 \(1\)) #endif #if ( `BEPATH' == 2 ) #call ACCU2(AB p1.p2 p1.p1 p2.p2 p6.p6,Benz rewrite 0 \(2\)) id p1.p2 = p1.p1/2+p2.p2/2-p6.p6/2; #call ACCU2(AB p2.p7 p2.p2 p7.p7 p3.p3,Benz rewrite 1 \(2\)) id p2.p7 = p2.p2/2+p7.p7/2-p3.p3/2; #call ACCU2(AB Q.p1 p1.p1 Q.Q p5.p5,Benz rewrite 2 \(2\)) id Q.p1 = p1.p1/2+Q.Q/2-p5.p5/2; #call ACCU2(AB Q.p7 Q.p2 Q.Q p3.p3 p4.p4,Benz rewrite 3 \(2\)) id Q.p7 = Q.p2-Q.Q/2-p3.p3/2+p4.p4/2; #call ACCU2(AB p1.p7 p2.p2 p6.p6 p3.p3 p8.p8,Benz rewrite 4 \(2\)) id p1.p7 = p2.p2/2-p6.p6/2-p3.p3/2+p8.p8/2; #call ACCU(Benz rewrite 5 \(2\)) #endif #if ( `BEPATH' == 3 ) #call ACCU2(AB p6.p8 p6.p6 p8.p8 p7.p7,Benz rewrite 0 \(3\)) id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; #call ACCU2(AB p2.p6 p2.p2 p6.p6 p1.p1,Benz rewrite 1 \(3\)) id p2.p6 = p2.p2/2+p6.p6/2-p1.p1/2; #call ACCU2(AB p2.p8 p3.p3 p1.p1 p7.p7 p6.p6,Benz rewrite 2 \(3\)) id p2.p8 = p3.p3/2-p1.p1/2-p7.p7/2+p6.p6/2; #call ACCU2(AB Q.p8 p3.p3 p4.p4 p1.p1 p5.p5,Benz rewrite 3 \(3\)) id Q.p8 = p3.p3/2-p4.p4/2-p1.p1/2+p5.p5/2; #call ACCU2(AB Q.p6 Q.p2 Q.Q p1.p1 p5.p5,Benz rewrite 4 \(3\)) id Q.p6 = Q.p2-Q.Q/2-p1.p1/2+p5.p5/2; #call ACCU(Benz rewrite 5 \(3\)) #endif #if ( `BEPATH' == 4 ) #call ACCU2(AB p6.p8 p6.p6 p8.p8 p7.p7,Benz rewrite 0 \(4\)) id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; #call ACCU2(AB p4.p8 p4.p4 p8.p8 p5.p5,Benz rewrite 1 \(4\)) id p4.p8 = p4.p4/2+p8.p8/2-p5.p5/2; #call ACCU2(AB Q.p4 p3.p3 Q.Q p4.p4,Benz rewrite 2 \(4\)) id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; #call ACCU2(AB Q.p8 p3.p3 p4.p4 p1.p1 p5.p5,Benz rewrite 3 \(4\)) id Q.p8 = p3.p3/2-p4.p4/2-p1.p1/2+p5.p5/2; #call ACCU2(AB p4.p6 Q.p6 p1.p1 p2.p2 p7.p7 p8.p8,Benz rewrite 4 \(4\)) id p4.p6 = -Q.p6-p1.p1/2+p2.p2/2+p8.p8/2-p7.p7/2; #call ACCU(Benz rewrite 5 \(4\)) #endif #if ( `BEPATH' == 5 ) #call ACCU2(AB p1.p6 p2.p2 p1.p1 p6.p6,Benz rewrite 0 \(5\)) id p1.p6 = p2.p2/2-p1.p1/2-p6.p6/2; #call ACCU2(AB p6.p7 p6.p6 p7.p7 p8.p8,Benz rewrite 1 \(5\)) id p6.p7 = p6.p6/2+p7.p7/2-p8.p8/2; #call ACCU2(AB Q.p1 p1.p1 Q.Q p5.p5,Benz rewrite 2 \(5\)) id Q.p1 = p1.p1/2+Q.Q/2-p5.p5/2; #call ACCU2(AB p1.p7 p2.p2 p6.p6 p3.p3 p8.p8,Benz rewrite 3 \(5\)) id p1.p7 = p2.p2/2-p6.p6/2-p3.p3/2+p8.p8/2; #call ACCU2(AB Q.p6 Q.p2 Q.Q p1.p1 p5.p5,Benz rewrite 4 \(5\)) id Q.p6 = Q.p7+p3.p3/2-p4.p4/2-p1.p1/2+p5.p5/2; #call ACCU(Benz rewrite 5 \(5\)) #endif #if ( `BEPATH' == 6 ) #call ACCU2(AB p5.p8 p4.p4 p5.p5 p8.p8,Benz rewrite 0 \(6\)) id p5.p8 = p4.p4/2-p5.p5/2-p8.p8/2; #call ACCU2(AB p6.p8 p6.p6 p8.p8 p7.p7,Benz rewrite 1 \(6\)) id p6.p8 = p6.p6/2+p8.p8/2-p7.p7/2; #call ACCU2(AB Q.p5 p1.p1 Q.Q p5.p5,Benz rewrite 2 \(6\)) id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; #call ACCU2(AB p5.p6 p2.p2 p1.p1 p6.p6 Q.p6,Benz rewrite 3 \(6\)) id p5.p6 = p2.p2/2-p1.p1/2-p6.p6/2-Q.p6; #call ACCU2(AB Q.p8 p3.p3 p4.p4 p1.p1 p5.p5,Benz rewrite 4 \(6\)) id Q.p8 = p3.p3/2-p4.p4/2-p1.p1/2+p5.p5/2; #call ACCU(Benz rewrite 5 \(6\)) #endif #if ( `BEPATH' == 7 ) #call ACCU2(AB p4.p5 p4.p4 p5.p5 p8.p8,Benz rewrite 0 \(7\)) id p4.p5 = p4.p4/2+p5.p5/2-p8.p8/2; #call ACCU2(AB Q.p4 p3.p3 Q.Q p4.p4,Benz rewrite 1 \(7\)) id Q.p4 = p3.p3/2-Q.Q/2-p4.p4/2; #call ACCU2(AB Q.p5 p1.p1 Q.Q p5.p5,Benz rewrite 2 \(7\)) id Q.p5 = p1.p1/2-Q.Q/2-p5.p5/2; #call ACCU2(AB p2.p4 p2.p2 p3.p3 p7.p7 Q.p2,Benz rewrite 3 \(7\)) id p2.p4 = p2.p2/2+p3.p3/2-p7.p7/2-Q.p2; #call ACCU2(AB p2.p5 p2.p2 p1.p1 p6.p6 Q.p2,Benz rewrite 4 \(7\)) id p2.p5 = p2.p2/2+p1.p1/2-p6.p6/2-Q.p2; #call ACCU(Benz rewrite 5 \(7\)) #endif #if ( `BEPATH' == 8 ) #call ACCU2(AB p2.p6 p2.p2 p1.p1 p6.p6,Benz rewrite 0 \(8\)) id p2.p6 = p2.p2/2+p6.p6/2-p1.p1/2; #call ACCU2(AB p2.p7 p2.p2 p7.p7 p3.p3,Benz rewrite 1 \(8\)) id p2.p7 = p2.p2/2+p7.p7/2-p3.p3/2; #call ACCU2(AB p6.p7 p6.p6 p7.p7 p8.p8,Benz rewrite 2 \(8\)) id p6.p7 = p6.p6/2+p7.p7/2-p8.p8/2; #call ACCU2(AB Q.p6 Q.p2 Q.Q p1.p1 p5.p5,Benz rewrite 3 \(8\)) id Q.p6 = Q.p2-Q.Q/2-p1.p1/2+p5.p5/2; #call ACCU2(AB Q.p7 Q.p2 Q.Q p3.p3 p4.p4,Benz rewrite 4 \(8\)) id Q.p7 = Q.p2-Q.Q/2-p3.p3/2+p4.p4/2; #call ACCU(Benz rewrite 5 \(8\)) #endif #endif * #break *--#] be : *--#[ no : #case no * #ifndef `NOSPEC' #call ACCU2(AB p1.Q p1.p1 Q.Q p6.p6,no rewrite 0) id p1.Q = p1.p1/2+Q.Q/2-p6.p6/2; #call ACCU2(AB p3.Q p3.p3 Q.Q p4.p4,no rewrite 1) id p3.Q = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p7.p7,no rewrite 2) id p1.p2 = p1.p1/2+p2.p2/2-p7.p7/2; #call ACCU2(AB p2.p3 p3.p3 p2.p2 p8.p8,no rewrite 3) id p3.p2 = p3.p3/2+p2.p2/2-p8.p8/2; #call ACCU(no rewrite 4) id p1.p3 = -p2.Q+p1.p1/2+p2.p2/2+p3.p3/2+p5.p5/2 +Q.Q/2-p4.p4/2-p6.p6/2-p7.p7/2-p8.p8/2; #call ACCU(no rewrite 5) #else #if ( `NOSPEC' == 0 ) #call ACCU2(AB p1.Q p1.p1 Q.Q p6.p6,no rewrite 0) id p1.Q = p1.p1/2+Q.Q/2-p6.p6/2; #call ACCU2(AB p3.Q p3.p3 Q.Q p4.p4,no rewrite 1) id p3.Q = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p7.p7,no rewrite 2) id p1.p2 = p1.p1/2+p2.p2/2-p7.p7/2; #call ACCU2(AB p2.p3 p3.p3 p2.p2 p8.p8,no rewrite 3) id p2.p3 = p3.p3/2+p2.p2/2-p8.p8/2; #call ACCU(no rewrite 4) id p1.p3 = -p2.Q+p1.p1/2+p2.p2/2+p3.p3/2+p5.p5/2 +Q.Q/2-p4.p4/2-p6.p6/2-p7.p7/2-p8.p8/2; #call ACCU(no rewrite 5) #endif #if ( `NOSPEC' == 1 ) id p2.p7 = p2.p2/2+p7.p7/2-p1.p1/2; #call ACCU2(AB p2.p8 p3.p3 p2.p2 p8.p8,no rewrite 0) id p2.p8 = -p3.p3/2+p2.p2/2+p8.p8/2; #call ACCU2(AB p7.Q Q.p2 p1.p1 Q.Q p6.p6,no rewrite 2) id p7.Q = Q.p2-p1.p1/2-Q.Q/2+p6.p6/2; #call ACCU2(AB p8.Q p3.p3 Q.Q p4.p4 Q.p2,no rewrite 3) id p8.Q = Q.p2-p3.p3/2-Q.Q/2+p4.p4/2; #call ACCU(no rewrite 4) id,p1.p3 = -p2.Q+p1.p1/2+p2.p2/2+p3.p3/2+p5.p5/2 +Q.Q/2-p4.p4/2-p6.p6/2-p7.p7/2-p8.p8/2; #call ACCU(no rewrite 5) #endif #if ( `NOSPEC' == 2 ) #call ACCU2(AB p1.Q p1.p1 Q.Q p6.p6,no rewrite 0) id p1.Q = p1.p1/2+Q.Q/2-p6.p6/2; #call ACCU2(AB p8.Q p2.Q p3.p3 Q.Q p4.p4,no rewrite 1) id p8.Q = p2.Q-p3.p3/2-Q.Q/2+p4.p4/2; #call ACCU2(AB p1.p2 p1.p1 p2.p2 p7.p7,no rewrite 2) id p1.p2 = p1.p1/2+p2.p2/2-p7.p7/2; #call ACCU2(AB p2.p8 p3.p3 p2.p2 p8.p8,no rewrite 3) id p2.p8 = p8.p8/2+p2.p2/2-p3.p3/2; #call ACCU2(AB p1.p8 p2.Q p3.p3 p5.p5 Q.Q p4.p4 p6.p6 p8.p8,no rewrite 4) id p1.p8 = +p2.Q-p3.p3/2-p5.p5/2 -Q.Q/2+p4.p4/2+p6.p6/2+p8.p8/2; #call ACCU(no rewrite 5) #endif #endif * #break *--#] no : *--#[ fa : #case fa * * #break *--#] fa : *--#[ bu : #case bu * * #break *--#] bu : *--#[ o1 : #case o1 * #ifndef `O1PATH' id p1.p2 = p1.p1/2+p2.p2/2-p5.p5/2; #call ACCU(o1 rewite 1) id Q.p1 = p1.p1/2+Q.Q/2-p4.p4/2; id Q.p2 = p2.p2/2+Q.Q/2-p3.p3/2; #call ACCU(o1 rewite 2) #else #if ( `O1PATH' == 0 ) id p1.p2 = p1.p1/2+p2.p2/2-p5.p5/2; #call ACCU(o1 rewite 1\(0\)) id Q.p1 = p1.p1/2+Q.Q/2-p4.p4/2; id Q.p2 = p2.p2/2+Q.Q/2-p3.p3/2; #call ACCU(o1 rewite 2\(0\)) #endif #if ( `O1PATH' == 1 ) id p1.p7 = -p1.p6+p1.p1/2+p5.p5/2-p2.p2/2; id p6.p7 = p5.p5/2-p6.p6/2-p7.p7/2; #call ACCU(o1 rewite 1\(1\)) id Q.p1 = p1.p1/2+Q.Q/2-p4.p4/2; id Q.p7 = -Q.p6+p1.p1/2-p2.p2/2+p3.p3/2-p4.p4/2; #call ACCU(o1 rewite 2\(1\)) #endif #if ( `O1PATH' == 2 ) id p1.p5 = p1.p1/2+p5.p5/2-p2.p2/2; id p5.p6 = p5.p5/2+p6.p6/2-p7.p7/2; #call ACCU(o1 rewite 1\(2\)) id Q.p1 = p1.p1/2+Q.Q/2-p4.p4/2; id Q.p5 = p1.p1/2-p2.p2/2+p3.p3/2-p4.p4/2; #call ACCU(o1 rewite 2\(2\)) #endif #endif * #break *--#] o1 : *--#[ o2 : #case o2 * id p4.p6 = p4.p4/2+p6.p6/2-p7.p7/2; id p3.p4 = p3.p3/2+p4.p4/2-p5.p5/2; #call ACCU(o2 rewrite 1) id Q.p3 = p2.p2/2-Q.Q/2-p3.p3/2; id Q.p4 = p1.p1/2-Q.Q/2-p4.p4/2; #call ACCU(o2 rewrite 2) * #break *--#] o2 : *--#[ o3 : #case o3 * id Q.p6 = p6.p6/2+Q.Q/2-p7.p7/2; id p1.p2 = p1.p1/2+p2.p2/2-p5.p5/2; #call ACCU(o3 rewrite 1) id Q.p1 = p1.p1/2+Q.Q/2-p4.p4/2; id Q.p2 = p2.p2/2+Q.Q/2-p3.p3/2; #call ACCU(o3 rewrite 2) * #break *--#] o3 : *--#[ o4 : #case o4 * id Q.p6 = p6.p6/2+Q.Q/2-p7.p7/2; id p1.p2 = p1.p1/2+p2.p2/2-p5.p5/2; #call ACCU(o4 rewrite 1) id p1.p6 = p1.p1/2+p6.p6/2-p4.p4/2; id p2.p6 = p2.p2/2+p6.p6/2-p3.p3/2; #call ACCU(o4 rewrite 2) * #break *--#] o4 : *--#[ o5 : #case o5 * id p3.p6 = p3.p3/2+p6.p6/2-p7.p7/2; id p3.p4 = p3.p3/2+p4.p4/2-p5.p5/2; #call ACCU(o5 rewrite 1) id Q.p3 = p2.p2/2-Q.Q/2-p3.p3/2; id Q.p4 = p1.p1/2-Q.Q/2-p4.p4/2; #call ACCU(o5 rewrite 2) * #break *--#] o5 : *--#[ o6 : #case o6 * id Q.p6 = p6.p6/2+Q.Q/2-p7.p7/2; id p1.p2 = p1.p1/2+p2.p2/2-p5.p5/2; #call ACCU(o3 rewrite 1) id Q.p1 = p1.p1/2+Q.Q/2-p4.p4/2; id Q.p2 = p2.p2/2+Q.Q/2-p3.p3/2; #call ACCU(o3 rewrite 2) * #break *--#] o6 : *--#[ y1 : #case y1 * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(y1 rewrite) * #break *--#] y1 : *--#[ y2 : #case y2 * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; #call ACCU(y2 rewrite 1) id p1.p5 = p1.p1/2+p5.p5/2-p6.p6/2; #call ACCU(y2 rewrite 2) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(y2 rewrite 3) * #break *--#] y2 : *--#[ y3 : #case y3 * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; #call ACCU(y3 rewrite 1) id p3.p5 = p3.p3/2+p5.p5/2-p6.p6/2; #call ACCU(y3 rewrite 2) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(y3 rewrite 3) * #break *--#] y3 : *--#[ y4 : #case y4 * id Q.p5 = p5.p5/2+Q.Q/2-p6.p6/2; #call ACCU(y4 rewrite 1) id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; #call ACCU(y4 rewrite 2) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(y4 rewrite 3) * #break *--#] y4 : *--#[ y5 : #case y5 * id Q.p5 = p5.p5/2+Q.Q/2-p6.p6/2; #call ACCU(y5 rewrite 1) id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU(y5 rewrite 2) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(y5 rewrite 3) * #break *--#] y5 : *--#[ y6 : #case y6 * id Q.p5 = p5.p5/2+Q.Q/2-p6.p6/2; #call ACCU(y4 rewrite 1) id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; #call ACCU(y4 rewrite 2) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(y4 rewrite 3) * #break *--#] y6 : *--#[ t1 : #case t1 * id p1.p2 = p1.p1/2+p2.p2/2-p5.p5/2; #call ACCU(t1 rewrite 1) id Q.p1 = p1.p1/2+Q.Q/2-p4.p4/2; #call ACCU(t1 rewrite 2) id Q.p2 = p2.p2/2+Q.Q/2-p3.p3/2; #call ACCU(t1 rewrite 3) * #break *--#] t1 : *--#[ t2 : #case t2 * id p1.p3 = p1.p1/2+p3.p3/2-p4.p4/2; #call ACCU(t2 rewrite 1) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(t2 rewrite 2) * #break *--#] t2 : *--#[ t3 : #case t3 * id Q.p3 = p3.p3/2+Q.Q/2-p4.p4/2; #call ACCU(t3 rewrite 1) id Q.p1 = p1.p1/2+Q.Q/2-p2.p2/2; #call ACCU(t3 rewrite 2) * #break *--#] t3 : *--#[ l1 : #case l1 * * #break *--#] l1 : *--#[ l2 : #case l2 * * #break *--#] l2 : *--#[ l3 : #case l3 * * #break *--#] l3 : *--#[ tr : #case tr * * #break *--#] tr : #endswitch #endprocedure *--#] scalars : *--#[ simplify : #procedure simplify * * Note: The acc's are leftovers when the gamma's are normalized. * In that case two gamma's had to be reduced down, so that the * first part is one. Actually the first acc can be cancelled * against the factors in the definition of the exp's. * if ( match(mncG(?a,0,0)) ); id mncG(mncx1?,0,mncy1?,0,0,0) = mncaccm(mncT00(mncx1,mncy1)); id mncG(mncx1?,1,mncy1?,0,0,0) = mncexp10*mncaccm(mncT10(mncx1,mncy1)); id mncG(mncx1?,0,mncy1?,1,0,0) = mncexp10*mncaccm(mncT10(mncy1,mncx1)); id mncG(mncx1?,2,mncy1?,0,0,0) = mncexp20*mncaccm(mncT20(mncx1,mncy1)); id mncG(mncx1?,0,mncy1?,2,0,0) = mncexp20*mncaccm(mncT20(mncy1,mncx1)); id mncG(mncx1?,1,mncy1?,1,0,0) = mncexp11*mncaccm(mncT11(mncx1,mncy1)); id mncaccm(mncT00(mncx?,mncy?)) = mncG(mncx,0,mncy,0,0,0); id mncaccm(mncT10(mncx?,mncy?)) = mncG(mncx,1,mncy,0,0,0)/mncexp10; id mncaccm(mncT20(mncx?,mncy?)) = mncG(mncx,2,mncy,0,0,0)/mncexp20; id mncaccm(mncT11(mncx?,mncy?)) = mncG(mncx,1,mncy,1,0,0)/mncexp11; id mncaccm(mncx?) = acc(mncx); endif; if ( count(mncG,1) ); id mncG(mncx1?,mncy1?,mncx2?,mncy2?,D?,mncs?) = mncpo(mncx1+mncx2-mncs-2,1+mncy1+mncy2) *mncpo(2-mncx1+D-mncs,-1-mncy1)*mncpo(2-mncx2+mncs,-1-mncy2) *acc(1-2*ep-ep*mncy1-ep*mncy2) *mncpoinv(mncx1,mncy1)*mncpoinv(mncx2,mncy2)*mncpoinv(4-mncx1-mncx2+D,-2-mncy1-mncy2) *mncG(1,mncy1,1,mncy2,0,0); id mncG(1,0,1,0,0,0) = 1; id mncG(1,1,1,1,0,0) = mncexp11; *1/3 id mncG(1,0,1,1,0,0) = mncexp10; *1/2 id mncG(1,1,1,0,0,0) = mncexp10; *1/2 id mncG(1,0,1,2,0,0) = mncexp20; *1/3 id mncG(1,2,1,0,0,0) = mncexp20; *1/3 id mncpo(1,?a) = 1; id mncpoinv(1,?a) = 1; id mncpo(mncx1?pos_,0) = fac_(mncx1-1); id mncpoinv(mncx1?pos_,0) = invfac_(mncx1-1); id,many,mncpo(mncx1?neg0_,mncx2?) = acc(mncPO(mncx1,mncx2))/mncx2/ep; id,many,mncpo(mncx1?,mncx2?) = acc(mncPO(mncx1,mncx2)); id,many,mncpoinv(mncx1?neg0_,mncx2?) = acc(mncPOINV(mncx1,mncx2))*mncx2*ep; id,many,mncpoinv(mncx1?,mncx2?) = acc(mncPOINV(mncx1,mncx2)); endif; id mncexp10*mncexp20 = mncexp11*acc(1+ep+3*ep^2+9*ep^3+27*ep^4+81*ep^5+243*ep^6); multiply ep; #endprocedure *--#] simplify : *--#[ special : #procedure special(TOPO) #switch `TOPO' *--#[ la : #case la * id mncDg(?a,mncp?[mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,mncp?[-mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[-mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[-mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[-mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[-mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[-mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; if ( ( count(mncx5,1) > 0 ) && ( count(mncx2,1) == 0 ) ); multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,-p7,p8,-p8, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); multiply,replace_(mncx1,mncx6,mncx6,mncx1,mncx2,mncx5,mncx5,mncx2,mncx3,mncx4,mncx4,mncx3); endif; if ( ( count(mncx2,1) > 0 ) && ( count(mncx6,1) > 0 ) ); multiply,replace_( [P-p1],[P+p3],[P+p1],[P-p3],[P-p4],[P+p6],[P+p4],[P-p6] ,[P-p3],[P+p1],[P+p3],[P-p1],[P-p6],[P+p4],[P+p6],[P-p4] ,[P-p2],[P+p2],[P+p2],[P-p2],[P-p5],[P+p5],[P+p5],[P-p5] ,[P-p7],[P+p8],[P+p7],[P-p8],[P-p8],[P+p7],[P+p8],[P-p7] ,p1,-p3,p3,-p1,p4,-p6,p6,-p4,p2,-p2,p5,-p5,p7,-p8,p8,-p7,Q,-Q ,[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; multiply,replace_(mncx1,mncx3,mncx3,mncx1,mncx4,mncx6,mncx6,mncx4,mncx7,mncx8,mncx8,mncx7); endif; if ( match(mncx2*mncx8*mncx4) ); if ( match(mncDg(?a,[P-p2])) || match(mncDg(?a,-[P-p2])) || match(mncfp(?a,[P-p2])) || match(mncfp(?a,-[P-p2])) || match(mncDgh(?a,[P-p2])) || match(mncDgh(?a,-[P-p2])) ); multiply,replace_([P+p8],p8,[P+p4],p4,p4,-[P-p4],p3,-[P-p3],mncx8,mncx3,mncx3,mncx8); else; multiply,replace_([P-p8],-p8,[P-p4],-p4,p4,[P+p4],p3,[P+p3],mncx8,mncx3,mncx3,mncx8); endif; endif; if ( count(mncx7,1,mncx8,1) > 0 ); if ( match(mncx7*mncx8) > 0 ); redefine LATRANS "3"; if ( count(mncx5,1) > 0 ) multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,-p7,p8,-p8, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); elseif ( (match(mncx7*mncx1) > 0) || (match(mncx7*mncx6) > 0) ); redefine LATRANS "2"; if ( count(mncx6,1) > 0 ) multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,-p7,p8,-p8, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); elseif ( (match(mncx8*mncx3) > 0) || (match(mncx8*mncx4) > 0) ); redefine LATRANS "2"; multiply,replace_( [P-p1],[P+p3],[P+p1],[P-p3],[P-p4],[P+p6],[P+p4],[P-p6] ,[P-p3],[P+p1],[P+p3],[P-p1],[P-p6],[P+p4],[P+p6],[P-p4] ,[P-p2],[P+p2],[P+p2],[P-p2],[P-p5],[P+p5],[P+p5],[P-p5] ,[P-p7],[P+p8],[P+p7],[P-p8],[P-p8],[P+p7],[P+p8],[P-p7] ,p1,-p3,p3,-p1,p4,-p6,p6,-p4,p2,-p2,p5,-p5,p7,-p8,p8,-p7,Q,-Q ,[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; if ( count(mncx6,1) > 0 ) multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,-p7,p8,-p8, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); else; redefine LATRANS "1"; if ( count(mncx8,1) > 0 ) multiply,replace_( [P-p1],[P+p3],[P+p1],[P-p3],[P-p4],[P+p6],[P+p4],[P-p6] ,[P-p3],[P+p1],[P+p3],[P-p1],[P-p6],[P+p4],[P+p6],[P-p4] ,[P-p2],[P+p2],[P+p2],[P-p2],[P-p5],[P+p5],[P+p5],[P-p5] ,[P-p7],[P+p8],[P+p7],[P-p8],[P-p8],[P+p7],[P+p8],[P-p7] ,p1,-p3,p3,-p1,p4,-p6,p6,-p4,p2,-p2,p5,-p5,p7,-p8,p8,-p7,Q,-Q ,[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; if ( count(mncx5,1) > 0 ) multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,-p7,p8,-p8, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); endif; elseif ( count(mncx4,1,mncx5,1,mncx6,1) > count(mncx1,1,mncx2,1,mncx3,1) ); multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,-p7,p8,-p8, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); endif; repeat,id mncx?[mncx18] = 1; * #break *--#] la : *--#[ be : #case be * id mncDg(?a,mncp?[mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,mncp?[-mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[-mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[-mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[-mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[-mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[-mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; if ( match(mncx4*mncx5) ); redefine BEPATH "7";* 1,5,4 or 3,4,5 or 4,5 if ( count(mncx3,1) > 0 ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; elseif ( match(mncx4*mncx6*mncx8) || match(mncx5*mncx7*mncx8) ); redefine BEPATH "4";* 4,8,6 or 5,8,7 or 4,8 or 5,8 if ( count(mncx5,1) > 0 ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; elseif ( ( count(mncx4,1,mncx5,1) > 0 ) && ( count(mncx1,1,mncx3,1) == 0 ) ); label 6; redefine BEPATH "6";* 4,8,7,or 5,8,6 or 4,8 or 5,8 if ( count(mncx4,1) > 0 ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; elseif ( match(mncx1*mncx6*mncx7) || match(mncx3*mncx6*mncx7) ); redefine BEPATH "5";* 1,6,7 or 3,7,6 if ( count(mncx3,1) > 0 ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; elseif ( match(mncx6*mncx7) ); redefine BEPATH "8";* 6,7 elseif ( match(mncx2*mncx8) ); redefine BEPATH "3";* 2,6,8 or 2,7,8 if ( count(mncx7,1) > 0 ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; elseif ( match(mncx2*mncx7) || match(mncx2*mncx6) ); redefine BEPATH "2";* 1,2,7 or 3,2,6 if ( count(mncx6,1) > 0 ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; elseif ( match(mncx6) || match(mncx7) || match(mncx8) ); if ( match(mncx1*mncx5*mncx6) || match(mncx3*mncx4*mncx7) ); if ( count(mncx3,1) ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q] ,mncx3,mncx1,mncx1,mncx3,mncx4,mncx5,mncx5,mncx4,mncx6,mncx7,mncx7,mncx6)*mncsgn3; if ( match(mncDg(?a,[P-p6])) || match(mncDg(?a,-[P-p6])) || match(mncfp(?a,[P-p6])) || match(mncfp(?a,-[P-p6])) || match(mncDgh(?a,[P-p6])) || match(mncDgh(?a,-[P-p6])) ); multiply,replace_([P+p5],p5,[P+p1],p1,[P-p6],-p6, p6,[P+p6],p8,[P+p8],p5,-[P-p5],[P-p5],-p5,[P-p1],-p1,[P+p6],p6, mncx1,mncx8,mncx8,mncx1); else; * * This one still needs correcting in some databases * multiply,replace_([P+p5],p5,[P+p1],p1,[P-p6],-p6, p6,-[P-p6],p8,-[P-p8],p5,[P+p5],[P-p5],-p5,[P-p1],-p1,[P+p6],p6, mncx1,mncx8,mncx8,mncx1); endif; goto 6; endif; if ( match(mncx3*mncx4*mncx8) || match(mncx1*mncx5*mncx8) ); if ( count(mncx3,1) ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q] ,mncx3,mncx1,mncx1,mncx3,mncx4,mncx5,mncx5,mncx4,mncx6,mncx7,mncx7,mncx6)*mncsgn3; if ( match(mncDg(?a,[P+p1])) || match(mncDg(?a,-[P+p1])) || match(mncfp(?a,[P+p1])) || match(mncfp(?a,-[P+p1])) || match(mncDgh(?a,[P+p1])) || match(mncDgh(?a,-[P+p1])) ); multiply,replace_(p1,-[P-p1],p6,[P+p6],p8,[P+p8] ,[P+p1],p1,[P+p5],p5,[P-p8],-p8 ,[P-p1],-p1,[P-p5],-p5,[P+p8],p8 ,mncx5,mncx6,mncx6,mncx5); else; * * This one still needs correcting in some databases * multiply,replace_(p1,[P+p1],p6,-[P-p6],p8,-[P-p8] ,[P+p1],p1,[P+p5],p5,[P-p8],-p8 ,[P-p1],-p1,[P-p5],-p5,[P+p8],p8 ,mncx5,mncx6,mncx6,mncx5); endif; endif; redefine BEPATH "1";* 1,6,8 or 1,6 or 6,8 or 5,1,6 or vv if ( count(mncx7,1) > 0 ) multiply,replace_(p1,-p3,p3,-p1,p2,-p2,p6,-p7,p7,-p6,p4,-p5,p5,-p4,Q,-Q ,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1] ,[P+p4],[P-p5],[P+p5],[P-p4],[P-p4],[P+p5],[P-p5],[P+p4] ,[P+p6],[P-p7],[P+p7],[P-p6],[P-p6],[P+p7],[P-p7],[P+p6] ,[P+p2],[P-p2],[P-p2],[P+p2],[P+Q],[P-Q],[P-Q],[P+Q])*mncsgn3; endif; repeat,id mncx?[mncx18] = 1; * #break *--#] be : *--#[ no : #case no * id mncDg(?a,mncp?[mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,mncp?[-mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[-mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[-mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[-mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[-mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[-mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; repeat id mncx?[mncx18]^2 = mncx; if ( match(mncx2*mncx7*mncx8) || match(mncx5*mncx7*mncx8) || match(mncx2*mncx5*mncx7) || match(mncx2*mncx5*mncx8) ); redefine NOSPEC "1"; if ( count(mncx2,1) == 0 ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); multiply,replace_(mncx1,mncx6,mncx6,mncx1,mncx2,mncx5,mncx5,mncx2,mncx3,mncx4,mncx4,mncx3,mncx7,mncx8,mncx8,mncx7); elseif ( count(mncx7,1) == 0 ); multiply,replace_( p1,-p6,p6,-p1,[P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1], p7,p5,p5,p7,[P+p7],[P+p5],[P+p5],[P+p7],[P-p7],[P-p5],[P-p5],[P-p7], p2,-p8,p8,-p2,[P-p2],[P+p8],[P+p2],[P-p8],[P+p8],[P-p2],[P-p8],[P+p2], mncx1,mncx6,mncx6,mncx1,mncx5,mncx7,mncx7,mncx5,mncx2,mncx8,mncx8,mncx2); elseif ( count(mncx8,1) == 0 ); multiply,replace_([P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,[P-p2],[P+p7],[P+p2],[P-p7],[P+p7],[P-p2],[P-p7],[P+p2] ,[P+p5],[P+p8],[P-p5],[P-p8],[P+p8],[P+p5],[P-p8],[P-p5]); multiply,replace_(p2,-p7,p7,-p2,p8,p5,p5,p8,p3,-p4,p4,-p3); multiply,replace_(mncx2,mncx7,mncx7,mncx2,mncx8,mncx5,mncx5,mncx8,mncx3,mncx4,mncx4,mncx3); endif; * * We have now a configuration with 7,2,8 * Now minimize the number of fermions * id mncfp(?a, mncp?mncPcenter,?b) = mncfp(?a, mncp,?b)*mncx; id mncfp(?a,-mncp?mncPcenter,?b) = mncfp(?a,-mncp,?b)*mncx; id mncfp(?a, mncp?mncpcenter,?b ) = mncfp(?a, mncp,?b)/mncx; id mncfp(?a,-mncp?mncpcenter,?b ) = mncfp(?a,-mncp,?b)/mncx; if ( count(mncx,1) > 0 ); if ( match(mncDg(?a,[P-p7])) || match(mncDg(?a,-[P-p7])) || match(mncfp(?a,[P-p7])) || match(mncfp(?a,-[P-p7])) || match(mncDgh(?a,[P-p7])) || match(mncDgh(?a,-[P-p7])) ); multiply,replace_([P-p7],-p7,[P-p2],-p2,[P-p8],-p8, p7,[P+p7],p5,-[P-p5],p8,[P+p8],mncx2,mncx5,mncx5,mncx2); else; multiply,replace_([P+p7],p7,[P+p2],p2,[P+p8],p8, p7,-[P-p7],p5,[P+p5],p8,-[P-p8],mncx2,mncx5,mncx5,mncx2); endif; multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); multiply,replace_(mncx1,mncx6,mncx6,mncx1,mncx2,mncx5,mncx5,mncx2,mncx3,mncx4,mncx4,mncx3,mncx7,mncx8,mncx8,mncx7); endif; id mncx = 1; id 1/mncx = 1; else; if ( ( count(mncx3,1) > 0 ) && ( count(mncx1,1,mncx4,1,mncx6,1) == 0 ) ); multiply,replace_( p1,-p3,p3,-p1,[P+p1],[P-p3],[P+p3],[P-p1],[P-p1],[P+p3],[P-p3],[P+p1], p4,-p6,p6,-p4,[P+p4],[P-p6],[P+p6],[P-p4],[P-p4],[P+p6],[P-p6],[P+p4], p2,-p2,[P+p2],[P-p2],[P-p2],[P+p2], p5,-p5,[P+p5],[P-p5],[P-p5],[P+p5], p7,-p8,p8,-p7,[P+p7],[P-p8],[P+p8],[P-p7],[P-p7],[P+p8],[P-p8],[P+p7], Q,-Q,[P+Q],[P-Q],[P-Q],[P+Q], mncx1,mncx3,mncx3,mncx1,mncx4,mncx6,mncx6,mncx4,mncx7,mncx8,mncx8,mncx7)*mncsgn3; endif; if ( ( count(mncx4,1) > 0 ) && ( count(mncx1,1,mncx3,1,mncx6,1) == 0 ) ); multiply,replace_( p1,p4,p4,p1,[P+p1],[P+p4],[P+p4],[P+p1],[P-p1],[P-p4],[P-p4],[P-p1], p2,p5,p5,p2,[P+p2],[P+p5],[P+p5],[P+p2],[P-p2],[P-p5],[P-p5],[P-p2], p3,p6,p6,p3,[P+p3],[P+p6],[P+p6],[P+p3],[P-p3],[P-p6],[P-p6],[P-p3], p7,-p7,[P+p7],[P-p7],[P-p7],[P+p7], p8,-p8,[P+p8],[P-p8],[P-p8],[P+p8], Q,-Q,[P+Q],[P-Q],[P-Q],[P+Q], mncx1,mncx4,mncx4,mncx1,mncx2,mncx5,mncx5,mncx2,mncx3,mncx6,mncx6,mncx3)*mncsgn3; endif; if ( ( count(mncx6,1) > 0 ) && ( count(mncx1,1) == 0 ) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); multiply,replace_(mncx1,mncx6,mncx6,mncx1,mncx2,mncx5,mncx5,mncx2,mncx3,mncx4,mncx4,mncx3,mncx7,mncx8,mncx8,mncx7); endif; if ( match(mncx1*mncx7) > 0 ); multiply,replace_([P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,[P-p2],[P+p7],[P+p2],[P-p7],[P+p7],[P-p2],[P-p7],[P+p2] ,[P+p5],[P+p8],[P-p5],[P-p8],[P+p8],[P+p5],[P-p8],[P-p5]); multiply,replace_(p2,-p7,p7,-p2,p8,p5,p5,p8,p3,-p4,p4,-p3); multiply,replace_(mncx2,mncx7,mncx7,mncx2,mncx8,mncx5,mncx5,mncx8,mncx3,mncx4,mncx4,mncx3); endif; if ( match(mncx1*mncx2*mncx8) > 0 ); redefine NOSPEC "2"; endif; endif; repeat,id mncx?[mncx18] = 1; * #break *--#] no : *--#[ fa : #case fa * * #break *--#] fa : *--#[ bu : #case bu * * #break *--#] bu : *--#[ o1 : #case o1 * id mncDg(?a,mncp?[mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,mncp?[-mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[-mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[-mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[-mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[-mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[-mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; if ( match(mncx6*mncx7) > 0 ); redefine O1PATH "1"; elseif ( ( count(mncx6,1,mncx7,1) > 0 ) && ( count(mncx3,1,mncx4,1) > 0 ) ); multiply replace_( p1,-p4,p4,-p1,[P+p1],[P-p4],[P-p1],[P+p4],[P+p4],[P-p1],[P-p4],[P+p1], p2,-p3,p3,-p2,[P+p2],[P-p3],[P-p2],[P+p3],[P+p3],[P-p2],[P-p3],[P+p2], p5,-p5,[P-p5],[P+p5],[P+p5],[P-p5], p6,-p6,[P-p6],[P+p6],[P+p6],[P-p6], p7,-p7,[P-p7],[P+p7],[P+p7],[P-p7], mncx1,mncx4,mncx4,mncx1,mncx2,mncx3,mncx3,mncx2); endif; if ( count(mncx3,1,mncx4,1) > count(mncx1,1,mncx2,1) ); multiply replace_( p1,-p4,p4,-p1,[P+p1],[P-p4],[P-p1],[P+p4],[P+p4],[P-p1],[P-p4],[P+p1], p2,-p3,p3,-p2,[P+p2],[P-p3],[P-p2],[P+p3],[P+p3],[P-p2],[P-p3],[P+p2], p5,-p5,[P-p5],[P+p5],[P+p5],[P-p5], p6,-p6,[P-p6],[P+p6],[P+p6],[P-p6], p7,-p7,[P-p7],[P+p7],[P+p7],[P-p7], mncx1,mncx4,mncx4,mncx1,mncx2,mncx3,mncx3,mncx2); endif; if ( ( count(mncx7,1) > 0 ) && ( count(mncx6,1) == 0 ) ); multiply replace_(p6,p7,p7,p6,[P+p6],[P+p7],[P+p7],[P+p6], [P-p6],[P-p7],[P-p7],[P-p6],mncx6,mncx7,mncx7,mncx6); endif; if ( ( count(mncx2,1) > 0 ) && ( count(mncx1,1) == 0 ) ); multiply replace_( p1,-p2,p2,-p1,[P+p1],[P-p2],[P-p1],[P+p2],[P+p2],[P-p1],[P-p2],[P+p1], p4,-p3,p3,-p4,[P+p4],[P-p3],[P-p4],[P+p3],[P+p3],[P-p4],[P-p3],[P+p4], Q,-Q,[P-Q],[P+Q],[P+Q],[P-Q],mncx1,mncx2,mncx2,mncx1,mncx4,mncx3,mncx3,mncx4)*mncsgn3; endif; if ( count(mncx5,1) > 0 ); redefine O1PATH "2"; endif; repeat,id mncx?[mncx18] = 1; * #break *--#] o1 : *--#[ o2 : #case o2 * id mncDg(?a,mncp?[mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,mncp?[-mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[-mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[-mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[-mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[-mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[-mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; if ( ( count(mncx7,1) > 0 ) && ( count(mncx6,1) == 0 ) ); multiply replace_( p6,p7,p7,p6,[P+p6],[P+p7],[P+p7],[P+p6],[P-p6],[P-p7],[P-p7],[P-p6] mncx6,mncx7,mncx7,mncx6); endif; if ( match(mncx6*mncx2*mncx1) ); if ( match(mncDg(?a,[P-p2])) || match(mncDg(?a,-[P-p2])) || match(mncfp(?a,[P-p2])) || match(mncfp(?a,-[P-p2])) || match(mncDgh(?a,[P-p2])) || match(mncDgh(?a,-[P-p2])) ); Multiply,replace_([P-p2],-p2,p2,[P+p2],[P-p1],-p1,[P-p4],-p4 ,[P-p6],-p6,p6,[P+p6],p4,[P+p4],p3,[P+p3],mncx1,mncx3,mncx3,mncx1); else; Multiply,replace_([P+p2],p2,p2,-[P-p2],[P+p4],p4,p4,-[P-p4],[P+p6],p6, p6,-[P-p6],p3,-[P-p3],[P+p1],p1,mncx1,mncx3,mncx3,mncx1); endif; endif; repeat,id mncx?[mncx18] = 1; * #break *--#] o2 : *--#[ o3 : #case o3 * * #break *--#] o3 : *--#[ o4 : #case o4 * * #break *--#] o4 : *--#[ o5 : #case o5 * id mncDg(?a,mncp?[mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,mncp?[-mncpp18][mncx]) = mncDg(?a,mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDg(?a,-mncp?[-mncpp18][mncx]) = mncDg(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,mncp?[-mncpp18][mncx]) = mncDgh(?a,mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncDgh(?a,-mncp?[-mncpp18][mncx]) = mncDgh(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,mncp?[-mncpp18][mncx]) = mncfp(?a,mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; id mncfp(?a,-mncp?[-mncpp18][mncx]) = mncfp(?a,-mncp)*[mncx18][mncx]; if ( ( count(mncx7,1) > 0 ) && ( count(mncx6,1) == 0 ) ); multiply replace_( p6,p7,p7,p6,[P+p6],[P+p7],[P+p7],[P+p6],[P-p6],[P-p7],[P-p7],[P-p6] mncx6,mncx7,mncx7,mncx6); endif; if ( match(mncx6*mncx2*mncx1) ); if ( match(mncDg(?a,[P-p2])) || match(mncDg(?a,-[P-p2])) || match(mncfp(?a,[P-p2])) || match(mncfp(?a,-[P-p2])) || match(mncDgh(?a,[P-p2])) || match(mncDgh(?a,-[P-p2])) ); Multiply,replace_([P-p2],-p2,p2,[P+p2],[P-p1],-p1,p1,[P+p1],[P-p4],-p4,[P-p3],-p3 ,[P-p6],-p6,p6,[P+p6],p4,[P+p4],p3,[P+p3],mncx2,mncx4,mncx4,mncx2); else; Multiply,replace_([P+p2],p2,p2,-[P-p2],[P+p4],p4,p4,-[P-p4],[P+p6],p6, p6,-[P-p6],[P+p3],p3,p3,-[P-p3],[P+p1],p1,p1,-[P-p1],mncx2,mncx4,mncx4,mncx2); endif; endif; repeat,id mncx?[mncx18] = 1; * #break *--#] o5 : *--#[ o6 : #case o6 * * #break *--#] o6 : *--#[ y1 : #case y1 * * #break *--#] y1 : *--#[ y2 : #case y2 * * #break *--#] y2 : *--#[ y3 : #case y3 * * #break *--#] y3 : *--#[ y4 : #case y4 * * #break *--#] y4 : *--#[ y5 : #case y5 * * #break *--#] y5 : *--#[ y6 : #case y6 * * #break *--#] y6 : *--#[ t1 : #case t1 * * #break *--#] t1 : *--#[ t2 : #case t2 * * #break *--#] t2 : *--#[ t3 : #case t3 * * #break *--#] t3 : *--#[ l1 : #case l1 * * #break *--#] l1 : *--#[ l2 : #case l2 * * #break *--#] l2 : *--#[ l3 : #case l3 * * #break *--#] l3 : *--#[ tr : #case tr * * #break *--#] tr : #endswitch #endprocedure *--#] special : *--#[ subint : #procedure subint id mncexp20*mncexp10 = 1 + ep * ( 3 ) + ep^2 * ( 13 ) + ep^3 * ( 55 - 22*z3 ) + ep^4 * ( 229 - 66*z3 - 33*z4 ) + ep^5 * ( 943 - 286*z3 - 99*z4 - 234*z5 ) + ep^6 * ( 3853 - 1210*z3 + 242*z3^2 - 429*z4 - 702*z5 - 530*z6 ); id mncexp11 = 1 + ep * ( 2 ) + ep^2 * ( 8 ) + ep^3 * ( 32 - 22*z3 ) + ep^4 * ( 128 - 44*z3 - 33*z4 ) + ep^5 * ( 512 - 176*z3 - 66*z4 - 234*z5 ) + ep^6 * ( 2048 - 704*z3 + 242*z3^2 - 264*z4 - 468*z5 - 530*z6 ); id mncexp20 = 1 + ep * ( 2 ) + ep^2 * ( 8 ) + ep^3 * ( 32 - 16*z3 ) + ep^4 * ( 128 - 32*z3 - 24*z4 ) + ep^5 * ( 512 - 128*z3 - 48*z4 - 192*z5 ) + ep^6 * ( 2048 - 512*z3 + 128*z3^2 - 192*z4 - 384*z5 - 440*z6 ); id mncexp10 = 1 + ep * ( 1 ) + ep^2 * ( 3 ) + ep^3 * ( 9 - 6*z3 ) + ep^4 * ( 27 - 6*z3 - 9*z4 ) + ep^5 * ( 81 - 18*z3 - 9*z4 - 42*z5 ) + ep^6 * ( 243 - 54*z3 + 18*z3^2 - 27*z4 - 42*z5 - 90*z6 ); * * This integral is from the paper, but apparently there is a problem * with the relative normalization. We correct that here with the * factor 1-2*ep. It makes that all our results are in agreement with * the mincer paper. * id mncG311 = (1-2*ep)*(6*z3+9*z4*ep+102*z5*ep^2); *id mncG311 = (1-2*ep)*(6*z3+9*z4*ep+102*z5*ep^2+240*z6*ep^3-186*ep^3*z3^2); * id mncF321 = 20*z5; *id mncF321 = (20*z5+50*z6*ep+68*z3^2*ep)*(1+2*ep); *id mncF321 = (20*z5+50*z6*ep+68*z3^2*ep+450*z7*ep^2+204*z3*z4*ep^2)*(1+2*ep+4*ep^2); id ep = 0; #endprocedure *--#] subint : *--#[ sym1 : #procedure sym1(TOPO) #switch `TOPO' *--#[ la : #case la * #ifdef `LATRANS' *#if ( `LATRANS' == 0 ) *if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1,[P+p3].[P+p3],1, * [P-p1].[P-p1],1,[P-p2].[P-p2],1,[P-p3].[P-p3],1) > * count([P+p4].[P+p4],1,[P+p5].[P+p5],1,[P+p6].[P+p6],1, * [P-p4].[P-p4],1,[P-p5].[P-p5],1,[P-p6].[P-p6],1) ); * multiply,replace_( * [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] * ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] * ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); * multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3, * [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); * id p7 = -p7; * id p8 = -p8; *endif; *if ( count([P+p1].[P+p1],1,[P+p6].[P+p6],1, * [P-p1].[P-p1],1,[P-p6].[P-p6],1) > * count([P+p3].[P+p3],1,[P+p4].[P+p4],1, * [P-p3].[P-p3],1,[P-p4].[P-p4],1) ); * multiply,replace_( * [P-p1],[P+p3],[P+p1],[P-p3],[P-p4],[P+p6],[P+p4],[P-p6] * ,[P-p3],[P+p1],[P+p3],[P-p1],[P-p6],[P+p4],[P+p6],[P-p4] * ,[P-p2],[P+p2],[P+p2],[P-p2],[P-p5],[P+p5],[P+p5],[P-p5] * ,[P-p7],[P+p8],[P+p7],[P-p8],[P-p8],[P+p7],[P+p8],[P-p7] * ,p1,-p3,p3,-p1,p4,-p6,p6,-p4,p2,-p2,p5,-p5,p7,-p8,p8,-p7,Q,-Q * ,[P+Q],[P-Q],[P-Q],[P+Q]); *endif; *#endif #else #ifdef `LASYM' #if ( `LASYM' == 1 ) multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); id p7 = -p7; id p8 = -p8; #else #if ( `LASYM' == 2 ) multiply,replace_( [P-p1],[P+p3],[P+p1],[P-p3],[P-p4],[P+p6],[P+p4],[P-p6] ,[P-p3],[P+p1],[P+p3],[P-p1],[P-p6],[P+p4],[P+p6],[P-p4] ,[P-p2],[P+p2],[P+p2],[P-p2],[P-p5],[P+p5],[P+p5],[P-p5] ,[P-p7],[P+p8],[P+p7],[P-p8],[P-p8],[P+p7],[P+p8],[P-p7] ,p1,-p3,p3,-p1,p4,-p6,p6,-p4,p2,-p2,p5,-p5,p7,-p8,p8,-p7,Q,-Q ,[P+Q],[P-Q],[P-Q],[P+Q]); #else #if ( `LASYM' == 3 ) multiply,replace_( [P-p1],[P+p3],[P+p1],[P-p3],[P-p4],[P+p6],[P+p4],[P-p6] ,[P-p3],[P+p1],[P+p3],[P-p1],[P-p6],[P+p4],[P+p6],[P-p4] ,[P-p2],[P+p2],[P+p2],[P-p2],[P-p5],[P+p5],[P+p5],[P-p5] ,[P-p7],[P+p8],[P+p7],[P-p8],[P-p8],[P+p7],[P+p8],[P-p7] ,p1,-p3,p3,-p1,p4,-p6,p6,-p4,p2,-p2,p5,-p5,p7,-p8,p8,-p7,Q,-Q ,[P+Q],[P-Q],[P-Q],[P+Q]); multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); id p7 = -p7; id p8 = -p8; #endif #endif #endif #else if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1,[P+p3].[P+p3],1, [P-p1].[P-p1],1,[P-p2].[P-p2],1,[P-p3].[P-p3],1) > count([P+p4].[P+p4],1,[P+p5].[P+p5],1,[P+p6].[P+p6],1, [P-p4].[P-p4],1,[P-p5].[P-p5],1,[P-p6].[P-p6],1) ); multiply,replace_( [P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3, [P+p7],[P-p7],[P-p7],[P+p7],[P+p8],[P-p8],[P-p8],[P+p8]); id p7 = -p7; id p8 = -p8; endif; if ( count([P+p1].[P+p1],1,[P+p6].[P+p6],1, [P-p1].[P-p1],1,[P-p6].[P-p6],1) > count([P+p3].[P+p3],1,[P+p4].[P+p4],1, [P-p3].[P-p3],1,[P-p4].[P-p4],1) ); multiply,replace_( [P-p1],[P+p3],[P+p1],[P-p3],[P-p4],[P+p6],[P+p4],[P-p6] ,[P-p3],[P+p1],[P+p3],[P-p1],[P-p6],[P+p4],[P+p6],[P-p4] ,[P-p2],[P+p2],[P+p2],[P-p2],[P-p5],[P+p5],[P+p5],[P-p5] ,[P-p7],[P+p8],[P+p7],[P-p8],[P-p8],[P+p7],[P+p8],[P-p7] ,p1,-p3,p3,-p1,p4,-p6,p6,-p4,p2,-p2,p5,-p5,p7,-p8,p8,-p7,Q,-Q ,[P+Q],[P-Q],[P-Q],[P+Q]); endif; #endif #endif * #break *--#] la : *--#[ be : #case be * * #break *--#] be : *--#[ no : #case no * #ifdef `NOSPEC' #if ( `NOSPEC' == 1 ) if ( count([P+p2].[P+p2],1,[P-p2].[P-p2],1) == 0 ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); elseif( count([P+p7].[P+p7],1,[P-p7].[P-p7],1) == 0 ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p8],[P+p2],[P-p8],[P+p8],[P-p2],[P-p8],[P+p2] ,[P+p5],[P+p7],[P-p5],[P-p7],[P+p7],[P+p5],[P-p7],[P-p5]); multiply,replace_(p2,-p8,p8,-p2,p7,p5,p5,p7,p1,-p6,p6,-p1); elseif ( count([P+p8].[P+p8],1,[P-p8].[P-p8],1) == 0 ); multiply,replace_([P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,[P-p2],[P+p7],[P+p2],[P-p7],[P+p7],[P-p2],[P-p7],[P+p2] ,[P+p5],[P+p8],[P-p5],[P-p8],[P+p8],[P+p5],[P-p8],[P-p5]); multiply,replace_(p2,-p7,p7,-p2,p8,p5,p5,p8,p3,-p4,p4,-p3); else; if ( count([P+p2].[P+p2],1,[P-p2].[P-p2],1) > count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); endif; if ( count([P+p7].[P+p7],1,[P-p7].[P-p7],1) > count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p8],[P+p2],[P-p8],[P+p8],[P-p2],[P-p8],[P+p2] ,[P+p5],[P+p7],[P-p5],[P-p7],[P+p7],[P+p5],[P-p7],[P-p5]); multiply,replace_(p2,-p8,p8,-p2,p7,p5,p5,p7,p1,-p6,p6,-p1); if ( count([P+p2].[P+p2],1,[P-p2].[P-p2],1) > count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); endif; elseif ( count([P+p8].[P+p8],1,[P-p8].[P-p8],1) > count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,[P-p2],[P+p7],[P+p2],[P-p7],[P+p7],[P-p2],[P-p7],[P+p2] ,[P+p5],[P+p8],[P-p5],[P-p8],[P+p8],[P+p5],[P-p8],[P-p5]); multiply,replace_(p2,-p7,p7,-p2,p8,p5,p5,p8,p3,-p4,p4,-p3); endif; endif; #else #if ( `NOSPEC' == 0 ) if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1,[P+p3].[P+p3],1, [P-p1].[P-p1],1,[P-p2].[P-p2],1,[P-p3].[P-p3],1) > count([P+p4].[P+p4],1,[P+p5].[P+p5],1,[P+p6].[P+p6],1, [P-p4].[P-p4],1,[P-p5].[P-p5],1,[P-p6].[P-p6],1) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); endif; if ( count([P+p2].[P+p2],1,[P+p3].[P+p3],1, [P-p2].[P-p2],1,[P-p3].[P-p3],1) > count([P+p4].[P+p4],1,[P+p7].[P+p7],1, [P-p4].[P-p4],1,[P-p7].[P-p7],1) ); multiply,replace_([P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,[P-p2],[P+p7],[P+p2],[P-p7],[P+p7],[P-p2],[P-p7],[P+p2] ,[P+p5],[P+p8],[P-p5],[P-p8],[P+p8],[P+p5],[P-p8],[P-p5]); multiply,replace_(p2,-p7,p7,-p2,p8,p5,p5,p8,p3,-p4,p4,-p3); endif; if ( count([P+p2].[P+p2],1,[P+p1].[P+p1],1, [P-p2].[P-p2],1,[P-p1].[P-p1],1) > count([P+p6].[P+p6],1,[P+p8].[P+p8],1, [P-p6].[P-p6],1,[P-p8].[P-p8],1) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p8],[P+p2],[P-p8],[P+p8],[P-p2],[P-p8],[P+p2] ,[P+p5],[P+p7],[P-p5],[P-p7],[P+p7],[P+p5],[P-p7],[P-p5]); multiply,replace_(p2,-p8,p8,-p2,p7,p5,p5,p7,p1,-p6,p6,-p1); endif; #endif #endif #else if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1,[P+p3].[P+p3],1, [P-p1].[P-p1],1,[P-p2].[P-p2],1,[P-p3].[P-p3],1) > count([P+p4].[P+p4],1,[P+p5].[P+p5],1,[P+p6].[P+p6],1, [P-p4].[P-p4],1,[P-p5].[P-p5],1,[P-p6].[P-p6],1) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p5],[P+p2],[P-p5],[P+p5],[P-p2],[P-p5],[P+p2] ,[P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3]); multiply,replace_(p1,-p6,p6,-p1,p2,-p5,p5,-p2,p3,-p4,p4,-p3,p7,p8,p8,p7 ,[P+p8],[P+p7],[P+p7],[P+p8],[P-p8],[P-p7],[P-p7],[P-p8]); endif; if ( count([P+p2].[P+p2],1,[P+p3].[P+p3],1, [P-p2].[P-p2],1,[P-p3].[P-p3],1) > count([P+p4].[P+p4],1,[P+p7].[P+p7],1, [P-p4].[P-p4],1,[P-p7].[P-p7],1) ); multiply,replace_([P-p3],[P+p4],[P+p3],[P-p4],[P+p4],[P-p3],[P-p4],[P+p3] ,[P-p2],[P+p7],[P+p2],[P-p7],[P+p7],[P-p2],[P-p7],[P+p2] ,[P+p5],[P+p8],[P-p5],[P-p8],[P+p8],[P+p5],[P-p8],[P-p5]); multiply,replace_(p2,-p7,p7,-p2,p8,p5,p5,p8,p3,-p4,p4,-p3); endif; if ( count([P+p2].[P+p2],1,[P+p1].[P+p1],1, [P-p2].[P-p2],1,[P-p1].[P-p1],1) > count([P+p6].[P+p6],1,[P+p8].[P+p8],1, [P-p6].[P-p6],1,[P-p8].[P-p8],1) ); multiply,replace_([P-p1],[P+p6],[P+p1],[P-p6],[P+p6],[P-p1],[P-p6],[P+p1] ,[P-p2],[P+p8],[P+p2],[P-p8],[P+p8],[P-p2],[P-p8],[P+p2] ,[P+p5],[P+p7],[P-p5],[P-p7],[P+p7],[P+p5],[P-p7],[P-p5]); multiply,replace_(p2,-p8,p8,-p2,p7,p5,p5,p7,p1,-p6,p6,-p1); endif; #endif * #break *--#] no : *--#[ fa : #case fa * * #break *--#] fa : *--#[ bu : #case bu * * #break *--#] bu : *--#[ o1 : #case o1 * *if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) > * count([P+p7].[P+p7],1,[P-p7].[P-p7],1) ); * multiply,replace_([P+p6],[P+p7],[P+p7],[P+p6],[P-p6],[P-p7],[P-p7],[P-p6] * p6,p7,p7,p6); *endif; *if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1, * [P-p1].[P-p1],1,[P-p2].[P-p2],1) > * count([P+p3].[P+p3],1,[P+p4].[P+p4],1, * [P-p3].[P-p3],1,[P-p4].[P-p4],1) ); * multiply,replace_([P-p1],[P+p4],[P+p1],[P-p4],[P+p4],[P-p1],[P-p4],[P+p1] * ,[P-p2],[P+p3],[P+p2],[P-p3],[P+p3],[P-p2],[P-p3],[P+p2] * ,[P-p5],[P+p5],[P+p5],[P-p5],[P-p6],[P+p6],[P+p6],[P-p6] * ,[P-p7],[P+p7],[P+p7],[P-p7]); * multiply,replace_(p1,-p4,p4,-p1,p2,-p3,p3,-p2); * id p5 = -p5; * id p6 = -p6; * id p7 = -p7; *endif; * #break *--#] o1 : *--#[ o2 : #case o2 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) > count([P+p7].[P+p7],1,[P-p7].[P-p7],1) ); multiply,replace_([P+p6],[P+p7],[P+p7],[P+p6],[P-p6],[P-p7],[P-p7],[P-p6] p6,p7,p7,p6); endif; * #break *--#] o2 : *--#[ o3 : #case o3 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) > count([P+p7].[P+p7],1,[P-p7].[P-p7],1) ); multiply,replace_([P+p6],[P+p7],[P+p7],[P+p6],[P-p6],[P-p7],[P-p7],[P-p6] ,p6,p7,p7,p6); endif; if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1, [P-p1].[P-p1],1,[P-p2].[P-p2],1) > count([P+p3].[P+p3],1,[P+p4].[P+p4],1, [P-p3].[P-p3],1,[P-p4].[P-p4],1) ); multiply,replace_([P-p1],[P+p4],[P+p1],[P-p4],[P+p4],[P-p1],[P-p4],[P+p1] ,[P-p2],[P+p3],[P+p2],[P-p3],[P+p3],[P-p2],[P-p3],[P+p2] ,[P-p5],[P+p5],[P+p5],[P-p5]); multiply,replace_(p1,-p4,p4,-p1,p2,-p3,p3,-p2); id p5 = -p5; endif; * #break *--#] o3 : *--#[ o4 : #case o4 * if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1, [P-p1].[P-p1],1,[P-p2].[P-p2],1) > count([P+p4].[P+p4],1,[P+p3].[P+p3],1, [P-p4].[P-p4],1,[P-p3].[P-p3],1) ); multiply,replace_([P-p1],[P+p4],[P+p1],[P-p4],[P+p4],[P-p1],[P-p4],[P+p1] ,[P-p2],[P+p3],[P+p2],[P-p3],[P+p3],[P-p2],[P-p3],[P+p2] ,[P-p5],[P+p5],[P+p5],[P-p5]); multiply,replace_(p1,-p4,p4,-p1,p2,-p3,p3,-p2); id p5 = -p5; endif; * #break *--#] o4 : *--#[ o5 : #case o5 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) > count([P+p7].[P+p7],1,[P-p7].[P-p7],1) ); multiply,replace_([P+p6],[P+p7],[P+p7],[P+p6],[P-p6],[P-p7],[P-p7],[P-p6] p6,p7,p7,p6); endif; * #break *--#] o5 : *--#[ o6 : #case o6 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) > count([P+p7].[P+p7],1,[P-p7].[P-p7],1) ); multiply,replace_([P+p6],[P+p7],[P+p7],[P+p6],[P-p6],[P-p7],[P-p7],[P-p6] ,p6,p7,p7,p6); endif; if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1, [P-p1].[P-p1],1,[P-p2].[P-p2],1) > count([P+p3].[P+p3],1,[P+p4].[P+p4],1, [P-p3].[P-p3],1,[P-p4].[P-p4],1) ); multiply,replace_([P-p1],[P+p4],[P+p1],[P-p4],[P+p4],[P-p1],[P-p4],[P+p1] ,[P-p2],[P+p3],[P+p2],[P-p3],[P+p3],[P-p2],[P-p3],[P+p2] ,[P-p5],[P+p5],[P+p5],[P-p5]); multiply,replace_(p1,-p4,p4,-p1,p2,-p3,p3,-p2); id p5 = -p5; endif; * #break *--#] o6 : *--#[ y1 : #case y1 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) < count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P+p6],[P+p5],[P+p5],[P+p6],[P-p6],[P-p5],[P-p5],[P-p6] p6,p5,p5,p6); endif; if ( count([P+p4].[P+p4],1,[P-p4].[P-p4],1) < count([P+p3].[P+p3],1,[P-p3].[P-p3],1) ); multiply,replace_([P+p4],[P+p3],[P+p3],[P+p4],[P-p4],[P-p3],[P-p3],[P-p4] p4,p3,p3,p4); endif; * #break *--#] y1 : *--#[ y2 : #case y2 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) < count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P+p6],[P+p5],[P+p5],[P+p6],[P-p6],[P-p5],[P-p5],[P-p6] p6,p5,p5,p6); endif; if ( count([P+p4].[P+p4],1,[P-p4].[P-p4],1) < count([P+p3].[P+p3],1,[P-p3].[P-p3],1) ); multiply,replace_([P+p4],[P+p3],[P+p3],[P+p4],[P-p4],[P-p3],[P-p3],[P-p4] p4,p3,p3,p4); endif; * #break *--#] y2 : *--#[ y3 : #case y3 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) < count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P+p6],[P+p5],[P+p5],[P+p6],[P-p6],[P-p5],[P-p5],[P-p6] p6,p5,p5,p6); endif; * #break *--#] y3 : *--#[ y4 : #case y4 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) < count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P+p6],[P+p5],[P+p5],[P+p6],[P-p6],[P-p5],[P-p5],[P-p6] p6,p5,p5,p6); endif; if ( count([P+p4].[P+p4],1,[P-p4].[P-p4],1) < count([P+p3].[P+p3],1,[P-p3].[P-p3],1) ); multiply,replace_([P+p4],[P+p3],[P+p3],[P+p4],[P-p4],[P-p3],[P-p3],[P-p4] p4,p3,p3,p4); endif; * #break *--#] y4 : *--#[ y5 : #case y5 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) < count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P+p6],[P+p5],[P+p5],[P+p6],[P-p6],[P-p5],[P-p5],[P-p6] p6,p5,p5,p6); endif; if ( count([P+p4].[P+p4],1,[P-p4].[P-p4],1) < count([P+p3].[P+p3],1,[P-p3].[P-p3],1) ); multiply,replace_([P+p4],[P+p3],[P+p3],[P+p4],[P-p4],[P-p3],[P-p3],[P-p4] p4,p3,p3,p4); endif; if ( count([P+p2].[P+p2],1,[P-p2].[P-p2],1) < count([P+p1].[P+p1],1,[P-p1].[P-p1],1) ); multiply,replace_([P+p2],[P+p1],[P+p1],[P+p2],[P-p2],[P-p1],[P-p1],[P-p2] p2,p1,p1,p2); endif; * #break *--#] y5 : *--#[ y6 : #case y6 * if ( count([P+p6].[P+p6],1,[P-p6].[P-p6],1) < count([P+p5].[P+p5],1,[P-p5].[P-p5],1) ); multiply,replace_([P+p6],[P+p5],[P+p5],[P+p6],[P-p6],[P-p5],[P-p5],[P-p6] p6,p5,p5,p6); endif; if ( count([P+p4].[P+p4],1,[P-p4].[P-p4],1) < count([P+p3].[P+p3],1,[P-p3].[P-p3],1) ); multiply,replace_([P+p4],[P+p3],[P+p3],[P+p4],[P-p4],[P-p3],[P-p3],[P-p4] p4,p3,p3,p4); endif; * #break *--#] y6 : *--#[ t1 : #case t1 * if ( count([P+p1].[P+p1],1,[P+p2].[P+p2],1, [P-p1].[P-p1],1,[P-p2].[P-p2],1) > count([P+p4].[P+p4],1,[P+p3].[P+p3],1, [P-p4].[P-p4],1,[P-p3].[P-p3],1) ); multiply,replace_([P-p1],[P+p4],[P+p1],[P-p4],[P+p4],[P-p1],[P-p4],[P+p1] ,[P-p2],[P+p3],[P+p2],[P-p3],[P+p3],[P-p2],[P-p3],[P+p2] ,[P-p5],[P+p5],[P+p5],[P-p5]); multiply,replace_(p1,-p4,p4,-p1,p2,-p3,p3,-p2,mnce1,mnce4,mnce4,mnce1,mnce2,mnce3,mnce3,mnce2); id p5 = -p5; endif; * #break *--#] t1 : *--#[ t2 : #case t2 * if ( count([P+p4].[P+p4],1,[P-p4].[P-p4],1) < count([P+p3].[P+p3],1,[P-p3].[P-p3],1) ); multiply,replace_([P+p4],[P+p3],[P+p3],[P+p4],[P-p4],[P-p3],[P-p3],[P-p4] p4,p3,p3,p4,mnce3,mnce4,mnce4,mnce3); endif; * #break *--#] t2 : *--#[ t3 : #case t3 * if ( count([P+p4].[P+p4],1,[P-p4].[P-p4],1) < count([P+p3].[P+p3],1,[P-p3].[P-p3],1) ); multiply,replace_([P+p4],[P+p3],[P+p3],[P+p4],[P-p4],[P-p3],[P-p3],[P-p4] p4,p3,p3,p4,mnce3,mnce4,mnce4,mnce3); endif; if ( count([P+p2].[P+p2],1,[P-p2].[P-p2],1) < count([P+p1].[P+p1],1,[P-p1].[P-p1],1) ); multiply,replace_([P+p2],[P+p1],[P+p1],[P+p2],[P-p2],[P-p1],[P-p1],[P-p2] p2,p1,p1,p2,mnce1,mnce2,mnce2,mnce1); endif; * #break *--#] t3 : *--#[ l1 : #case l1 * * #break *--#] l1 : *--#[ l2 : #case l2 * * #break *--#] l2 : *--#[ l3 : #case l3 * * #break *--#] l3 : *--#[ tr : #case tr * * #break *--#] tr : #endswitch #endprocedure *--#] sym1 : *--#[ sym2 : #procedure sym2(TOPO) #switch `TOPO' *--#[ la : #case la * #ifdef `LATRANS' #if ( `LATRANS' != 1 ) #if ( `LATRANS' != 2 ) if ( count(p7.p7,1) < count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p6.p6,1) == count(p4.p4,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; #endif #endif #else if ( count(p7.p7,1) < count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; #endif * #break *--#] la : *--#[ be : #case be * #ifndef `BEPATH' if ( count(p6.p6,1) < count(p7.p7,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p6.p6,1) == count(p7.p7,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p5.p5,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); endif; endif; #else #if ( `BEPATH' == 0 ) if ( count(p6.p6,1) < count(p7.p7,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p6.p6,1) == count(p7.p7,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p5.p5,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); endif; endif; #endif #if ( `BEPATH' == 7 ) if ( count(p6.p6,1) < count(p7.p7,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p6.p6,1) == count(p7.p7,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p5.p5,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); endif; endif; #endif #if ( `BEPATH' == 8 ) if ( count(p6.p6,1) < count(p7.p7,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p6.p6,1) == count(p7.p7,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p5.p5,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p5,p5,p4,p6,p7,p7,p6,p8,-p8); endif; endif; #endif #endif * #break *--#] be : *--#[ no : #case no * #ifndef `NOSPEC' if ( count(p7.p7,1) < count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; #else #if ( `NOSPEC' != 2 ) if ( count(p7.p7,1) < count(p8.p8,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p7.p7,1) == count(p8.p8,1) ); if ( count(p1.p1,1) < count(p3.p3,1) ); multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); elseif ( count(p1.p1,1) == count(p3.p3,1) ); if ( count(p6.p6,1) < count(p4.p4,1) ) multiply replace_(p1,p3,p3,p1,p4,p6,p6,p4,p7,p8,p8,p7); endif; endif; #endif #endif * #break *--#] no : *--#[ fa : #case fa * * #break *--#] fa : *--#[ bu : #case bu * * #break *--#] bu : *--#[ o1 : #case o1 * * #break *--#] o1 : *--#[ o2 : #case o2 * * #break *--#] o2 : *--#[ o3 : #case o3 * * #break *--#] o3 : *--#[ o4 : #case o4 * * #break *--#] o4 : *--#[ o5 : #case o5 * * #break *--#] o5 : *--#[ o6 : #case o6 * * #break *--#] o6 : *--#[ y1 : #case y1 * * #break *--#] y1 : *--#[ y2 : #case y2 * * #break *--#] y2 : *--#[ y3 : #case y3 * * #break *--#] y3 : *--#[ y4 : #case y4 * * #break *--#] y4 : *--#[ y5 : #case y5 * * #break *--#] y5 : *--#[ y6 : #case y6 * * #break *--#] y6 : *--#[ t1 : #case t1 * * #break *--#] t1 : *--#[ t2 : #case t2 * * #break *--#] t2 : *--#[ t3 : #case t3 * * #break *--#] t3 : *--#[ l1 : #case l1 * * #break *--#] l1 : *--#[ l2 : #case l2 * * #break *--#] l2 : *--#[ l3 : #case l3 * * #break *--#] l3 : *--#[ tr : #case tr * * #break *--#] tr : #endswitch #endprocedure *--#] sym2 : *--#[ tabtwo : #procedure tabtwo(n) Ctable,check,strict,mncTabTwo({-`n'+2}:`n'); * Program for the procedure (positive values. Negative to be added) * #- * CF num,den,den1,G,Gamma,InvGamma; * S ep,mncexp11,mncG311,G00,G01,mncG10,mncG20,n1,n2,n3,n4,n,z3,z4,z5,z6,x,x1,x2; * Format nospaces; * Format 80; * .global * G F1 = mncG311; * G [H1] = mncG311; * .store * #do i = 2,26 * G F`i' = -F{`i'-1}*num(`i'+ep-2+2*ep)*den(`i'+ep-1+ep) * -num(3-3*ep-2*(`i'+ep))*den(`i'+ep-1+ep)*G(1,`i',ep,0,0)*G(1,`i',ep+ep,0,0); * G [H{-`i'+2}] = -[H{-`i'+3}]*den(({-`i'+3})+ep-2+2*ep)*num(({-`i'+3})+ep-1+ep) * -num(3-3*ep-2*(({-`i'+3})+ep))*den(({-`i'+3})+ep-2+2*ep)*G(1,({-`i'+3}),ep,0,0)*G(1,({-`i'+3}),ep+ep,0,0); * * id G(n1?,n2?,n?,n3?,n4?) = Gamma(n1+n2+n-n4-2+ep)*Gamma(2-ep-n1+n3-n4) * *Gamma(2-ep-n2-n+n4)*InvGamma(n1)*InvGamma(n2+n)*InvGamma(4-2*ep-n1-n2-n+n3) * *InvGamma(ep+n)*InvGamma(1-ep)*InvGamma(1-ep-n)*Gamma(2-2*ep-n)*Gamma(1+n)*G(n); * .sort * id G(ep) = mncG10/ep; * id G(2*ep) = mncG20/ep; * id Gamma(x?number_) = fac_(x-1); * id InvGamma(x?number_) = invfac_(x-1); * SplitArg,((ep)),Gamma,InvGamma; * id Gamma(x?) = Gamma(0,x); * id InvGamma(x?) = InvGamma(0,x); * repeat id Gamma(x?{>1},x1?) = Gamma(x-1,x1)*num(x-1+x1); * repeat id InvGamma(x?{>1},x1?) = InvGamma(x-1,x1)*den(x-1+x1); * repeat id Gamma(x?neg0_,x1?) = Gamma(x+1,x1)*den(x+x1); * repeat id InvGamma(x?neg0_,x1?) = InvGamma(x+1,x1)*num(x+x1); * id Gamma(x1?,x2?) = Gamma(x1+x2); * id InvGamma(x1?,x2?) = InvGamma(x1+x2); * id Gamma(x?)*InvGamma(x?) = 1; * id num(x?)*den(x?) = 1; * .sort * splitarg,den; * id den(x?) = 1/x; * id mncG10*mncG20 = mncexp11*(1+ep+3*ep^2+9*ep^3+27*ep^4+81*ep^5+243*ep^6)/3; * id ep^4 = 0; * .sort * #do i = 1,1 * id,once,den(x1?,x2?)=den1(x1,x2); * repeat; * id den1(x1?,x2?) = 1/x1-x2/x1*den1(x1,x2); * id ep^4=0; * endrepeat; * if ( count(den,1) ) redefine i "0"; * .sort * #enddo * #do i = 1,1 * id,once,num(x?) = x; * id,once,num(x?) = x; * id ep^4=0; * if ( count(num,1) ) redefine i "0"; * .sort * #enddo * Print +f +s; * .store * #enddo * .end * #if ( `n' > 12 ) Fill mncTabTwo(-11)= -1/36*ep^-2*mncexp11 +20239/997920*ep^-1*mncexp11 +6100472680597/7302858393600*ep*mncexp11 -1/6*ep*mncG311 +4337250881169876763/1417046642694144000*ep^2*mncexp11 -90641/166320*ep^2*mncG311 +2091812554174566396199387/196402664677408358400000*ep^3*mncexp11 -2374960501/1536796800*ep^3*mncG311 +1090841057/5532468480*mncexp11 ; Fill mncTabTwo(-12)= +1/39*ep^-2*mncexp11 -240007/14054040*ep^-1*mncexp11 -13602195770972309/17381411548300800*ep*mncexp11 +2/13*ep*mncG311 -126089727300984118341343/43844958258819734016000*ep^2*mncexp11 +1201433/2342340*ep^2*mncG311 -791462137880746814741946553891/78999845790741396750028800000*ep^3* mncexp11 +411081820769/281361880800*ep^3*mncG311 -185130132773/1012902770880*mncexp11 ; #endif #if ( `n' > 14 ) Fill mncTabTwo(-13)= -1/42*ep^-2*mncexp11 +218227/15135120*ep^-1*mncexp11 +96615712133749103/131029102441036800*ep*mncexp11 -1/7*ep*mncG311 +128330609845270447137163/47217647355652021248000*ep^2*mncexp11 -1223213/2522520*ep^2*mncG311 +806437143502720334013825585391/85076757005413811884646400000*ep^3* mncexp11 -420364841549/303005102400*ep^3*mncG311 +37176314653/218163673728*mncexp11 ; Fill mncTabTwo(-14)= +1/45*ep^-2*mncexp11 -39527/3243240*ep^-1*mncexp11 -489372048271962043/701941620219840000*ep*mncexp11 +2/15*ep*mncG311 -651802463411113795203911/252951682262421542400000*ep^2*mncexp11 +248761/540540*ep^2*mncG311 -820053293102922261930228979519/91153668220086227019264000000*ep^3* mncexp11 +429255677789/324648324000*ep^3*mncG311 -932246700037/5843669832000*mncexp11 ; #endif #if ( `n' > 16 ) Fill mncTabTwo(-15)= -1/48*ep^-2*mncexp11 +356231/34594560*ep^-1*mncexp11 +3965025206576904973/5989901825875968000*ep*mncexp11 -1/8*ep*mncG311 +10591912614360039408002357/4317042043945327656960000*ep^2*mncexp11 -2526649/5765760*ep^2*mncG311 +26680062946841205007366078530809/3111378541912276548924211200000*ep^3* mncexp11 -1751152491841/1385166182400*ep^3*mncG311 +3739701326971/24932991283200*mncexp11 ; Fill mncTabTwo(-16)= +1/51*ep^-2*mncexp11 -5425297/624864240*ep^-1*mncexp11 -19704672113639282688689/31267661899936670208000*ep*mncexp11 +2/17*ep*mncG311 -897165022393987602347339676917/383098897836880068189265920000*ep^2* mncexp11 +43583663/104144040*ep^2*mncG311 -38455320697994403420164576387353627573/ 4693819640032935446671251475660800000*ep^3*mncexp11 +515566734862579/425332590883200*ep^3*mncG311 -1083095292344179/7655986635897600*mncexp11 ; #endif #if ( `n' > 18 ) Fill mncTabTwo(-17)= -1/54*ep^-2*mncexp11 +4824697/661620960*ep^-1*mncexp11 +6642238931730812316163/11035645376448236544000*ep*mncexp11 -1/9*ep*mncG311 +101074910958324854680006747813/45070458569044713904619520000*ep^2* mncexp11 -44184263/110270160*ep^2*mncG311 +4336657379681819493336208121320064197/ 552214075297992405490735467724800000*ep^3*mncexp11 -58300111178131/50039128339200*ep^3*mncG311 +1085239500610379/8106338790950400*mncexp11 ; Fill mncTabTwo(-18)= +1/57*ep^-2*mncexp11 -26926121/4423058640*ep^-1*mncexp11 -414252621011788053328688873/719088170552055317325312000*ep*mncexp11 +2/19*ep*mncG311 -120064470375697425044084448311403037/55799458696176523527257244426240000 *ep^2*mncexp11 +283463959/737176440*ep^2*mncG311 -97966132225971532793728441924688581206532487/ 12989698836497195123810443708530140774400000*ep^3*mncexp11 +577794401298163817/514827571917859200*ep^3*mncG311 -392335219349419459/3088965431507155200*mncexp11 ; #endif #if ( `n' > 20 ) Fill mncTabTwo(-19)= -1/60*ep^-2*mncexp11 +23454653/4655851200*ep^-1*mncexp11 +392842091381033407/3251542559481216000*mncexp11 -1/10*ep*mncG311 +418414662672056948887520549/756934916370584544552960000*ep*mncexp11 -286935427/775975200*ep^2*mncG311 +121573556148907442332611413858749561/58736272311764761607639204659200000 *ep^2*mncexp11 -587014385228765261/541923759913536000*ep^3*mncG311 +99289525250498040852083706224918378124179051/ 13673367196312836972432046008979095552000000*ep^3*mncexp11 ; Fill mncTabTwo(-20)= +1/63*ep^-2*mncexp11 -4025809/977728752*ep^-1*mncexp11 -78637423738306427/682823937491055360*mncexp11 +2/21*ep*mncG311 -84458825245491925152559753/158956332437822754356121600*ep*mncexp11 +58052207/162954792*ep^2*mncG311 -24597577924272779352797800833315149/12334617185470599937604232978432000* ep^2*mncexp11 +23837371521979469/22760797916368512*ep^3*mncG311 -2872318661116624447065765853785787881132481/ 410201015889385109172961380269372866560000*ep^3*mncexp11 ; #endif #if ( `n' > 22 ) Fill mncTabTwo(-21)= -1/66*ep^-2*mncexp11 +1129187/341429088*ep^-1*mncexp11 +78696634161637187/715339363085867520*mncexp11 -1/11*ep*mncG311 +7747511993476572164820563/15138698327411690891059200*ep*mncexp11 -19563485/56904848*ep^2*mncG311 +3554115033672452949527955889972867/1845997129798321079097232146432000* ep^2*mncexp11 -24182993362304165/23844645436195584*ep^3*mncG311 +20353972296734615546100852841245444473118847/ 3008140783188824133935050121975401021440000*ep^3*mncexp11 ; Fill mncTabTwo(-22)= +1/69*ep^-2*mncexp11 -21268421/8209817616*ep^-1*mncexp11 -41648411239129765523/395615183212079550720*mncexp11 +2/23*ep*mncG311 -1045628386955050669541958115031/2118214239320607495322448793600*ep* mncexp11 +454663035/1368302936*ep^2*mncG311 -1005196430283141997917974196042236743747/ 540066850199887058599996202048299008000*ep^2*mncexp11 +12970120181935054805/13187172773735985024*ep^3*mncG311 -132510917789003115544858242447530765386646895578921/ 20241490685296083433260464230281223924562657280000*ep^3*mncexp11 ; #endif #if ( `n' > 24 ) Fill mncTabTwo(-23)= -1/72*ep^-2*mncexp11 +1860211/951862912*ep^-1*mncexp11 +41661904629000236033/412815843351735183360*mncexp11 -1/12*ep*mncG311 +1054208556985464870405904586201/2210310510595416516858207436800*ep* mncexp11 -459189557/1427794368*ep^2*mncG311 +1015730115258410382500455890369698833837/ 563548017599882148104343863006920704000*ep^2*mncexp11 -13142274710440840631/13760528111724506112*ep^3*mncG311 +134011341193052040338470352268890201416410485783231/ 21121555497700260973837006153336929312587120640000*ep^3*mncexp11 ; Fill mncTabTwo(-24)= +1/75*ep^-2*mncexp11 -928439549/669278610000*ep^-1*mncexp11 -5208087172499993406193/53752062936423852000000*mncexp11 +2/25*ep*mncG311 -663944298056175065463097805223293/1439004238668890961496228800000000*ep* mncexp11 +34766419651/111546435000*ep^2*mncG311 -3205394556273599356654129936530668684470693/ 1834466203124616367527161012392320000000000*ep^2*mncexp11 +8318492645368169264459/8958677156070642000000*ep^3*mncG311 -2116184870428199767751218360444041578560058792819308403/ 343775317345381851787711688693634917197056000000000000*ep^3*mncexp11 ; #endif #if ( `n' > 10 ) fill mncTabTwo(-10) = + 1/33*ep^-2*mncexp11 - 22129/914760*ep^-1*mncexp11 - 216938023/1014285888*mncexp11 - 5997222836107/6694286860800*ep*mncexp11 - 4249965245766403333/1298959422469632000*ep^2*mncexp11 - 2047223673498737416560637/180035775954290995200000*ep^3*mncexp11 + 2/11*ep*mncG311 + 88751/152460*ep^2*mncG311 + 2314681471/1408730400*ep^3*mncG311; fill mncTabTwo(-9) = - 1/30*ep^-2*mncexp11 + 439/15120*ep^-1*mncexp11 + 44567623/190512000*mncexp11 + 22148701837/22861440000*ep*mncexp11 + 1422368328652361/403275801600000*ep^2*mncexp11 + 12441442444649011943/1016255020032000000*ep^3*mncexp11 - 1/5*ep*mncG311 - 1577/2520*ep^2*mncG311 - 18605911/10584000*ep^3*mncG311; #endif #if ( `n' > 8 ) fill mncTabTwo(-8) = + 1/27*ep^-2*mncexp11 - 797/22680*ep^-1*mncexp11 - 44217371/171460800*mncexp11 - 65104918307/61725888000*ep*mncexp11 - 4166135527435991/1088844664320000*ep^2*mncexp11 - 36393341868100266377/2743888554086400000*ep^3*mncexp11 + 2/9*ep*mncG311 + 2563/3780*ep^2*mncG311 + 74297/39200*ep^3*mncG311; fill mncTabTwo(-7) = - 1/24*ep^-2*mncexp11 + 289/6720*ep^-1*mncexp11 + 4876579/16934400*mncexp11 + 2364251101/2032128000*ep*mncexp11 + 16751468663557/3982970880000*ep^2*mncexp11 + 48704651163860173/3345695539200000*ep^3*mncexp11 - 1/4*ep*mncG311 - 831/1120*ep^2*mncG311 - 5823947/2822400*ep^3*mncG311; #endif #if ( `n' > 6 ) fill mncTabTwo(-6) = 1/21*ep^-2*mncexp11 - 157/2940*ep^-1*mncexp11 - 172243/529200*mncexp11 - 288228947/222264000*ep*mncexp11 - 113013415303/24202080000*ep^2*mncexp11 - 1476575820814739/91483862400000*ep^3*mncexp11 + 2/7*ep*mncG311 + 403/490*ep^2*mncG311 + 1404743/617400*ep^3*mncG311; fill mncTabTwo(-5) = - 1/18*ep^-2*mncexp11 + 73/1080*ep^-1*mncexp11 + 24389/64800*mncexp11 + 1917641/1296000*ep*mncexp11 + 15283541/2880000*ep^2*mncexp11 + 9491140693/518400000*ep^3*mncexp11 - 1/3*ep*mncG311 - 167/180*ep^2*mncG311 - 1021/400*ep^3*mncG311; #endif #if ( `n' > 4 ) fill mncTabTwo(-4) = 1/15*ep^-2*mncexp11 - 79/900*ep^-1*mncexp11 - 24007/54000*mncexp11 - 1857983/1080000*ep*mncexp11 - 398148641/64800000*ep^2*mncexp11 - 82309007731/3888000000*ep^3*mncexp11 + 2/5*ep*mncG311 + 161/150*ep^2*mncG311 + 8807/3000*ep^3*mncG311; fill mncTabTwo(-3) = - 1/12*ep^-2*mncexp11 + 17/144*ep^-1*mncexp11 + 955/1728*mncexp11 + 1619/768*ep*mncexp11 + 621317/82944*ep^2*mncexp11 + 25618703/995328*ep^3*mncexp11 - 1/2*ep*mncG311 - 31/24*ep^2*mncG311 - 337/96*ep^3*mncG311; #endif fill mncTabTwo(-2) = 1/9*ep^-2*mncexp11 - 1/6*ep^-1*mncexp11 - 233/324*mncexp11 - 5251/1944*ep*mncexp11 - 111641/11664*ep^2*mncexp11 - 2301799/69984*ep^3*mncexp11 + 2/3*ep*mncG311 + 5/3*ep^2*mncG311 + 9/2*ep^3*mncG311; fill mncTabTwo(-1) = - 1/6*ep^-2*mncexp11 + 1/4*ep^-1*mncexp11 + 9/8*mncexp11 + 203/48*ep*mncexp11 + 477/32*ep^2*mncexp11 + 3261/64*ep^3*mncexp11 - ep*mncG311 - 5/2*ep^2*mncG311 - 27/4*ep^3*mncG311; fill mncTabTwo(0) = + 1/3*ep^-2*mncexp11 - 1/3*ep^-1*mncexp11 - 5/3*mncexp11 - 7*ep*mncexp11 - 27*ep^2*mncexp11 - 99*ep^3*mncexp11 + 2*ep*mncG311 + 6*ep^2*mncG311 + 18*ep^3*mncG311; fill mncTabTwo(1) = mncG311; fill mncTabTwo(2) = + 1/3*ep^-2*mncexp11 - 2*ep^-1*mncexp11 + 28*ep*mncexp11 - 132*ep^2*mncexp11 + 436*ep^3*mncexp11 - 3*ep*mncG311 + 6*ep^2*mncG311 - 12*ep^3*mncG311; fill mncTabTwo(3) = - 1/6*ep^-2*mncexp11 + 2/3*ep^-1*mncexp11 + 23/6*mncexp11 - 373/12*ep*mncexp11 + 2429/24*ep^2*mncexp11 - 10693/48*ep^3*mncexp11 + 3/2*ep*mncG311 - 3*ep^3*mncG311; fill mncTabTwo(4) = + 1/9*ep^-2*mncexp11 - 19/54*ep^-1*mncexp11 - 227/81*mncexp11 + 8801/486*ep*mncexp11 - 148589/2916*ep^2*mncexp11 + 1631399/17496*ep^3*mncexp11 - ep*mncG311 - 5/6*ep^2*mncG311 + 23/9*ep^3*mncG311; fill mncTabTwo(5) = - 1/12*ep^-2*mncexp11 + 2/9*ep^-1*mncexp11 + 995/432*mncexp11 - 65743/5184*ep*mncexp11 + 1861109/62208*ep^2*mncexp11 - 33766519/746496*ep^3*mncexp11 + 3/4*ep*mncG311 + ep^2*mncG311 - 43/24*ep^3*mncG311; fill mncTabTwo(6) = 1/15*ep^-2*mncexp11 - 139/900*ep^-1*mncexp11 - 12799/6750*mncexp11 + 7720709/810000*ep*mncexp11 - 999124577/48600000*ep^2*mncexp11 + 76898788103/2916000000*ep^3*mncexp11 - 3/5*ep*mncG311 - 101/100*ep^2*mncG311 + 464/375*ep^3*mncG311; #if ( `n' > 6 ) fill mncTabTwo(7) = - 1/18*ep^-2*mncexp11 + 41/360*ep^-1*mncexp11 + 13183/8100*mncexp11 - 2437711/324000*ep*mncexp11 + 856633049/58320000*ep^2*mncexp11 - 19656659797/1166400000*ep^3*mncexp11 + 1/2*ep*mncG311 + 39/40*ep^2*mncG311 - 383/450*ep^3*mncG311; fill mncTabTwo(8) = 1/21*ep^-2*mncexp11 - 257/2940*ep^-1*mncexp11 - 2620213/1852200*mncexp11 + 266505851/43218000*ep*mncexp11 - 1832447625539/163364040000*ep^2*mncexp11 + 254648720594909/22870965600000*ep^3*mncexp11 - 3/7*ep*mncG311 - 909/980*ep^2*mncG311 + 118681/205800*ep^3*mncG311; #endif #if ( `n' > 8 ) fill mncTabTwo(9) = - 1/24*ep^-2*mncexp11 + 29/420*ep^-1*mncexp11 + 5316251/4233600*mncexp11 - 6129986999/1185408000*ep*mncexp11 + 26135084020949/2987228160000*ep^2*mncexp11 - 2198751676783421/278807961600000*ep^3*mncexp11 + 3/8*ep*mncG311 + 123/140*ep^2*mncG311 - 88531/235200*ep^3*mncG311; fill mncTabTwo(10) = 1/27*ep^-2*mncexp11 - 3791/68040*ep^-1*mncexp11 - 6029953/5358150*mncexp11 + 478951433329/108020304000*ep*mncexp11 - 1922783114144729/272211166080000*ep^2*mncexp11 + 3804584745942884587/685972138521600000*ep^3*mncexp11 - 1/3*ep*mncG311 - 6289/7560*ep^2*mncG311 + 539599/2381400*ep^3*mncG311; #endif #if ( `n' > 10 ) fill mncTabTwo(11) = - 1/30*ep^-2*mncexp11 + 691/15120*ep^-1*mncexp11 + 12161273/11907000*mncexp11 - 462440372497/120022560000*ep*mncexp11 + 1749242338593257/302456851200000*ep^2*mncexp11 - 3135287147784104059/762191265024000000*ep^3*mncexp11 + 3/10*ep*mncG311 + 265/336*ep^2*mncG311 - 296629/2646000*ep^3*mncG311; fill mncTabTwo(12) = + 1/33*ep^-2*mncexp11 - 34729/914760*ep^-1*mncexp11 - 1183461847/1267857360*mncexp11 + 119387071076071/35145006019200*ep*mncexp11 - 188324238814636153/38968782674088960*ep^2*mncexp11 + 402330866351205405392621/135026831965718246400000*ep^3*mncexp11 - 3/11*ep*mncG311 - 76151/101640*ep^2*mncG311 + 16227353/704365200*ep^3*mncG311; #endif #if ( `n' > 12 ) fill mncTabTwo(13) = +mncexp11*(118985473/138311712-1/36*ep^-2+31789/997920*ep^-1- 115845953484031/38340006566400*ep+173427037149010237/42511399280824320* ep^2-331178083656667835129321/147301998508056268800000*ep^3) +mncG311*(1/4*ep+79091/110880*ep^2+9086983/192099600*ep^3); fill mncTabTwo(14) = +mncexp11*(-80726970169/101290277088+1/39*ep^-2-378607/14054040*ep^-1+ 19057983628915939/7019416202198400*ep-917828713158387269051/ 263069749552918404096*ep^2+96982930360467673021945950803/ 59249884343056047562521600000*ep^3) +mncG311*(-3/13*ep-1062833/1561560*ep^2-29138373491/281361880800*ep^3); #endif #if ( `n' > 14 ) fill mncTabTwo(15) = +mncexp11*(31163414417/41954552640-1/42*ep^-2+49561/2162160*ep^-1- 34465390136310241/14038832404396800*ep+608514247855190980417/ 202361345809937233920*ep^2-78326389799039898454344465203/ 63807567754060358913484800000*ep^3) +mncG311*(3/14*ep+22337/34320*ep^2+45158205011/303005102400*ep^3); fill mncTabTwo(16) = +mncexp11*(-156220820947/224756532000+1/45*ep^-2-63551/3243240*ep^-1+ 1177467131554197689/526456215164880000*ep-496032103090787825106767/ 189713761696816156800000*ep^2+59696467372353531589643837207/ 68365251165064670264448000000*ep^3) +mncG311*(-1/5*ep-224737/360360*ep^2-60421943501/324648324000*ep^3); #endif #if ( `n' > 16 ) fill mncTabTwo(17) = -1/48*ep^-2*mncexp11 +36341/2162160*ep^-1*mncexp11 -9197044416984034249/4492426369406976000*ep*mncexp11 +3/16*ep*mncG311 +7406071119949915594782149/3237781532958995742720000*ep^2*mncexp11 +143839/240240*ep^2*mncG311 -1469249356813091246078334302257/2333533906434207411693158400000*ep^3* mncexp11 +74998145141/346291545600*ep^3*mncG311 +313260416543/479480601600*mncexp11 ; fill mncTabTwo(18) = +1/51*ep^-2*mncexp11 -9028897/624864240*ep^-1*mncexp11 +44198387591377070187407/23450746424952502656000*ep*mncexp11 -3/17*ep*mncG311 -578494640885671113688726388969/287324173377660051141949440000*ep^2* mncexp11 -39980063/69429360*ep^2*mncG311 +1456597704750079615919598045938433029/3520364730024701585003438606745600\ 000*ep^3*mncexp11 -25705837121579/106333147720800*ep^3*mncG311 -22675805832983/36807628057200*mncexp11 ; #endif #if ( `n' > 18 ) fill mncTabTwo(19) = -1/54*ep^-2*mncexp11 +914233/73513440*ep^-1*mncexp11 -4804676536172077713623/2758911344112059136000*ep*mncexp11 +1/6*ep*mncG311 +541823298035903404576139231369/304225595341051818856181760000*ep^2* mncexp11 +4531207/8168160*ep^2*mncG311 -12086502741765690259876029009105109/46017839608166033790894622310400000* ep^3*mncexp11 +29571569291879/112588038763200*ep^3*mncG311 +22719045556433/38972782648800*mncexp11 ; fill mncTabTwo(20) = +1/57*ep^-2*mncexp11 -47346521/4423058640*ep^-1*mncexp11 +32289602952180473422990237/19974671404223758814592000*ep*mncexp11 -3/19*ep*mncG311 -66216776579743878776789051647946609/41849594022132392645442933319680000* ep^2*mncexp11 -263043559/491450960*ep^2*mncG311 +410886238297640666965038605417159731323917/32474247091242987809526109271\ 32535193600000*ep^3*mncexp11 -3004004582171291/10725574414955400*ep^3*mncG311 -16426028172582961/29701590687568800*mncexp11 ; #endif #if ( `n' > 20 ) fill mncTabTwo(21) = -1/60*ep^-2*mncexp11 +42854033/4655851200*ep^-1*mncexp11 +8224570412118719/15632416151352000*mncexp11 +3/20*ep*mncG311 -31642751898923484600251741/21025969899182904015360000*ep*mncexp11 +267536047/517316800*ep^2*mncG311 +62175374925202186690451898489457817/44052204233823571205729403494400000* ep^2*mncexp11 +13306235198169707/45160313326128000*ep^3*mncG311 -103123425161910876432530714755884403590821/ 3418341799078209243108011502244773888000000*ep^3*mncexp11 ; fill mncTabTwo(22) = +1/63*ep^-2*mncexp11 -857881/108636528*ep^-1*mncexp11 -6586465629283471/13131229567135680*mncexp11 -1/7*ep*mncG311 +18627534934151276385171067/13246361036485229529676800*ep*mncexp11 -18119029/36212176*ep^2*mncG311 -467304336531272503807955138154121/370038515564117998128126989352960*ep^2 *mncexp11 -1163990258200027/3793466319394752*ep^3*mncG311 -8274922161803686291111381013441054732447/ 143570355561284788210536483094280503296000*ep^3*mncexp11 ; #endif #if ( `n' > 22 ) fill mncTabTwo(23) = -1/66*ep^-2*mncexp11 +209537/31039008*ep^-1*mncexp11 +6593340582654751/13756526213189760*mncexp11 +3/22*ep*mncG311 -18278829109221221412169147/13877140133460716650137600*ep*mncexp11 +455895/940576*ep^2*mncG311 +2197495236777597510541059642122861/1938296986288237133052093753753600* ep^2*mncexp11 +1260033012442891/3974107572699264*ep^3*mncG311 +18057703135230592977701174594817271748447/ 150407039159441206696752506098770051072000*ep^3*mncexp11 ; fill mncTabTwo(24) = +1/69*ep^-2*mncexp11 -47134261/8209817616*ep^-1*mncexp11 -3490545536559365929/7607984292539991360*mncexp11 -3/23*ep*mncG311 +218451110710127794777775882549/176517853276717291276870732800*ep* mncexp11 -1286391585/2736605872*ep^2*mncG311 -578382028156674817512156943480671625301/ 567070192709881411529996012150713958400*ep^2*mncexp11 -715670746037876689/2197862128955997504*ep^3*mncG311 -179541016399842706507746374726804615624472510721/ 1012074534264804171663023211514061196228132864000*ep^3*mncexp11 ; #endif #if ( `n' > 24 ) fill mncTabTwo(25) = -1/72*ep^-2*mncexp11 +124589987/25700298624*ep^-1*mncexp11 +1746619878756647717/3969383109151299840*mncexp11 +1/8*ep*mncG311 -23844550087585480054603715821/20465838061068671452390809600*ep*mncexp11 +1303204381/2855588736*ep^2*mncG311 +21778607797627277070435024292800992825/ 23669016739195050220382442246290669568*ep^2*mncexp11 +190802034994322767/573355337988521088*ep^3*mncG311 +230257568613348547730654395291283142407911406021/ 1056077774885013048691850307666846465629356032000*ep^3*mncexp11 ; fill mncTabTwo(26) = +1/75*ep^-2*mncexp11 -2713182509/669278610000*ep^-1*mncexp11 -873797113583605563133/2067387036016302000000*mncexp11 -3/25*ep*mncG311 +14652368812358093830178337408169/13324113321008249643483600000000*ep* mncexp11 -32981676691/74364290000*ep^2*mncG311 -8005388011168216979263203812860982949967547/ 9630947566404235929517595315059680000000000*ep^2*mncexp11 -1011594085585797015227/2986225718690214000000*ep^3*mncG311 -21963008831511894502373954790334055916171462415430887/ 85943829336345462946927922173408729299264000000000000*ep^3*mncexp11 ; #endif #endprocedure *--#] tabtwo : *--#[ transfor : #procedure transfor(TOPOL) * * This file contains topology transformations. * The topology assignments of Paulo (lili or convert) sometimes * give a diagram a topology that is too complicated, because he * could not take the 4 and 5 point vertices into account properly. * This file also makes some diagrams zero of which it can be * easily seen that this must be the case. * #switch `TOPOL' *--#[ la : #case la * if ( count(mncx1,1) == 0 ); multiply,replace_( p8,-p5,[P+p8],[P-p5],[P-p8],[P+p5] ,p7,-p7,[P+p7],[P-p7],[P-p7],[P+p7] ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] ,p3,p2,[P+p3],[P+p2],[P-p3],[P-p2] ,p4,p3,[P+p4],[P+p3],[P-p4],[P-p3] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ); multiply,replace_(mncx8,mncx5,mncx2,mncx1,mncx3,mncx2,mncx4,mncx3,mncx5,mncx4); redefine TOPO "o2"; Print,"Topology changed from la to o2"; elseif ( count(mncx2,1) == 0 ); multiply,replace_( p1,-p5,[P+p1],[P-p5],[P-p1],[P+p5] ,p3,-p4,[P+p3],[P-p4],[P-p3],[P+p4] ,p4,-p3,[P+p4],[P-p3],[P-p4],[P+p3] ,p5,-p2,[P+p5],[P-p2],[P-p5],[P+p2] ,p6,-p1,[P+p6],[P-p1],[P-p6],[P+p1] ,p7,p6,[P+p7],[P+p6],[P-p7],[P-p6] ,p8,p7,[P+p8],[P+p7],[P-p8],[P-p7] ); multiply,replace_(mncx1,mncx5,mncx3,mncx4,mncx4,mncx3,mncx5,mncx2,mncx6,mncx1,mncx7,mncx6,mncx8,mncx7); redefine TOPO "be"; Print,"Topology changed from la to be"; elseif ( count(mncx3,1) == 0 ); multiply,replace_( Q,-Q,[P+Q],[P-Q],[P-Q],[P+Q] ,p1,-p2,[P+p1],[P-p2],[P-p1],[P+p2] ,p2,-p1,[P+p2],[P-p1],[P-p2],[P+p1] ,p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p5,-p4,[P+p5],[P-p4],[P-p5],[P+p4] ,p6,-p3,[P+p6],[P-p3],[P-p6],[P+p3] ,p4,-p6,[P+p4],[P-p6],[P-p4],[P+p6] ,p8,p7,[P+p8],[P+p7],[P-p8],[P-p7] )*mncsgn3; multiply,replace_(mncx1,mncx2,mncx2,mncx1,mncx7,mncx5,mncx5,mncx4,mncx6,mncx3,mncx4,mncx6,mncx8,mncx7); redefine TOPO "o2"; Print,"Topology changed from la to o2"; elseif ( count(mncx4,1) == 0 ); multiply,replace_( Q,-Q,[P+Q],[P-Q],[P-Q],[P+Q] ,p7,-p5,[P+p7],[P-p5],[P-p7],[P+p5] ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] ,p2,p4,[P+p2],[P+p4],[P-p2],[P-p4] ,p5,p1,[P+p5],[P+p1],[P-p5],[P-p1] ,p6,p2,[P+p6],[P+p2],[P-p6],[P-p2] ,p3,p6,[P+p3],[P+p6],[P-p3],[P-p6] ,p8,-p7,[P+p8],[P-p7],[P-p8],[P+p7] )*mncsgn3; multiply,replace_(mncx7,mncx5,mncx1,mncx3,mncx2,mncx4,mncx5,mncx1,mncx6,mncx2,mncx3,mncx6,mncx8,mncx7); redefine TOPO "o2"; Print,"Topology changed from la to o2"; elseif ( count(mncx5,1) == 0 ); multiply,replace_( p7,-p6,[P+p7],[P-p6],[P-p7],[P+p6] ,p8,-p7,[P+p8],[P-p7],[P-p8],[P+p7] ,p6,p5,[P+p6],[P+p5],[P-p6],[P-p5] ); multiply,replace_(mncx7,mncx6,mncx8,mncx7,mncx6,mncx5); redefine TOPO "be"; Print,"Topology changed from la to be"; elseif ( count(mncx6,1) == 0 ); multiply,replace_( p1,-p6,[P+p1],[P-p6],[P-p1],[P+p6] ,p2,-p4,[P+p2],[P-p4],[P-p2],[P+p4] ,p3,-p3,[P+p3],[P-p3],[P-p3],[P+p3] ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] ,p5,-p1,[P+p5],[P-p1],[P-p5],[P+p1] ,p8,p5,[P+p8],[P+p5],[P-p8],[P-p5] ); multiply,replace_(mncx1,mncx6,mncx2,mncx4,mncx4,mncx2,mncx5,mncx1,mncx8,mncx5); redefine TOPO "o2"; Print,"Topology changed from la to o2"; elseif ( count(mncx7,1) == 0 ); multiply,replace_( p1,p7,[P+p1],[P+p7],[P-p1],[P-p7] ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] ,p3,p2,[P+p3],[P+p2],[P-p3],[P-p2] ,p4,p3,[P+p4],[P+p3],[P-p4],[P-p3] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ,p8,-p5,[P+p8],[P-p5],[P-p8],[P+p5] ); multiply,replace_(mncx1,mncx7,mncx2,mncx1,mncx3,mncx2,mncx4,mncx3,mncx5,mncx4,mncx8,mncx5); redefine TOPO "o3"; Print,"Topology changed from la to o3"; elseif ( count(mncx8,1) == 0 ); multiply,replace_( p3,p7,[P+p3],[P+p7],[P-p3],[P-p7] ,p4,-p6,[P+p4],[P-p6],[P-p4],[P+p6] ,p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p5,p3,[P+p5],[P+p3],[P-p5],[P-p3] ,p6,p4,[P+p6],[P+p4],[P-p6],[P-p4] ); multiply,replace_(mncx3,mncx7,mncx4,mncx6,mncx7,mncx5,mncx5,mncx3,mncx6,mncx4); redefine TOPO "o3"; Print,"Topology changed from la to o3"; endif; * #break *--#] la : *--#[ be : #case be * if ( count(mncx1,1,mncx3,1) == 0 ); multiply,replace_( p2,p7,[P+p2],[P+p7],[P-p2],[P-p7] ,p8,p5,[P+p8],[P+p5],[P-p8],[P-p5] ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] ,p5,-p1,[P+p5],[P-p1],[P-p5],[P+p1] ,p7,p3,[P+p7],[P+p3],[P-p7],[P-p3] ,p6,p4,[P+p6],[P+p4],[P-p6],[P-p4] ); multiply,replace_(mncx2,mncx7,mncx8,mncx5,mncx4,mncx2,mncx5,mncx1,mncx7,mncx3,mncx6,mncx4); redefine TOPO "o4"; Print,"Topology changed from be to o4"; elseif ( count(mncx1,1,mncx8,1) == 0 ); multiply,replace_( p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] ,p3,p2,[P+p3],[P+p2],[P-p3],[P-p2] ,p4,p3,[P+p4],[P+p3],[P-p4],[P-p3] ,p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p5,p7,[P+p5],[P+p7],[P-p5],[P-p7] ); multiply,replace_(mncx2,mncx1,mncx3,mncx2,mncx4,mncx3,mncx7,mncx5,mncx5,mncx7); redefine TOPO "o2"; Print,"Topology changed from be to o2"; elseif ( count(mncx3,1,mncx8,1) == 0 ); multiply,replace_( Q,-Q,[P+Q],[P-Q],[P-Q],[P+Q] ,p1,-p2,[P+p1],[P-p2],[P-p1],[P+p2] ,p2,-p1,[P+p2],[P-p1],[P-p2],[P+p1] ,p6,-p5,[P+p6],[P-p5],[P-p6],[P+p5] ,p5,-p3,[P+p5],[P-p3],[P-p5],[P+p3] ,p4,-p6,[P+p4],[P-p6],[P-p4],[P+p6] ,p7,-p7,[P+p7],[P-p7],[P-p7],[P+p7] )*mncsgn3; multiply,replace_(mncx1,mncx2,mncx2,mncx1,mncx6,mncx5,mncx5,mncx3,mncx4,mncx6); redefine TOPO "o2"; Print,"Topology changed from be to o2"; elseif ( count(mncx2,1) == 0 ); multiply,replace_( p3,p2,[P+p3],[P+p2],[P-p3],[P-p2] ,p4,p3,[P+p4],[P+p3],[P-p4],[P-p3] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] ,p8,-p5,[P+p8],[P-p5],[P-p8],[P+p5] ); multiply,replace_(mncx3,mncx2,mncx4,mncx3,mncx5,mncx4,mncx8,mncx5); redefine TOPO "o1"; Print,"Topology changed from be to o1"; elseif ( count(mncx4,1) == 0 ); multiply,replace_( p1,p6,[P+p1],[P+p6],[P-p1],[P-p6] ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] ,p3,p2,[P+p3],[P+p2],[P-p3],[P-p2] ,p8,p3,[P+p8],[P+p3],[P-p8],[P-p3] ,p6,p4,[P+p6],[P+p4],[P-p6],[P-p4] ,p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p5,-p7,[P+p5],[P-p7],[P-p5],[P+p7] ); multiply,replace_(mncx1,mncx6,mncx2,mncx1,mncx3,mncx2,mncx8,mncx3,mncx6,mncx4,mncx7,mncx5,mncx5,mncx7); redefine TOPO "o4"; Print,"Topology changed from be to o4"; elseif ( count(mncx5,1) == 0 ); multiply,replace_( p8,-p4,[P+p8],[P-p4],[P-p8],[P+p4] ,p6,-p5,[P+p6],[P-p5],[P-p6],[P+p5] ,p3,p6,[P+p3],[P+p6],[P-p3],[P-p6] ,p4,-p7,[P+p4],[P-p7],[P-p4],[P+p7] ,p7,p3,[P+p7],[P+p3],[P-p7],[P-p3] ); multiply,replace_(mncx8,mncx4,mncx6,mncx5,mncx3,mncx6,mncx4,mncx7,mncx7,mncx3); redefine TOPO "o4"; Print,"Topology changed from be to o4"; elseif ( count(mncx6,1) == 0 ); multiply,replace_( Q,-Q,[P+Q],[P-Q],[P-Q],[P+Q] ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] ,p4,p1,[P+p4],[P+p1],[P-p4],[P-p1] ,p5,p2,[P+p5],[P+p2],[P-p5],[P-p2] ,p3,p4,[P+p3],[P+p4],[P-p3],[P-p4] ,p2,p6,[P+p2],[P+p6],[P-p2],[P-p6] ,p7,-p7,[P+p7],[P-p7],[P-p7],[P+p7] ,p8,p5,[P+p8],[P+p5],[P-p8],[P-p5] )*mncsgn3; multiply,replace_(mncx1,mncx3,mncx4,mncx1,mncx5,mncx2,mncx3,mncx4,mncx2,mncx6,mncx8,mncx5); redefine TOPO "o2"; Print,"Topology changed from be to o2"; elseif ( count(mncx7,1) == 0 ); multiply,replace_( p1,-p4,[P+p1],[P-p4],[P-p1],[P+p4] ,p2,-p7,[P+p2],[P-p7],[P-p2],[P+p7] ,p8,p5,[P+p8],[P+p5],[P-p8],[P-p5] ,p3,-p3,[P+p3],[P-p3],[P-p3],[P+p3] ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] ,p5,-p1,[P+p5],[P-p1],[P-p5],[P+p1] ); multiply,replace_(mncx1,mncx4,mncx2,mncx7,mncx8,mncx5,mncx4,mncx2,mncx5,mncx1); redefine TOPO "o2"; Print,"Topology changed from be to o2"; endif; * #break *--#] be : *--#[ no : #case no * * If we miss a line, we go to the benz topology * if ( count(mncx1,1) == 0 ); multiply,replace_(p8,p7,[P+p8],[P+p7],[P-p8],[P-p7] ,p5,p8,[P+p5],[P+p8],[P-p5],[P-p8] ,p7,p5,[P+p7],[P+p5],[P-p7],[P-p5]); multiply,replace_(mncx8,mncx7,mncx5,mncx8,mncx7,mncx5); redefine TOPO "be"; Print,"Topology changed from no to be"; elseif ( count(mncx2,1) == 0 ); multiply,replace_( p1,-p5,[P+p1],[P-p5],[P-p1],[P+p5] ,p3,-p4,[P+p3],[P-p4],[P-p3],[P+p4] ,p6,-p1,[P+p6],[P-p1],[P-p6],[P+p1] ,p5,-p2,[P+p5],[P-p2],[P-p5],[P+p2] ,p4,-p3,[P+p4],[P-p3],[P-p4],[P+p3] ,p8,p6,[P+p8],[P+p6],[P-p8],[P-p6] ); multiply,replace_(mncx1,mncx5,mncx3,mncx4,mncx6,mncx1,mncx5,mncx2,mncx4,mncx3,mncx8,mncx6); redefine TOPO "be"; Print,"Topology changed from no to be"; elseif ( count(mncx3,1) == 0 ); multiply,replace_( p8,p4,[P+p8],[P+p4],[P-p8],[P-p4] ,p6,p5,[P+p6],[P+p5],[P-p6],[P-p5] ,p7,p6,[P+p7],[P+p6],[P-p7],[P-p6] ,p4,p7,[P+p4],[P+p7],[P-p4],[P-p7] ,p5,-p8,[P+p5],[P-p8],[P-p5],[P+p8] ); multiply,replace_(mncx8,mncx4,mncx6,mncx5,mncx7,mncx6,mncx4,mncx7,mncx5,mncx8); redefine TOPO "be"; Print,"Topology changed from no to be"; elseif ( count(mncx4,1) == 0 ); multiply,replace_( p7,-p2,[P+p7],[P-p2],[P-p7],[P+p2] ,p2,-p6,[P+p2],[P-p6],[P-p2],[P+p6] ,p3,-p7,[P+p3],[P-p7],[P-p3],[P+p7] ,p8,-p8,[P+p8],[P-p8],[P-p8],[P+p8] ,p6,p5,[P+p6],[P+p5],[P-p6],[P-p5] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ); multiply,replace_(mncx7,mncx2,mncx2,mncx6,mncx3,mncx7,mncx6,mncx5,mncx5,mncx4); redefine TOPO "be"; Print,"Topology changed from no to be"; elseif ( count(mncx5,1) == 0 ); multiply,replace_( p7,p6,[P+p7],[P+p6],[P-p7],[P-p6] ,p8,p7,[P+p8],[P+p7],[P-p8],[P-p7] ,p6,p5,[P+p6],[P+p5],[P-p6],[P-p5] ); multiply,replace_(mncx7,mncx6,mncx8,mncx7,mncx6,mncx5); redefine TOPO "be"; Print,"Topology changed from no to be"; elseif ( count(mncx6,1) == 0 ); multiply,replace_( p8,-p2,[P+p8],[P-p2],[P-p8],[P+p2] ,p1,-p6,[P+p1],[P-p6],[P-p1],[P+p6] ,p2,-p7,[P+p2],[P-p7],[P-p2],[P+p7] ,p7,p8,[P+p7],[P+p8],[P-p7],[P-p8] ); multiply,replace_(mncx8,mncx2,mncx1,mncx6,mncx2,mncx7,mncx7,mncx8); redefine TOPO "be"; Print,"Topology changed from no to be"; elseif ( count(mncx7,1) == 0 ); multiply,replace_( p6,-p1,[P+p6],[P-p1],[P-p6],[P+p1] ,p1,-p5,[P+p1],[P-p5],[P-p1],[P+p5] ,p8,-p2,[P+p8],[P-p2],[P-p8],[P+p2] ,p5,p6,[P+p5],[P+p6],[P-p5],[P-p6] ,p2,-p7,[P+p2],[P-p7],[P-p2],[P+p7] ); multiply,replace_(mncx6,mncx1,mncx1,mncx5,mncx8,mncx2,mncx5,mncx6,mncx2,mncx7); redefine TOPO "be"; Print,"Topology changed from no to be"; elseif ( count(mncx8,1) == 0 ); multiply,replace_( p6,p5,[P+p6],[P+p5],[P-p6],[P-p5] ,p3,-p4,[P+p3],[P-p4],[P-p3],[P+p4] ,p4,-p3,[P+p4],[P-p3],[P-p4],[P+p3] ,p7,-p2,[P+p7],[P-p2],[P-p7],[P+p2] ,p2,-p6,[P+p2],[P-p6],[P-p2],[P+p6] ,p5,p7,[P+p5],[P+p7],[P-p5],[P-p7] ); multiply,replace_(mncx6,mncx5,mncx3,mncx4,mncx4,mncx3,mncx7,mncx2,mncx2,mncx6,mncx5,mncx7); redefine TOPO "be"; Print,"Topology changed from no to be"; endif; * #break *--#] no : *--#[ fa : #case fa * * #break *--#] fa : *--#[ bu : #case bu * * #break *--#] bu : *--#[ o1 : #case o1 * if ( count(mncx1,1) == 0 ); multiply,replace_( p3,-p1,[P+p3],[P-p1],[P-p3],[P+p1] ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] ,p5,p3,[P+p5],[P+p3],[P-p5],[P-p3] ,p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ); multiply,replace_(mncx3,mncx1,mncx5,mncx3,mncx7,mncx5); redefine TOPO "y3"; Print,"Topology changed from o1 to y3"; elseif ( count(mncx2,1) == 0 ); multiply,replace_( p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] ,p3,-p4,[P+p3],[P-p4],[P-p3],[P+p4] ,p5,-p3,[P+p5],[P-p3],[P-p5],[P+p3] ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] ,p7,-p5,[P+p7],[P-p5],[P-p7],[P+p5] ); multiply,replace_(mncx1,mncx2,mncx4,mncx1,mncx3,mncx4,mncx5,mncx3,mncx7,mncx5); redefine TOPO "y3"; Print,"Topology changed from o1 to y3"; elseif ( count(mncx3,1) == 0 ); multiply,replace_( p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] ,p2,p4,[P+p2],[P+p4],[P-p2],[P-p4] ,p5,p3,[P+p5],[P+p3],[P-p5],[P-p3] ,p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ); multiply,replace_(mncx4,mncx2,mncx2,mncx4,mncx5,mncx3,mncx7,mncx5); redefine TOPO "y3"; Print,"Topology changed from o1 to y3"; elseif ( count(mncx4,1) == 0 ); multiply,replace_( p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] ,p3,-p2,[P+p3],[P-p2],[P-p3],[P+p2] ,p1,p4,[P+p1],[P+p4],[P-p1],[P-p4] ,p5,-p3,[P+p5],[P-p3],[P-p5],[P+p3] ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] ,p7,-p5,[P+p7],[P-p5],[P-p7],[P+p5] ); multiply,replace_(mncx2,mncx1,mncx3,mncx2,mncx1,mncx4,mncx5,mncx3,mncx7,mncx5); redefine TOPO "y3"; Print,"Topology changed from o1 to y3"; elseif ( ( count(mncx6,1) == 0 ) || ( count(mncx7,1) == 0 ) ); Discard; endif; * #break *--#] o1 : *--#[ o2 : #case o2 * if ( count(mncx1,1) == 0 ); multiply,replace_( p3,-p1,[P+p3],[P-p1],[P-p3],[P+p1] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ,p4,-p3,[P+p4],[P-p3],[P-p4],[P+p3] ,p7,-p5,[P+p7],[P-p5],[P-p7],[P+p5] ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] ); multiply,replace_(mncx3,mncx1,mncx5,mncx4,mncx4,mncx3,mncx7,mncx5); redefine TOPO "y3"; Print,"Topology changed from o2 to y3"; elseif ( count(mncx2,1) == 0 ); multiply,replace_( p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] ,p5,-p5,[P+p5],[P-p5],[P-p5],[P+p5] ,p3,-p6,[P+p3],[P-p6],[P-p3],[P+p6] ,p6,-p3,[P+p6],[P-p3],[P-p6],[P+p3] ,p7,-p4,[P+p7],[P-p4],[P-p7],[P+p4] ); multiply,replace_(mncx1,mncx2,mncx4,mncx1,mncx3,mncx6,mncx6,mncx3,mncx7,mncx4); redefine TOPO "y2"; Print,"Topology changed from o2 to y2"; elseif ( count(mncx3,1) == 0 ); multiply,replace_( p2,p3,[P+p2],[P+p3],[P-p2],[P-p3] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] ,p7,-p5,[P+p7],[P-p5],[P-p7],[P+p5] ); multiply,replace_(mncx2,mncx3,mncx5,mncx4,mncx4,mncx2,mncx7,mncx5); redefine TOPO "y1"; Print,"Topology changed from o2 to y1"; elseif ( count(mncx5,1) == 0 ); multiply,replace_( p2,p5,[P+p2],[P+p5],[P-p2],[P-p5] ,p3,-p6,[P+p3],[P-p6],[P-p3],[P+p6] ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] ,p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] ,p6,-p3,[P+p6],[P-p3],[P-p6],[P+p3] ,p7,-p4,[P+p7],[P-p4],[P-p7],[P+p4] ); multiply,replace_(mncx2,mncx5,mncx3,mncx6,mncx4,mncx1,mncx1,mncx2,mncx6,mncx3,mncx7,mncx4); redefine TOPO "y4"; Print,"Topology changed from o2 to y4"; elseif ( ( count(mncx6,1) == 0 ) || ( count(mncx7,1) == 0 ) ); Discard; endif; * #break *--#] o2 : *--#[ o3 : #case o3 * if ( count(mncx5,1) == 0 ); multiply,replace_( p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] ,p3,-p2,[P+p3],[P-p2],[P-p3],[P+p2] ); multiply,replace_(mncx7,mncx5,mncx1,mncx3,mncx2,mncx1,mncx3,mncx2); redefine TOPO "y5"; Print,"Topology changed from o3 to y5"; elseif ( count(mncx1,1) == 0 ); multiply,replace_( p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p3,-p1,[P+p3],[P-p1],[P-p3],[P+p1] ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] ,p5,p3,[P+p5],[P+p3],[P-p5],[P-p3] ); multiply,replace_(mncx7,mncx5,mncx3,mncx1,mncx5,mncx3); redefine TOPO "y4"; Print,"Topology changed from o3 to y4"; elseif ( count(mncx2,1) == 0 ); multiply,replace_( p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] ,p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] ,p3,-p3,[P+p3],[P-p3],[P-p3],[P+p3] ,p5,-p4,[P+p5],[P-p4],[P-p5],[P+p4] ); multiply,replace_(mncx7,mncx5,mncx4,mncx1,mncx1,mncx2,mncx5,mncx4); redefine TOPO "y4"; Print,"Topology changed from o3 to y4"; elseif ( count(mncx3,1) == 0 ); multiply,replace_( p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] ,p2,p3,[P+p2],[P+p3],[P-p2],[P-p3] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ); multiply,replace_(mncx7,mncx5,mncx4,mncx2,mncx2,mncx3,mncx5,mncx4); redefine TOPO "y4"; Print,"Topology changed from o3 to y4"; elseif ( count(mncx4,1) == 0 ); multiply,replace_( p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] ,p3,-p2,[P+p3],[P-p2],[P-p3],[P+p2] ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] ,p5,-p4,[P+p5],[P-p4],[P-p5],[P+p4] ); multiply,replace_(mncx7,mncx5,mncx2,mncx1,mncx3,mncx2,mncx1,mncx3,mncx5,mncx4); redefine TOPO "y4"; Print,"Topology changed from o3 to y4"; elseif ( ( count(mncx6,1) == 0 ) || ( count(mncx7,1) == 0 ) ); Discard; endif; * #break *--#] o3 : *--#[ o4 : #case o4 * if ( count(mncx5,1) == 0 ); multiply,replace_( p6,p1,[P+p6],[P+p1],[P-p6],[P-p1] ,p7,p2,[P+p7],[P+p2],[P-p7],[P-p2] ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] ,p2,p5,[P+p2],[P+p5],[P-p2],[P-p5] ,p3,-p6,[P+p3],[P-p6],[P-p3],[P+p6] ); multiply,replace_(mncx6,mncx1,mncx7,mncx2,mncx1,mncx3,mncx2,mncx5,mncx3,mncx6); redefine TOPO "y2"; Print,"Topology changed from o4 to y2"; elseif ( count(mncx1,1) == 0 ); multiply,replace_( p6,p1,[P+p6],[P+p1],[P-p6],[P-p1] ,p7,p2,[P+p7],[P+p2],[P-p7],[P-p2] ,p2,p4,[P+p2],[P+p4],[P-p2],[P-p4] ,p3,-p3,[P+p3],[P-p3],[P-p3],[P+p3] ,p4,-p6,[P+p4],[P-p6],[P-p4],[P+p6] ); multiply,replace_(mncx6,mncx1,mncx7,mncx2,mncx2,mncx4,mncx4,mncx6); redefine TOPO "y3"; Print,"Topology changed from o4 to y3"; elseif ( count(mncx2,1) == 0 ); multiply,replace_( p6,p1,[P+p6],[P+p1],[P-p6],[P-p1] ,p7,p2,[P+p7],[P+p2],[P-p7],[P-p2] ,p1,p4,[P+p1],[P+p4],[P-p1],[P-p4] ,p4,-p3,[P+p4],[P-p3],[P-p4],[P+p3] ,p5,-p5,[P+p5],[P-p5],[P-p5],[P+p5] ,p3,-p6,[P+p3],[P-p6],[P-p3],[P+p6] ); multiply,replace_(mncx6,mncx1,mncx7,mncx2,mncx1,mncx4,mncx4,mncx3,mncx3,mncx6); redefine TOPO "y3"; Print,"Topology changed from o4 to y3"; elseif ( count(mncx3,1) == 0 ); multiply,replace_( p6,p1,[P+p6],[P+p1],[P-p6],[P-p1] ,p7,p2,[P+p7],[P+p2],[P-p7],[P-p2] ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] ,p2,p6,[P+p2],[P+p6],[P-p2],[P-p6] ); multiply,replace_(mncx6,mncx1,mncx7,mncx2,mncx1,mncx3,mncx2,mncx6); redefine TOPO "y3"; Print,"Topology changed from o4 to y3"; elseif ( count(mncx4,1) == 0 ); multiply,replace_( p6,p1,[P+p6],[P+p1],[P-p6],[P-p1] ,p7,p2,[P+p7],[P+p2],[P-p7],[P-p2] ,p1,p6,[P+p1],[P+p6],[P-p1],[P-p6] ,p5,-p5,[P+p5],[P-p5],[P-p5],[P+p5] ,p2,p3,[P+p2],[P+p3],[P-p2],[P-p3] ,p3,-p4,[P+p3],[P-p4],[P-p3],[P+p4] ); multiply,replace_(mncx6,mncx1,mncx7,mncx2,mncx1,mncx6,mncx2,mncx3,mncx3,mncx4); redefine TOPO "y3"; Print,"Topology changed from o4 to y3"; elseif ( count(mncx7,1) == 0 ); discard; endif; * #break *--#] o4 : *--#[ o5 : #case o5 * * These are still the old O2 rewritings * *if ( count(mncx1,1) == 0 ); * multiply,replace_( * p3,-p1,[P+p3],[P-p1],[P-p3],[P+p1] * ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] * ,p4,-p3,[P+p4],[P-p3],[P-p4],[P+p3] * ,p7,-p5,[P+p7],[P-p5],[P-p7],[P+p5] * ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] * ); * multiply,replace_(mncx3,mncx1,mncx5,mncx4,mncx4,mncx3,mncx7,mncx5); * redefine TOPO "y3"; * Print,"Topology changed from o2 to y3"; *elseif ( count(mncx2,1) == 0 ); * multiply,replace_( * p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] * ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] * ,p5,-p5,[P+p5],[P-p5],[P-p5],[P+p5] * ,p3,-p6,[P+p3],[P-p6],[P-p3],[P+p6] * ,p6,-p3,[P+p6],[P-p3],[P-p6],[P+p3] * ,p7,-p4,[P+p7],[P-p4],[P-p7],[P+p4] * ); * multiply,replace_(mncx1,mncx2,mncx4,mncx1,mncx3,mncx6,mncx6,mncx3,mncx7,mncx4); * redefine TOPO "y2"; * Print,"Topology changed from o2 to y2"; *elseif ( count(mncx3,1) == 0 ); * multiply,replace_( * p2,p3,[P+p2],[P+p3],[P-p2],[P-p3] * ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] * ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] * ,p6,-p6,[P+p6],[P-p6],[P-p6],[P+p6] * ,p7,-p5,[P+p7],[P-p5],[P-p7],[P+p5] * ); * multiply,replace_(mncx2,mncx3,mncx5,mncx4,mncx4,mncx2,mncx7,mncx5); * redefine TOPO "y1"; * Print,"Topology changed from o2 to y1"; *elseif ( count(mncx5,1) == 0 ); * multiply,replace_( * p2,p5,[P+p2],[P+p5],[P-p2],[P-p5] * ,p3,-p6,[P+p3],[P-p6],[P-p3],[P+p6] * ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] * ,p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] * ,p6,-p3,[P+p6],[P-p3],[P-p6],[P+p3] * ,p7,-p4,[P+p7],[P-p4],[P-p7],[P+p4] * ); * multiply,replace_(mncx2,mncx5,mncx3,mncx6,mncx4,mncx1,mncx1,mncx2,mncx6,mncx3,mncx7,mncx4); * redefine TOPO "y4"; * Print,"Topology changed from o2 to y4"; *elseif ( ( count(mncx6,1) == 0 ) || ( count(mncx7,1) == 0 ) ); * Discard; *endif; * #break *--#] o5 : *--#[ o6 : #case o6 * * These are still the O3 rewritings * *if ( count(mncx5,1) == 0 ); * multiply,replace_( * p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] * ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] * ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] * ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] * ,p3,-p2,[P+p3],[P-p2],[P-p3],[P+p2] * ); * multiply,replace_(mncx7,mncx5,mncx1,mncx3,mncx2,mncx1,mncx3,mncx2); * redefine TOPO "y5"; * Print,"Topology changed from o3 to y5"; *elseif ( count(mncx1,1) == 0 ); * multiply,replace_( * p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] * ,p3,-p1,[P+p3],[P-p1],[P-p3],[P+p1] * ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] * ,p5,p3,[P+p5],[P+p3],[P-p5],[P-p3] * ); * multiply,replace_(mncx7,mncx5,mncx3,mncx1,mncx5,mncx3); * redefine TOPO "y4"; * Print,"Topology changed from o3 to y4"; *elseif ( count(mncx2,1) == 0 ); * multiply,replace_( * p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] * ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] * ,p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] * ,p3,-p3,[P+p3],[P-p3],[P-p3],[P+p3] * ,p5,-p4,[P+p5],[P-p4],[P-p5],[P+p4] * ); * multiply,replace_(mncx7,mncx5,mncx4,mncx1,mncx1,mncx2,mncx5,mncx4); * redefine TOPO "y4"; * Print,"Topology changed from o3 to y4"; *elseif ( count(mncx3,1) == 0 ); * multiply,replace_( * p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] * ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] * ,p2,p3,[P+p2],[P+p3],[P-p2],[P-p3] * ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] * ); * multiply,replace_(mncx7,mncx5,mncx4,mncx2,mncx2,mncx3,mncx5,mncx4); * redefine TOPO "y4"; * Print,"Topology changed from o3 to y4"; *elseif ( count(mncx4,1) == 0 ); * multiply,replace_( * p7,p5,[P+p7],[P+p5],[P-p7],[P-p5] * ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] * ,p3,-p2,[P+p3],[P-p2],[P-p3],[P+p2] * ,p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] * ,p5,-p4,[P+p5],[P-p4],[P-p5],[P+p4] * ); * multiply,replace_(mncx7,mncx5,mncx2,mncx1,mncx3,mncx2,mncx1,mncx3,mncx5,mncx4); * redefine TOPO "y4"; * Print,"Topology changed from o3 to y4"; *elseif ( ( count(mncx6,1) == 0 ) || ( count(mncx7,1) == 0 ) ); * Discard; *endif; * #break *--#] o6 : *--#[ y1 : #case y1 * if ( count(mncx3,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; if ( count(mncx5,1) == 0 ) discard; if ( count(mncx6,1) == 0 ) discard; * #break *--#] y1 : *--#[ y2 : #case y2 * if ( count(mncx2,1) == 0 ) discard; if ( count(mncx3,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; if ( count(mncx5,1) == 0 ) discard; if ( count(mncx6,1) == 0 ) discard; * #break *--#] y2 : *--#[ y3 : #case y3 * if ( count(mncx2,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; if ( count(mncx5,1) == 0 ) discard; if ( count(mncx6,1) == 0 ) discard; * #break *--#] y3 : *--#[ y4 : #case y4 * if ( count(mncx2,1) == 0 ) discard; if ( count(mncx3,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; if ( count(mncx5,1) == 0 ) discard; if ( count(mncx6,1) == 0 ) discard; * #break *--#] y4 : *--#[ y5 : #case y5 * if ( count(mncx1,1) == 0 ) discard; if ( count(mncx2,1) == 0 ) discard; if ( count(mncx3,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; if ( count(mncx5,1) == 0 ) discard; if ( count(mncx6,1) == 0 ) discard; * #break *--#] y5 : *--#[ y6 : #case y6 * if ( count(mncx2,1) == 0 ) discard; if ( count(mncx3,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; if ( count(mncx5,1) == 0 ) discard; if ( count(mncx6,1) == 0 ) discard; * #break *--#] y6 : *--#[ t1 : #case t1 * * If 5 is missing we have t3, if 1,2,3,4 is missing, we have t2. * if ( count(mncx5,1) == 0 ); multiply,replace_(p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2] ,p2,p3,[P+p2],[P+p3],[P-p2],[P-p3] ,p3,-p4,[P+p3],[P-p4],[P-p3],[P+p4]); multiply,replace_(mncx4,mncx2,mncx2,mncx3,mncx3,mncx4); redefine TOPO "t3"; Print,"Topology changed from t1 to t3"; elseif ( count(mncx1,1) == 0 ); multiply,replace_(p5,p3,[P+p5],[P+p3],[P-p5],[P-p3] ,p4,-p4,[P+p4],[P-p4],[P-p4],[P+p4] ,p3,-p1,[P+p3],[P-p1],[P-p3],[P+p1]); multiply,replace_(mncx5,mncx3,mncx3,mncx1); redefine TOPO "t2"; Print,"Topology changed from t1 to t2"; elseif ( count(mncx2,1) == 0 ); multiply,replace_(p1,p2,[P+p1],[P+p2],[P-p1],[P-p2] ,p4,-p1,[P+p4],[P-p1],[P-p4],[P+p1] ,p5,-p3,[P+p5],[P-p3],[P-p5],[P+p3] ,p3,-p4,[P+p3],[P-p4],[P-p3],[P+p4]); multiply,replace_(mncx1,mncx2,mncx4,mncx1,mncx5,mncx3,mncx3,mncx4); redefine TOPO "t2"; Print,"Topology changed from t1 to t2"; elseif ( count(mncx3,1) == 0 ); multiply,replace_(p2,p3,[P+p2],[P+p3],[P-p2],[P-p3] ,p5,p4,[P+p5],[P+p4],[P-p5],[P-p4] ,p4,-p2,[P+p4],[P-p2],[P-p4],[P+p2]); multiply,replace_(mncx2,mncx3,mncx5,mncx4,mncx4,mncx2); redefine TOPO "t2"; Print,"Topology changed from t1 to t2"; elseif ( count(mncx4,1) == 0 ); multiply,replace_(p1,p3,[P+p1],[P+p3],[P-p1],[P-p3] ,p5,-p4,[P+p5],[P-p4],[P-p5],[P+p4] ,p2,p1,[P+p2],[P+p1],[P-p2],[P-p1] p3,-p2,[P+p3],[P-p2],[P-p3],[P+p2]); multiply,replace_(mncx1,mncx3,mncx5,mncx4,mncx2,mncx1,mncx3,mncx2); redefine TOPO "t2"; Print,"Topology changed from t1 to t2"; endif; #break *--#] t1 : *--#[ t2 : #case t2 * if ( count(mncx2,1) == 0 ) discard; if ( count(mncx3,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; * #break *--#] t2 : *--#[ t3 : #case t3 * if ( count(mncx1,1) == 0 ) discard; if ( count(mncx2,1) == 0 ) discard; if ( count(mncx3,1) == 0 ) discard; if ( count(mncx4,1) == 0 ) discard; * #break *--#] t3 : *--#[ l1 : #case l1 * * #break *--#] l1 : *--#[ l2 : #case l2 * * #break *--#] l2 : *--#[ l3 : #case l3 * * #break *--#] l3 : *--#[ tr : #case tr * * #break *--#] tr : #endswitch #endprocedure *--#] transfor : *--#[ triangl2 : #procedure triangl2(P,PA,PB,P1,P3,EA,EB) * * Routine solves the triangle recursion * P * N1 -------------------------- N3 * P1 \ N2 / P3 * \ / * A \ / B * PA \ / PB * \ / * \/ * * mncA,mncB,mncN1,mncN2,mncN3 are the powers of the denominators * mncA and mncB don't have to be integers here. * EA and EB are 1/PA.PA^ep and 1/PB.PB^ep * P is the momentum in mncN2. We need it here to determine the extra * momenta in the numerator. * * This routine differs from the routine triangle in that the final * substitution of mncftri involves gamma functions rather than factorials. * id `P' = mncx*`P'; if ( count(`P1'.`P1',1,`P3'.`P3',1,`P'.`P',1) < -4 ); id mncx^mncm?/`P1'.`P1'^mncN1?/`P'.`P'^mncN2?/`P3'.`P3'^mncN3?/`PA'.`PA'^mncA?/`PB'.`PB'^mncB? *`EA'^mncx1?*`EB'^mncx2? = mncftri(mncN1,mncN2,mncN3,mncA,mncB,mncx1,mncx2,mncm)*mncpoinv(mncA,mncx1)*mncpoinv(mncB,mncx2)*`EA'^mncx1*`EB'^mncx2; id mncpoinv(1,mncx1?) = 1; id mncpoinv(mncx1?,0) = invfac_(mncx1-1); id mncpoinv(mncx1?neg0_,mncx2?) = mncx2*acc(mncPOINV(mncx1,mncx2))*ep; id mncpoinv(mncx1?pos_,mncx2?) = acc(mncPOINV(mncx1,mncx2)); id mncftri(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncx1?,mncx2?,mncm?) = +sum_(mnck4,0,mncN3-1,sign_(mncN1+mnck4)*mncpo(5+mncm-2*mncN2-mncA-mncB-mncN1-mnck4,-2-mncx1-mncx2) *mncsumm1(mncN1,mncN2,mncN3,mncA,mncB,mncx1,mncx2,mncm,mnck4)*invfac_(mnck4))*invfac_(mncN1-1) +mncsumm2(mncN1,mncN2,mncN3,mncA,mncB,mncx1,mncx2,mncm)*mncN2*mncpoinv(4+mncm-2*mncN2-mncA-mncB+mncN2,-2-mncx1-mncx2) +sum_(mnck2,0,mncN1-1,sign_(mnck2+mncN3)*mncpo(5+mncm-2*mncN2-mncA-mncB-mnck2-mncN3,-2-mncx1-mncx2) *mncsumm3(mncN1,mncN2,mncN3,mncA,mncB,mncx1,mncx2,mncm,mnck2)*invfac_(mnck2))*invfac_(mncN3-1) ; * * Evaluate the gamma functions. * We multiply numerator and denominator with gamma(1-2*ep) * Then mncpo(mncx,-2) represents a normalized gamma function. * The following identities can then be applied: * (the table has overal factors ep taken out) * if ( count(mncsumm2,1) ); id mncpoinv(1,mncy1?) = 1; id mncpoinv(mncx1?neg0_,mncy1?) = mncy1*acc(mncPOINV(mncx1,mncy1))*ep; id mncpoinv(mncx1?pos_,mncy1?) = acc(mncPOINV(mncx1,mncy1)); id mncsumm2(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncx1?,mncx2?,mncm?) = +sum_(mnck2,0,mncN1-1,sum_(mnck4,0,mncN3-1,sign_(mnck2+mnck4)*fac_(mnck2+mncN2+mnck4-1) *mncpo(4+mncm-2*mncN2-mncA-mncB-mnck2-mnck4,-2-mncx1-mncx2) *mncsumm2(mncN1,mncN2,mncN3,mncA,mncB,mncx1,mncx2,mncm,mnck2,mnck4) *invfac_(mnck4))*invfac_(mnck2)); id mncpo(mncx1?,0) = fac_(mncx1-1); id mncpo(1,mncy1?) = 1; id mncpo(mncx1?neg0_,mncy1?) = acc(mncPO(mncx1,mncy1))/mncy1/ep; id mncpo(mncx1?pos_,mncy1?) = acc(mncPO(mncx1,mncy1)); id mncsumm2(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncx1?,mncx2?,mncm?,mnck2?,mnck4?) = sum_(mnck1,0,mncN2,invfac_(mnck1)*invfac_(mncN2-mnck1) *mncftri(mncN1-mnck2,0,mncN3-mnck4,mncA+mnck1+mnck2,mncB+mncN2-mnck1+mnck4,mncx1,mncx2)); else; id mncpo(mncx1?,0) = fac_(mncx1-1); id mncpo(1,mncy1?) = 1; id mncpo(mncx1?neg0_,mncy1?) = acc(mncPO(mncx1,mncy1))/mncy1/ep; id mncpo(mncx1?pos_,mncy1?) = acc(mncPO(mncx1,mncy1)); id mncsumm1(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncx1?,mncx2?,mncm?,mnck4?) = sum_(mnck1,0,mncN2-1,sum_(mnck3,0,mncN2-mnck1-1, fac_(mnck1+mncN1+mnck3+mnck4-1)*invfac_(mnck3) *mncpoinv(5+mncm-2*mncN2-mncA-mncB+mnck1+mnck3,-2-mncx1-mncx2) *mncftri(0,mncN2-mnck1-mnck3,mncN3-mnck4,mncA+mnck1+mncN1,mncB+mnck3+mnck4,mncx1,mncx2) )*invfac_(mnck1)); id mncsumm3(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncx1?,mncx2?,mncm?,mnck2?) = sum_(mnck3,0,mncN2-1,sum_(mnck1,0,mncN2-mnck3-1, fac_(mnck1+mnck2+mnck3+mncN3-1)*invfac_(mnck1) *mncpoinv(5+mncm-2*mncN2-mncA-mncB+mnck1+mnck3,-2-mncx1-mncx2) *mncftri(mncN1-mnck2,mncN2-mnck1-mnck3,0,mncA+mnck1+mnck2,mncB+mnck3+mncN3,mncx1,mncx2) )*invfac_(mnck3)); id mncpoinv(1,mncy1?) = 1; id mncpoinv(mncx1?neg0_,mncy1?) = mncy1*acc(mncPOINV(mncx1,mncy1))*ep; id mncpoinv(mncx1?pos_,mncy1?) = acc(mncPOINV(mncx1,mncy1)); endif; id mncftri(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncx1?,mncx2?) = mncpo(mncA,mncx1)*mncpo(mncB,mncx2) /`P1'.`P1'^mncN1/`P'.`P'^mncN2/`P3'.`P3'^mncN3/`PA'.`PA'^mncA/`PB'.`PB'^mncB; id mncpo(mncx1?,0) = fac_(mncx1-1); id mncpo(1,mncy1?) = 1; id mncpo(mncx1?neg0_,mncy1?) = acc(mncPO(mncx1,mncy1))/mncy1/ep; id mncpo(mncx1?pos_,mncy1?) = acc(mncPO(mncx1,mncy1)); else; repeat; if ( match(1/`P'.`P'/`P1'.`P1'/`P3'.`P3') > 0 ); id mncx^mncx4?/`PA'.`PA'^mncx1?/`PB'.`PB'^mncx2?/`P'.`P'^mncx3?*`EA'^mncy1?*`EB'^mncy2? = mncx^mncx4 /`PA'.`PA'^mncx1 /`PB'.`PB'^mncx2 /`P'.`P'^mncx3 *`EA'^mncy1*`EB'^mncy2*( +acc(mncx2+mncy2*ep)*`P'.`P'/`PB'.`PB'-acc(mncx2+mncy2*ep)*`P3'.`P3'/`PB'.`PB' +acc(mncx1+mncy1*ep)*`P'.`P'/`PA'.`PA'-acc(mncx1+mncy1*ep)*`P1'.`P1'/`PA'.`PA' )*mncdeno(4+mncx4-mncx1-mncx2-2*mncx3,-2-mncy1-mncy2); id,many,mncdeno(0,mncy1?) = 1/mncy1/ep; id,mncdeno(mncx1?,mncy1?) = acc(1-mncy1*ep/mncx1+mncy1^2*ep^2/mncx1^2-mncy1^3*ep^3/mncx1^3 +mncy1^4*ep^4/mncx1^4-mncy1^5*ep^5/mncx1^5+mncy1^6*ep^6/mncx1^6)/mncx1; endif; endrepeat; id mncx = 1; endif; #endprocedure *--#] triangl2 : *--#[ triangle : #procedure triangle(P,PA,PB,P1,P3) * * Routine solves the triangle recursion * P * N1 -------------------------- N3 * P1 \ N2 / P3 * \ / * A \ / B * PA \ / PB * \ / * \/ * * mncA,mncB,mncN1,mncN2,mncN3 are the powers of the denominators * We assume that mncA and mncB are integers here. Otherwise see triangl2. * P is the momentum in mncN2. We need it here to determine the extra * momenta in the numerator. * * We follow the algorithm of F.V.Tkachov Theor. Mat. Fiz. 56(1983)350. * * There are three sums: * One in which the power of 1 becomes zero, one for 2 and one for 3. * Each sum has 4 constants to sum over, except that for each * one of them has its maximal value: * mnck1 = (a-mncA)-mnck2 * mnck2 = mncN1-n1 sum1: mncN1 * mnck3 = (b-mncB)-mnck4 * mnck4 = mncN3-n3 sum3: mncN3 * mnck1+mnck3 = mncN2-n2 sum2: mncN2 * The gamma functions are evaluated using the tables in pochtabl.prc * * It turns out that the easy cases are faster when the regular recursion * is used. We do that here is there are fewer than 6 powers in P,P1 and P3 * combined. Test timings don't use these special cases. * * Programmed by J.A.M.Vermaseren 28-oct-1990 + 13-nov-1990 * * Test versus benzbar: * 1/p1.p1^3/mncp.mncp/p3.p3/pa.pa/pb.pb -> 0.96 sec versus 0.80 sec * 1/p1.p1^3/mncp.mncp^3/p3.p3/pa.pa/pb.pb -> 3.07 sec versus 20.34 sec * 1/p1.p1^3/mncp.mncp^3/p3.p3^3/pa.pa/pb.pb -> 6.21 sec versus 547.11 sec * triangle generates exactly the right number of terms * (times on Atari TT) * * For the easy cases we take the original recursion, because this is much * faster. This is done for the combined powers of P1,P2,P3 at most 4 * in the denominator. IT IS VERY DANGEROUS TO INCREASE THIS NUMBER! * In principle each two steps in the recursion can generate one * extra pole that has to be cancelled between the terms. This can * cause problems with the truncation of the powers of ep. We can * tolerate only one such pole here. * id `P' = mncx*`P'; if ( count(`P1'.`P1',1,`P3'.`P3',1,`P'.`P',1) < -4 ); id mncx^mncm?/`P1'.`P1'^mncN1?/`P'.`P'^mncN2?/`P3'.`P3'^mncN3?/`PA'.`PA'^mncA?/`PB'.`PB'^mncB? = mncftri(mncN1,mncN2,mncN3,mncA,mncB,mncm)*invfac_(mncA-1)*invfac_(mncB-1); id mncftri(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncm?) = +sum_(mnck4,0,mncN3-1,sign_(mncN1+mnck4)*mncpo(5+mncm-2*mncN2-mncA-mncB-mncN1-mnck4,-2) *mncsumm1(mncN1,mncN2,mncN3,mncA,mncB,mncm,mnck4)*invfac_(mnck4))*invfac_(mncN1-1) +mncsumm2(mncN1,mncN2,mncN3,mncA,mncB,mncm)*mncN2*mncpoinv(4+mncm-2*mncN2-mncA-mncB+mncN2,-2) +sum_(mnck2,0,mncN1-1,sign_(mnck2+mncN3)*mncpo(5+mncm-2*mncN2-mncA-mncB-mnck2-mncN3,-2) *mncsumm3(mncN1,mncN2,mncN3,mncA,mncB,mncm,mnck2)*invfac_(mnck2))*invfac_(mncN3-1) ; * * Evaluate the gamma functions. * We multiply numerator and denominator with gamma(1-2*ep) * Then mncpo(mncx,-2) represents a normalized gamma function. * The following identities can then be applied: * (the table has overal factors ep taken out) * if ( count(mncsumm2,1) ); id mncpoinv(1,-2) = 1; id mncpoinv(mncx1?neg0_,-2) = -2*acc(mncPOINV(mncx1,-2))*ep; id mncpoinv(mncx1?,-2) = acc(mncPOINV(mncx1,-2)); id mncsumm2(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncm?) = +sum_(mnck2,0,mncN1-1,sum_(mnck4,0,mncN3-1,sign_(mnck2+mnck4)*fac_(mnck2+mncN2+mnck4-1) *mncpo(4+mncm-2*mncN2-mncA-mncB-mnck2-mnck4,-2)*mncsumm2(mncN1,mncN2,mncN3,mncA,mncB,mncm,mnck2,mnck4) *invfac_(mnck4))*invfac_(mnck2)); id mncpo(1,-2) = 1; id mncpo(mncx1?neg0_,-2) = -acc(mncPO(mncx1,-2))/2/ep; id mncpo(mncx1?,-2) = acc(mncPO(mncx1,-2)); id mncsumm2(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncm?,mnck2?,mnck4?) = +sum_(mnck1,0,mncN2,invfac_(mnck1)*invfac_(mncN2-mnck1) *mncftri(mncN1-mnck2,0,mncN3-mnck4,mncA+mnck1+mnck2,mncB+mncN2-mnck1+mnck4)); else; id mncpo(1,-2) = 1; id mncpo(mncx1?neg0_,-2) = -acc(mncPO(mncx1,-2))/2/ep; id mncpo(mncx1?,-2) = acc(mncPO(mncx1,-2)); id mncsumm1(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncm?,mnck4?) = sum_(mnck1,0,mncN2-1,sum_(mnck3,0,mncN2-mnck1-1, fac_(mnck1+mncN1+mnck3+mnck4-1)*invfac_(mnck3) *mncpoinv(5+mncm-2*mncN2-mncA-mncB+mnck1+mnck3,-2) *mncftri(0,mncN2-mnck1-mnck3,mncN3-mnck4,mncA+mnck1+mncN1,mncB+mnck3+mnck4) )*invfac_(mnck1)); id mncsumm3(mncN1?,mncN2?,mncN3?,mncA?,mncB?,mncm?,mnck2?) = sum_(mnck3,0,mncN2-1,sum_(mnck1,0,mncN2-mnck3-1, fac_(mnck1+mnck2+mnck3+mncN3-1)*invfac_(mnck1) *mncpoinv(5+mncm-2*mncN2-mncA-mncB+mnck1+mnck3,-2) *mncftri(mncN1-mnck2,mncN2-mnck1-mnck3,0,mncA+mnck1+mnck2,mncB+mnck3+mncN3) )*invfac_(mnck3)); id mncpoinv(1,-2) = 1; id mncpoinv(mncx1?neg0_,-2) = -2*acc(mncPOINV(mncx1,-2))*ep; id mncpoinv(mncx1?,-2) = acc(mncPOINV(mncx1,-2)); endif; id mncftri(mncN1?,mncN2?,mncN3?,mncA?,mncB?) = fac_(mncA-1)*fac_(mncB-1) /`P1'.`P1'^mncN1/`P'.`P'^mncN2/`P3'.`P3'^mncN3/`PA'.`PA'^mncA/`PB'.`PB'^mncB; else; repeat; if ( match(1/`P'.`P'/`P1'.`P1'/`P3'.`P3') > 0 ); id mncx^mncx4?/`PA'.`PA'^mncx1?/`PB'.`PB'^mncx2?/`P'.`P'^mncx3? = mncx^mncx4 /`PA'.`PA'^mncx1 /`PB'.`PB'^mncx2 /`P'.`P'^mncx3 *( +mncx2*`P'.`P'/`PB'.`PB'-mncx2*`P3'.`P3'/`PB'.`PB' +mncx1*`P'.`P'/`PA'.`PA'-mncx1*`P1'.`P1'/`PA'.`PA' )*mncdeno(4+mncx4-mncx1-mncx2-2*mncx3,-2); id,many,mncdeno(0,-2) = -1/2/ep; id,mncdeno(mncx1?,-2) = acc(1+2*ep/mncx1+4*ep^2/mncx1^2+8*ep^3/mncx1^3 +16*ep^4/mncx1^4+32*ep^5/mncx1^5+64*ep^6/mncx1^6)/mncx1; endif; endrepeat; id mncx = 1; endif; #endprocedure *--#] triangle : *--#[ trim : #procedure trim(TOPO) #switch `TOPO' *--#[ la : * * *--#] la : *--#[ be : * * *--#] be : *--#[ no : * * *--#] no : *--#[ fa : * * *--#] fa : *--#[ bu : * * *--#] bu : *--#[ o1 : * * *--#] o1 : *--#[ o2 : * * *--#] o2 : *--#[ o3 : * * *--#] o3 : *--#[ o4 : * * *--#] o4 : *--#[ o5 : * * *--#] o5 : *--#[ o6 : * * *--#] o6 : *--#[ y1 : * * *--#] y1 : *--#[ y2 : * * *--#] y2 : *--#[ y3 : * * *--#] y3 : *--#[ y4 : * * *--#] y4 : *--#[ y5 : * * *--#] y5 : *--#[ y6 : * * *--#] y6 : *--#[ t1 : #case t1 * #if 'TRIM' > 0 id ep = 0; #endif * #break *--#] t1 : *--#[ t2 : #case t2 * #if 'TRIM' > 0 id ep = 0; #endif * #break *--#] t2 : *--#[ t3 : #case t3 * #if 'TRIM' > 0 id ep = 0; #endif * #break *--#] t3 : *--#[ l1 : #case l1 * #if 'TRIM' > 0 id ep^{3-'TRIM'} = 0; #endif * #break *--#] l1 : *--#[ l2 : #case l2 * * #break *--#] l2 : *--#[ l3 : #case l3 * * #break *--#] l3 : *--#[ tr : #case tr * #if 'TRIM' > 0 id ep^{4-'TRIM'} = 0; #endif * #break *--#] tr : #endswitch #endprocedure *--#] trim : *--#[ two : #procedure two(P1,E1,P2,E2,P3,E3,P4,E4,P5,E5,Q,EQ,REDUCTION,INTS) * * Routine for the reduction of two loop diagrams. * All particles are massless and it treats only two point functions. * For the algorithm, see "Mincer:...." S.G.Gorishny, S.A.Larin, * L.R.Surguladze and F.V.Tkachov, Comp. Phys. Comm. 55(1989)381. * The core of this routine consists of the equations (3.8)-(3.11). * Note that equation 3.10 isn't right, but the equation 4.29 in * K.G.Chetyrkin and F.V.Tkachov, Nucl.Phys. B192(1981)159 is correct. * The odd parameters are the vectors and the even parameters * are symbols for 1/(p.p^ep). The last parameter indicates whether * there should be a tensor reduction first. * * This routine is (mostly) superceeded by the routine newtwo. Only when * we have to calculate extra elements in the table tabtwo we need this * routine. * #if ( `REDUCTION' > 0 ) id `P4' = `P1'-`Q'; id `P3' = `P2'-`Q'; id `P5' = `P1'-`P2'; .sort: Two loop momenta; id `P1'.`Q' = `P1'.`P1'/2+`Q'.`Q'/2-`P4'.`P4'/2; id `P2'.`Q' = `P2'.`P2'/2+`Q'.`Q'/2-`P3'.`P3'/2; id `P1'.`P2' = `P1'.`P1'/2+`P2'.`P2'/2-`P5'.`P5'/2; .sort: Two loop scalars; #endif repeat; if ( ( ( count(`P1'.`P1',1) < 0 ) || ( count(`E1',1) > 0 ) ) && ( ( count(`P2'.`P2',1) < 0 ) || ( count(`E2',1) > 0 ) ) && ( ( count(`P3'.`P3',1) < 0 ) || ( count(`E3',1) > 0 ) ) && ( ( count(`P4'.`P4',1) < 0 ) || ( count(`E4',1) > 0 ) ) && ( ( count(`P5'.`P5',1) < 0 ) || ( count(`E5',1) > 0 ) ) ); if ( count(`E5',1) == 0 ); if ( count(`E2',1,`E3',1) == 0 ); id `E1'^mncy1?/`P1'.`P1'^mncx1?/`P2'.`P2'^mncx2?/`P3'.`P3'^mncx3?* `E4'^mncy4?/`P4'.`P4'^mncx4?/`P5'.`P5'^mncx5?*`E5'^mncy5? = `E1'^mncy1/`P1'.`P1'^mncx1/`P2'.`P2'^mncx2/`P3'.`P3'^mncx3* `E4'^mncy4/`P4'.`P4'^mncx4/`P5'.`P5'^mncx5*`E5'^mncy5*( + acc(mncx1,mncy1)*`P5'.`P5'/`P1'.`P1' + acc(mncx4,mncy4)*`P5'.`P5'/`P4'.`P4' - acc(mncx1,mncy1)*`P2'.`P2'/`P1'.`P1' - acc(mncx4,mncy4)*`P3'.`P3'/`P4'.`P4' )*mncdeno(4-mncx1-mncx4-2*mncx5,-mncy1-mncy4-2*mncy5-2); else; id `E1'^mncy1?/`P1'.`P1'^mncx1?*`E2'^mncy2?/`P2'.`P2'^mncx2?* `E3'^mncy3?/`P3'.`P3'^mncx3?*`E4'^mncy4?/`P4'.`P4'^mncx4?* `E5'^mncy5?/`P5'.`P5'^mncx5? = `E1'^mncy1/`P1'.`P1'^mncx1*`E2'^mncy2/`P2'.`P2'^mncx2* `E3'^mncy3/`P3'.`P3'^mncx3*`E4'^mncy4/`P4'.`P4'^mncx4* `E5'^mncy5/`P5'.`P5'^mncx5*( + acc(mncx3,mncy3)*`P5'.`P5'/`P3'.`P3' + acc(mncx2,mncy2)*`P5'.`P5'/`P2'.`P2' - acc(mncx3,mncy3)*`P4'.`P4'/`P3'.`P3' - acc(mncx2,mncy2)*`P1'.`P1'/`P2'.`P2' )*mncdeno(4-mncx2-mncx3-2*mncx5,-mncy2-mncy3-2*mncy5-2); endif; else; if ( ( count(`P1'.`P1',1) < -1 ) && ( count(`E1',1) == 0 ) ); id `E1'^mncy1?/`P1'.`P1'^mncx1?*`E2'^mncy2?/`P2'.`P2'^mncx2?* `E3'^mncy3?/`P3'.`P3'^mncx3?*`E4'^mncy4?/`P4'.`P4'^mncx4?* `E5'^mncy5?/`P5'.`P5'^mncx5? = `E1'^mncy1/`P1'.`P1'^mncx1*`E2'^mncy2/`P2'.`P2'^mncx2* `E3'^mncy3/`P3'.`P3'^mncx3*`E4'^mncy4/`P4'.`P4'^mncx4* `E5'^mncy5/`P5'.`P5'^mncx5*( +acc(2*mncx4+mncx1+mncx5-5,+2*mncy4+mncy1+mncy5+2)*`P1'.`P1'*mncdeno(mncx1-1,mncy1) +`P4'.`P4' +acc(mncx5,mncy5)*`P4'.`P4'*`P1'.`P1'/`P5'.`P5'*mncdeno(mncx1-1,mncy1) -acc(mncx5,mncy5)*`P3'.`P3'*`P1'.`P1'/`P5'.`P5'*mncdeno(mncx1-1,mncy1) )/`Q'.`Q'; else; if ( ( count(`P2'.`P2',1) < -1 ) && ( count(`E2',1) == 0 ) ); id `E1'^mncy1?/`P1'.`P1'^mncx1?*`E2'^mncy2?/`P2'.`P2'^mncx2?* `E3'^mncy3?/`P3'.`P3'^mncx3?*`E4'^mncy4?/`P4'.`P4'^mncx4?* `E5'^mncy5?/`P5'.`P5'^mncx5? = `E1'^mncy1/`P1'.`P1'^mncx1*`E2'^mncy2/`P2'.`P2'^mncx2* `E3'^mncy3/`P3'.`P3'^mncx3*`E4'^mncy4/`P4'.`P4'^mncx4* `E5'^mncy5/`P5'.`P5'^mncx5*( +acc(2*mncx3+mncx2+mncx5-5,+2*mncy3+mncy2+mncy5+2)*`P2'.`P2'*mncdeno(mncx2-1,mncy2) +`P3'.`P3' +acc(mncx5,mncy5)*`P3'.`P3'*`P2'.`P2'/`P5'.`P5'*mncdeno(mncx2-1,mncy2) -acc(mncx5,mncy5)*`P4'.`P4'*`P2'.`P2'/`P5'.`P5'*mncdeno(mncx2-1,mncy2) )/`Q'.`Q'; else; if ( ( count(`P3'.`P3',1) < -1 ) && ( count(`E3',1) == 0 ) ); id `E1'^mncy1?/`P1'.`P1'^mncx1?*`E2'^mncy2?/`P2'.`P2'^mncx2?* `E3'^mncy3?/`P3'.`P3'^mncx3?*`E4'^mncy4?/`P4'.`P4'^mncx4?* `E5'^mncy5?/`P5'.`P5'^mncx5? = `E1'^mncy1/`P1'.`P1'^mncx1*`E2'^mncy2/`P2'.`P2'^mncx2* `E3'^mncy3/`P3'.`P3'^mncx3*`E4'^mncy4/`P4'.`P4'^mncx4* `E5'^mncy5/`P5'.`P5'^mncx5*( +acc(2*mncx2+mncx3+mncx5-5,+2*mncy2+mncy3+mncy5+2)*`P3'.`P3'*mncdeno(mncx3-1,mncy3) +`P2'.`P2' +acc(mncx5,mncy5)*`P2'.`P2'*`P3'.`P3'/`P5'.`P5'*mncdeno(mncx3-1,mncy3) -acc(mncx5,mncy5)*`P1'.`P1'*`P3'.`P3'/`P5'.`P5'*mncdeno(mncx3-1,mncy3) )/`Q'.`Q'; else; if ( ( count(`P4'.`P4',1) < -1 ) && ( count(`E4',1) == 0 ) ); id `E1'^mncy1?/`P1'.`P1'^mncx1?*`E2'^mncy2?/`P2'.`P2'^mncx2?* `E3'^mncy3?/`P3'.`P3'^mncx3?*`E4'^mncy4?/`P4'.`P4'^mncx4?* `E5'^mncy5?/`P5'.`P5'^mncx5? = `E1'^mncy1/`P1'.`P1'^mncx1*`E2'^mncy2/`P2'.`P2'^mncx2* `E3'^mncy3/`P3'.`P3'^mncx3*`E4'^mncy4/`P4'.`P4'^mncx4* `E5'^mncy5/`P5'.`P5'^mncx5*( +acc(2*mncx1+mncx4+mncx5-5,+2*mncy1+mncy4+mncy5+2)*`P4'.`P4'*mncdeno(mncx4-1,mncy4) +`P1'.`P1' +acc(mncx5,mncy5)*`P1'.`P1'*`P4'.`P4'/`P5'.`P5'*mncdeno(mncx4-1,mncy4) -acc(mncx5,mncy5)*`P2'.`P2'*`P4'.`P4'/`P5'.`P5'*mncdeno(mncx4-1,mncy4) )/`Q'.`Q'; else; if ( count(`E1',1,`E2',1,`E3',1,`E4',1) == 0 ); if ( count(`P5'.`P5',1) < -1 ); * * Note: The equation 3.10 in the Mincer paper is wrong! * id 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3' /`P4'.`P4'/`P5'.`P5'^mncx5?*`E5'^mncy5? = -acc(mncx5-2,2+mncy5)*mncdeno(mncx5-1,1+mncy5)*`P5'.`P5'/`Q'.`Q' /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5'^mncx5*`E5'^mncy5 -mncG(1,0,mncx5,mncy5,0,0)*mncG(1,0,mncx5,mncy5+1,0,0)*mncdeno(mncx5-1,1+mncy5) *acc(3-2*mncx5-3*ep-2*mncy5*ep)*2*`EQ'^mncy5*`EQ'^2/`Q'.`Q'^mncx5/(`INTS'); else; if ( count(`P5'.`P5',1) >= 0 ); id 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3' /`P4'.`P4'/`P5'.`P5'^mncx5?*`E5'^mncy5? = -mncdeno(mncx5-1,2+mncy5)*acc(mncx5,1+mncy5)*`Q'.`Q'/`P5'.`P5' /`P1'.`P1'/`P2'.`P2'/`P3'.`P3'/`P4'.`P4'/`P5'.`P5'^mncx5*`E5'^mncy5 -mncG(1,0,mncx5+1,mncy5,0,0)*mncG(1,0,mncx5+1,mncy5+1,0,0)*mncdeno(mncx5-1,2+mncy5) *acc(1-2*mncx5-3*ep-2*mncy5*ep)*2*`EQ'^mncy5*`EQ'^2/`Q'.`Q'^mncx5/(`INTS'); else; id 1/`P1'.`P1'/`P2'.`P2'/`P3'.`P3' /`P4'.`P4'/`P5'.`P5'*`E5'^mncy5? = mncG311/`Q'.`Q'*`EQ'^2*`EQ'^mncy5 /(`INTS'); * * mncG311 = 6*z3+9*z4*ep+102*z5*ep^2+order_(ep,3); * There seems to be also a normalization problem * The above expansion may not be enough! * endif; endif; * else; * goto 1; endif; endif; endif; endif; endif; endif; endif; endrepeat; label 1; id mncdeno(0,mncy1?) = 1/mncy1/ep; id acc(0,mncx1?) = mncx1*ep; id acc(mncx1?,mncy1?) = acc(mncx1+mncy1*ep); id mncdeno(mncx1?,mncy1?) = mncaccm(1+ep*mncy1/mncx1)/mncx1; repeat id mncaccm(mncx1?)*mncaccm(mncx2?) = mncaccm(mncx1*mncx2); id mncaccm(mncx1?) = mncaccm(mncx1-1); id mncaccm(mncx1?) = mncaccm(mncx1-mncx1^2,mncx1^3); id mncaccm(mncx1?,mncx2?) = acc(1-mncx1-mncx2+mncx2*mncx1+mncx2^2); repeat id acc(mncx?)*acc(mncy?) = acc(mncx*mncy); id acc(mncx1?) = mncx1; #endprocedure *--#] two : *--#[ vertsub : #procedure vertsub #if 'GAUGE' == 0 id mncDg(mnci1?,mnci2?,mncp?) = d_(mnci1,mnci2)*mncDs(mncp); #else repeat; id,once,mncDg(mnci1?,mnci2?,mncp?)*mncV3G(?a,mnci1?,mncp?,?b) = mncV3G(?a,mnci2,mncp,?b)*mncDs(mncp) -mncxi*mncp(mnci2)*mncV3G(?a,mncp,mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci1?,mnci2?,mncp?)*mncV3G(?a,mnci1?,-mncp?,?b) = mncV3G(?a,mnci2,-mncp,?b)*mncDs(mncp) +mncxi*mncp(mnci2)*mncV3G(?a,-mncp,-mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci2?,mnci1?,mncp?)*mncV3G(?a,mnci1?,mncp?,?b) = mncV3G(?a,mnci2,mncp,?b)*mncDs(mncp) -mncxi*mncp(mnci2)*mncV3G(?a,mncp,mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci2?,mnci1?,mncp?)*mncV3G(?a,mnci1?,-mncp?,?b) = mncV3G(?a,mnci2,-mncp,?b)*mncDs(mncp) +mncxi*mncp(mnci2)*mncV3G(?a,-mncp,-mncp,?b)*mncDs(mncp)*mncDs(mncp); endrepeat; id mncDg(mnci1?,mnci2?,mncp?) = (d_(mnci1,mnci2)-mncxi*mncp(mnci1)*mncp(mnci2)*mncDs(mncp))*mncDs(mncp); #endif id mncDs(p1?) = 1/p1.p1; id mncDL(mnci1?,mncj1?,p1?) = d_(mnci1,mncj1)/p1.p1-p1(mnci1)*p1(mncj1)/p1.p1^2; .sort repeat; repeat; repeat; id,mncV3G(p1?,p1?,p2?,p2?,p3?,p3?) = 0; id,once,mncV3G(p1?,p1?,p2?,p2?,mnci3?,p3?) = p3.p3*p2(mnci3)-p2.p3*p3(mnci3); id,once,mncV3G(mnci3?,p3?,p1?,p1?,p2?,p2?) = p3.p3*p2(mnci3)-p2.p3*p3(mnci3); id,once,mncV3G(p2?,p2?,mnci3?,p3?,p1?,p1?) = p3.p3*p2(mnci3)-p2.p3*p3(mnci3); endrepeat; id,once,mncV3G(p1?,p1?,mnci2?,p2?,mnci3?,p3?) = p2(mnci2)*p2(mnci3)-p3(mnci2)*p3(mnci3)+p3.p3*d_(mnci2,mnci3)-p2.p2*d_(mnci2,mnci3); id,once,mncV3G(mnci3?,p3?,p1?,p1?,mnci2?,p2?) = p2(mnci2)*p2(mnci3)-p3(mnci2)*p3(mnci3)+p3.p3*d_(mnci2,mnci3)-p2.p2*d_(mnci2,mnci3); id,once,mncV3G(mnci2?,p2?,mnci3?,p3?,p1?,p1?) = p2(mnci2)*p2(mnci3)-p3(mnci2)*p3(mnci3)+p3.p3*d_(mnci2,mnci3)-p2.p2*d_(mnci2,mnci3); endrepeat; id,once,mncV3G(mnci1?,p1?,mnci2?,p2?,mnci3?,p3?) = 2*p1(mnci3)*d_(mnci1,mnci2)+p3(mnci3)*d_(mnci1,mnci2) +2*p2(mnci1)*d_(mnci2,mnci3)+p1(mnci1)*d_(mnci2,mnci3) +2*p3(mnci2)*d_(mnci3,mnci1)+p2(mnci2)*d_(mnci3,mnci1); endrepeat; id mncV4G(mnci1?,mnci2?,mnci3?,mnci4?,mncx1?,mncx2?,mncx3?) = +mncx1*(d_(mnci1,mnci3)*d_(mnci2,mnci4)-d_(mnci1,mnci4)*d_(mnci2,mnci3)) +mncx2*(d_(mnci1,mnci2)*d_(mnci3,mnci4)-d_(mnci1,mnci4)*d_(mnci2,mnci3)) +mncx3*(d_(mnci1,mnci3)*d_(mnci2,mnci4)-d_(mnci1,mnci2)*d_(mnci3,mnci4)); id D = acc(4-2*ep); #endprocedure *--#] vertsub : *--#[ vertsubm : #procedure vertsubm * Multiply replace_(Dg,mncDg,v2gp,mncv2gp,v2gi,mncv2gi,v2gc,mncv2gc, v3g,mncv3g,v3gp,mncv3gp,Ds,mncDs,DL,mncDL,v4g,mncv4g,V4G,mncV4G v3gc,mncv3gc,v3gi,mncv3gi,v4gc,mncv4gc,v4gp,mncv4gp); * multiply,replace_(mncv4gi,mncv4g); *id mncv4gp(?a) = mncx18*mncv4g(?a); id mncv4gp(?a) = mncv4g(?a); #ifdef `GAUGE' #if ( `GAUGE' == 0 ) id mncDg(mnci1?,mnci2?,mncp?) = -i_*d_(mnci1,mnci2)*mncDs(mncp); #else repeat; id mncDg(mnci1?,mnci2?,p1?)*mncv2gi(mnci1?,p1?,?a) = -i_*mncv2gi(mnci2,p1,?a)/p1.p1; id mncDg(mnci2?,mnci1?,p1?)*mncv2gi(mnci1?,p1?,?a) = -i_*mncv2gi(mnci2,p1,?a)/p1.p1; id mncDg(mnci1?,mnci2?,p1?)*mncv2gi(?a,mnci1?,p1?) = -i_*mncv2gi(?a,mnci2,p1)/p1.p1; id mncDg(mnci2?,mnci1?,p1?)*mncv2gi(?a,mnci1?,p1?) = -i_*mncv2gi(?a,mnci2,p1)/p1.p1; id mncDg(mnci1?,mnci2?,-p1?)*mncv2gi(mnci1?,p1?,?a) = -i_*mncv2gi(mnci2,p1,?a)/p1.p1; id mncDg(mnci2?,mnci1?,-p1?)*mncv2gi(mnci1?,p1?,?a) = -i_*mncv2gi(mnci2,p1,?a)/p1.p1; id mncDg(mnci1?,mnci2?,-p1?)*mncv2gi(?a,mnci1?,p1?) = -i_*mncv2gi(?a,mnci2,p1)/p1.p1; id mncDg(mnci2?,mnci1?,-p1?)*mncv2gi(?a,mnci1?,p1?) = -i_*mncv2gi(?a,mnci2,p1)/p1.p1; endrepeat; * repeat; * id mncDg(mnci1?,mnci2?,p1?)*mncv2gp(mnci1?,p1?,?a) = -i_*mncv2gp(mnci2,p1,?a)/p1.p1; * id mncDg(mnci2?,mnci1?,p1?)*mncv2gp(mnci1?,p1?,?a) = -i_*mncv2gp(mnci2,p1,?a)/p1.p1; * id mncDg(mnci1?,mnci2?,p1?)*mncv2gp(?a,mnci1?,p1?) = -i_*mncv2gp(?a,mnci2,p1)/p1.p1; * id mncDg(mnci2?,mnci1?,p1?)*mncv2gp(?a,mnci1?,p1?) = -i_*mncv2gp(?a,mnci2,p1)/p1.p1; * id mncDg(mnci1?,mnci2?,-p1?)*mncv2gp(mnci1?,p1?,?a) = -i_*mncv2gp(mnci2,p1,?a)/p1.p1; * id mncDg(mnci2?,mnci1?,-p1?)*mncv2gp(mnci1?,p1?,?a) = -i_*mncv2gp(mnci2,p1,?a)/p1.p1; * id mncDg(mnci1?,mnci2?,-p1?)*mncv2gp(?a,mnci1?,p1?) = -i_*mncv2gp(?a,mnci2,p1)/p1.p1; * id mncDg(mnci2?,mnci1?,-p1?)*mncv2gp(?a,mnci1?,p1?) = -i_*mncv2gp(?a,mnci2,p1)/p1.p1; * endrepeat; * repeat; * id mncDg(mnci1?,mnci2?,p1?)*mncv2gc(mnci1?,p1?,?a) = -i_*mncv2gc(mnci2,p1,?a)/p1.p1; * id mncDg(mnci2?,mnci1?,p1?)*mncv2gc(mnci1?,p1?,?a) = -i_*mncv2gc(mnci2,p1,?a)/p1.p1; * id mncDg(mnci1?,mnci2?,p1?)*mncv2gc(?a,mnci1?,p1?) = -i_*mncv2gc(?a,mnci2,p1)/p1.p1; * id mncDg(mnci2?,mnci1?,p1?)*mncv2gc(?a,mnci1?,p1?) = -i_*mncv2gc(?a,mnci2,p1)/p1.p1; * id mncDg(mnci1?,mnci2?,-p1?)*mncv2gc(mnci1?,p1?,?a) = -i_*mncv2gc(mnci2,p1,?a)/p1.p1; * id mncDg(mnci2?,mnci1?,-p1?)*mncv2gc(mnci1?,p1?,?a) = -i_*mncv2gc(mnci2,p1,?a)/p1.p1; * id mncDg(mnci1?,mnci2?,-p1?)*mncv2gc(?a,mnci1?,p1?) = -i_*mncv2gc(?a,mnci2,p1)/p1.p1; * id mncDg(mnci2?,mnci1?,-p1?)*mncv2gc(?a,mnci1?,p1?) = -i_*mncv2gc(?a,mnci2,p1)/p1.p1; * endrepeat; repeat; id,once,mncDg(mnci1?,mnci2?,mncp?)*mncv3g(?a,mnci1?,mncp?,?b) = -i_*mncv3g(?a,mnci2,mncp,?b)*mncDs(mncp) +i_*mncxi*mncp(mnci2)*mncv3g(?a,mncp,mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci1?,mnci2?,mncp?)*mncv3g(?a,mnci1?,-mncp?,?b) = -i_*mncv3g(?a,mnci2,-mncp,?b)*mncDs(mncp) -i_*mncxi*mncp(mnci2)*mncv3g(?a,-mncp,-mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci2?,mnci1?,mncp?)*mncv3g(?a,mnci1?,mncp?,?b) = -i_*mncv3g(?a,mnci2,mncp,?b)*mncDs(mncp) +i_*mncxi*mncp(mnci2)*mncv3g(?a,mncp,mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci2?,mnci1?,mncp?)*mncv3g(?a,mnci1?,-mncp?,?b) = -i_*mncv3g(?a,mnci2,-mncp,?b)*mncDs(mncp) -i_*mncxi*mncp(mnci2)*mncv3g(?a,-mncp,-mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci1?,mnci2?,mncp?)*mncv3gp(?a,mnci1?,mncp?,?b) = -i_*mncv3gp(?a,mnci2,mncp,?b)*mncDs(mncp) +i_*mncxi*mncp(mnci2)*mncv3gp(?a,mncp,mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci1?,mnci2?,mncp?)*mncv3gp(?a,mnci1?,-mncp?,?b) = -i_*mncv3gp(?a,mnci2,-mncp,?b)*mncDs(mncp) -i_*mncxi*mncp(mnci2)*mncv3gp(?a,-mncp,-mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci2?,mnci1?,mncp?)*mncv3gp(?a,mnci1?,mncp?,?b) = -i_*mncv3gp(?a,mnci2,mncp,?b)*mncDs(mncp) +i_*mncxi*mncp(mnci2)*mncv3gp(?a,mncp,mncp,?b)*mncDs(mncp)*mncDs(mncp); id,once,mncDg(mnci2?,mnci1?,mncp?)*mncv3gp(?a,mnci1?,-mncp?,?b) = -i_*mncv3gp(?a,mnci2,-mncp,?b)*mncDs(mncp) -i_*mncxi*mncp(mnci2)*mncv3gp(?a,-mncp,-mncp,?b)*mncDs(mncp)*mncDs(mncp); endrepeat; #endif #if ( `GAUGE' > 0 ) if ( count(mncxi,1) > `GAUGE' ) discard; #endif #else id mncDg(mnci1?,mnci2?,mncp?) = -i_*d_(mnci1,mnci2)*mncDs(mncp); #endif id mncDs(p1?) = 1/p1.p1; id mncDL(mnci1?,mncj1?,p1?) = -i_*d_(mnci1,mncj1)/p1.p1+i_*p1(mnci1)*p1(mncj1)/p1.p1^2; id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); .sort:Gluon Propagators; repeat; repeat; repeat; repeat; repeat; repeat; repeat; id,mncv3g(p1?,p1?,p2?,p2?,p3?,p3?) = 0; id,mncv2gi(p1?,p1?,?a) = 0; id,mncv2gi(p1?,-p1?,?a) = 0; id,mncv2gi(?a,p1?,p1?) = 0; id,mncv2gi(?a,p1?,-p1?) = 0; * id,mncv2gp(p1?,p1?,?a) = 0; * id,mncv2gp(p1?,-p1?,?a) = 0; * id,mncv2gp(?a,p1?,p1?) = 0; * id,mncv2gp(?a,p1?,-p1?) = 0; * id,mncv2gc(p1?,p1?,?a) = 0; * id,mncv2gc(p1?,-p1?,?a) = 0; * id,mncv2gc(?a,p1?,p1?) = 0; * id,mncv2gc(?a,p1?,-p1?) = 0; id,once,mncv3g(p1?,p1?,p2?,p2?,mnci3?,p3?) = -i_*p3.p3*p2(mnci3)+i_*p2.p3*p3(mnci3); id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); endrepeat; id,once,mncv3g(mnci3?,p3?,p1?,p1?,p2?,p2?) = -i_*p3.p3*p2(mnci3)+i_*p2.p3*p3(mnci3); id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); endrepeat; id,once,mncv3g(p2?,p2?,mnci3?,p3?,p1?,p1?) = -i_*p3.p3*p2(mnci3)+i_*p2.p3*p3(mnci3); id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); endrepeat; id,once,mncv3g(p1?,p1?,mnci2?,p2?,mnci3?,p3?) = -i_*p2(mnci2)*p2(mnci3)+i_*p3(mnci2)*p3(mnci3)-i_*p3.p3*d_(mnci2,mnci3)+i_*p2.p2*d_(mnci2,mnci3); id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); endrepeat; id,once,mncv3g(mnci3?,p3?,p1?,p1?,mnci2?,p2?) = -i_*p2(mnci2)*p2(mnci3)+i_*p3(mnci2)*p3(mnci3)-i_*p3.p3*d_(mnci2,mnci3)+i_*p2.p2*d_(mnci2,mnci3); id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); endrepeat; id,once,mncv3g(mnci2?,p2?,mnci3?,p3?,p1?,p1?) = -i_*p2(mnci2)*p2(mnci3)+i_*p3(mnci2)*p3(mnci3)-i_*p3.p3*d_(mnci2,mnci3)+i_*p2.p2*d_(mnci2,mnci3); id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); endrepeat; id,once,mncv3g(mnci1?,p1?,mnci2?,p2?,mnci3?,p3?) = -2*i_*p1(mnci3)*d_(mnci1,mnci2)-i_*p3(mnci3)*d_(mnci1,mnci2) -2*i_*p2(mnci1)*d_(mnci2,mnci3)-i_*p1(mnci1)*d_(mnci2,mnci3) -2*i_*p3(mnci2)*d_(mnci3,mnci1)-i_*p2(mnci2)*d_(mnci3,mnci1); id mncv3g(?a,p3?,-p3?) = -mncv3g(?a,-p3,-p3); id mncv3g(mnci1?index_,p1?,p2?,-p2?,?a) = -mncv3g(mnci1,p1,-p2,-p2,?a); id mncv3g(p3?,p1?,p2?,-p2?,?a) = -mncv3g(p3,p1,-p2,-p2,?a); id mncv3g(p1?,-p1?,?a) = -mncv3g(-p1,-p1,?a); endrepeat; id mncv4g(mnci1?,mnci2?,mnci3?,mnci4?) = -i_*(d_(mnci1,mnci3)*d_(mnci2,mnci4)-d_(mnci1,mnci4)*d_(mnci2,mnci3)); id mncV4G(mnci1?,mnci2?,mnci3?,mnci4?,mncx1?,mncx2?,mncx3?) = -i_*mncx1*(d_(mnci1,mnci3)*d_(mnci2,mnci4)-d_(mnci1,mnci4)*d_(mnci2,mnci3)) -i_*mncx2*(d_(mnci1,mnci2)*d_(mnci3,mnci4)-d_(mnci1,mnci4)*d_(mnci2,mnci3)) -i_*mncx3*(d_(mnci1,mnci3)*d_(mnci2,mnci4)-d_(mnci1,mnci2)*d_(mnci3,mnci4)); #ifdef `GAUGE' #if ( `GAUGE' != 0 ) id mncDg(mnci1?,mnci2?,mncp?) = -i_*(d_(mnci1,mnci2)-mncxi*mncp(mnci1)*mncp(mnci2)/mncp.mncp)/mncp.mncp; #endif #endif id D = acc(4-2*ep); id P.P = 0; id mncv2gi(mnci1?,p1?,mnci2?,p2?) = -i_*(d_(mnci1,mnci2)*p1.p2-p1(mnci2)*p2(mnci1)); id mncv3gi(mnci1?,p1?,mnci2?,p2?,mnci3?,p3?) = i_*( d_(mnci1,mnci2)*(p1(mnci3)-p2(mnci3))+d_(mnci2,mnci3)*(p2(mnci1)-p3(mnci1)) +d_(mnci3,mnci1)*(p3(mnci2)-p1(mnci2))); id mncv2gp(mnci1?,p1?,mnci2?,p2?) = -i_*(d_(mnci1,mnci2)*p1.p2-p1(mnci2)*p2(mnci1)); id mncv3gp(mnci1?,p1?,mnci2?,p2?,mnci3?,p3?) = i_*( d_(mnci1,mnci2)*(p1(mnci3)-p2(mnci3))+d_(mnci2,mnci3)*(p2(mnci1)-p3(mnci1)) +d_(mnci3,mnci1)*(p3(mnci2)-p1(mnci2))); id P.P = 0; id mncv2gc(mnci1?,p1?,mnci2?,p2?) = -i_*e_(mnci1,p1,mnci2,p2); id mncv3gc(mnci1?,p1?,mnci2?,p2?,mnci3?,p3?) = i_*( e_(mnci1,mnci2,mnci3,p1)+e_(mnci1,mnci2,mnci3,p2)+e_(mnci1,mnci2,mnci3,p3)); id mncv3gc(mncp?,mnci1?,mnci2?,mnci3?) = i_*e_(mnci1,mnci2,mnci3,mncp); id mncv3gc(mnci1?,mnci2?,mnci3?,mncp?) = -i_*e_(mnci1,mnci2,mnci3,mncp); *id mncv4gc(mnci1?,mnci2?,mnci3?,mnci4?) = -i_*e_(mnci1,mnci2,mnci3,mnci4); id mncv4gc(mnci1?,mnci2?,mnci3?,mnci4?) = 0; Contract; id P.P = 0; Multiply replace_(mncxi,xi); #endprocedure *--#] vertsubm : *--#[ ACCU : #procedure ACCU(TEXT) if ( count(ep,1) ); if ( count(acc,1) == 1 ); id ep^mncx?*acc(mncy?) = acc(ep^mncx*mncy); else; id ep^mncx? = acc(ep^mncx); endif; endif; .sort(PolyFun = acc):`TEXT'; #endprocedure *--#] ACCU : *--#[ ACCU2 : #procedure ACCU2(BRA,TEXT) if ( count(ep,1) ); if ( count(acc,1) == 1 ); id ep^mncx?*acc(mncy?) = acc(ep^mncx*mncy); else; id ep^mncx? = acc(ep^mncx); endif; endif; `BRA'; .sort(PolyFun = acc):`TEXT'; #endprocedure *--#] ACCU2 : *--#[ ACCUP : #procedure ACCUP(TEXT) id acc(mncx?) = mncx; .sort:`TEXT'; #endprocedure *--#] ACCUP : *--#] Procedures : *--#[ Tables : #call pochtabl(40) #call tabtwo(26) *--#[ notabl.h : CTable sparse mncnoptab(4); *Fill mncnoptab(3,3,3,3) = * - 18474865276279/324000 - 147056/3*ep^-3 - 9668041/30*ep^-2 + 85171103/ * 1800*ep^-1 - 484428616/3*z3 + 246960000*z5; *Fill mncnoptab(4,2,2,4) = * - 6586797294014227/250047000 - 269984/27*ep^-3 - 57006874/945*ep^-2 + * 955059143/22050*ep^-1 - 1942771744/27*z3 + 109760000*z5; *Fill mncnoptab(4,3,1,4) = * - 3041096169814853/357210000 - 291704/135*ep^-3 - 993209/75*ep^-2 + * 158917319/18900*ep^-1 - 3110543296/135*z3 + 35123200*z5; *Fill mncnoptab(4,3,2,3) = * - 91660413154999/2976750 - 193760/9*ep^-3 - 6413092/45*ep^-2 + 27103277/ * 1890*ep^-1 - 775759936/9*z3 + 131712000*z5; *Fill mncnoptab(4,3,3,2) = * - 357433853456101/14883750 - 1156064/45*ep^-3 - 4163404/25*ep^-2 + * 64087288/1575*ep^-1 - 3094354816/45*z3 + 105369600*z5; *Fill mncnoptab(4,4,2,2) = * - 86747864238209/8930250 - 417088/27*ep^-3 - 38521988/405*ep^-2 + * 264311666/4725*ep^-1 - 769912640/27*z3 + 43904000*z5; *Fill mncnoptab(4,4,3,1) = * - 1515457055404949/357210000 - 82712/135*ep^-3 - 18631369/2025*ep^-2 - * 89285363/2835*ep^-1 - 1559578048/135*z3 + 17561600*z5; *Fill mncnoptab(5,1,1,5) = * - 54699046462671221/32006016000 + 39923/216*ep^-3 + 65445179/60480* * ep^-2 - 453971069/313600*ep^-1 - 121886869/27*z3 + 6860000*z5; *Fill mncnoptab(5,2,1,4) = * - 10775201906664373/2000376000 + 860/27*ep^-3 - 1053382/945*ep^-2 - * 266829113/35280*ep^-1 - 390135008/27*z3 + 21952000*z5; *Fill mncnoptab(5,2,2,3) = * - 2654032230525247/208372500 - 108592/45*ep^-3 - 35031746/1575*ep^-2 - * 1264086542/33075*ep^-1 - 1558464128/45*z3 + 52684800*z5; *Fill mncnoptab(5,3,1,3) = * - 1553281109396459/381024000 + 6559/9*ep^-3 + 172871/540*ep^-2 - * 2946557347/100800*ep^-1 - 97752760/9*z3 + 16464000*z5; *Fill mncnoptab(5,3,2,2) = * - 349190112856271/59535000 - 381136/45*ep^-3 - 36449102/675*ep^-2 + * 193339331/9450*ep^-1 - 770935424/45*z3 + 26342400*z5; *Fill mncnoptab(5,3,3,1) = * - 495589548067253/317520000 - 19369/45*ep^-3 - 12264643/1800*ep^-2 - * 745482991/30240*ep^-1 - 195095096/45*z3 + 6585600*z5; *Fill mncnoptab(5,4,1,2) = * - 1404687254200169/2000376000 - 22196/27*ep^-3 - 18341056/2835*ep^-2 - * 7901872933/1587600*ep^-1 - 55213792/27*z3 + 3136000*z5; *Fill mncnoptab(5,4,2,1) = * - 2703599746937443/5000940000 - 141956/135*ep^-3 - 206700143/28350* * ep^-2 - 395097751/264600*ep^-1 - 219587104/135*z3 + 2508800*z5; *Fill mncnoptab(5,5,1,1) = * - 2629892605029463/128024064000 - 9421/108*ep^-3 - 169868023/362880* * ep^-2 - 170678409/627200*ep^-1 - 1745339/27*z3 + 98000*z5; *Fill mncnoptab(6,1,1,4) = * - 21394537161736301/25004700000 - 204262/675*ep^-3 - 11650321/10500* * ep^-2 + 954399088/165375*ep^-1 - 1550442608/675*z3 + 3512320*z5; *Fill mncnoptab(6,2,1,3) = * - 1355689314527311/1041862500 + 9944/225*ep^-3 + 4198591/23625*ep^-2 - * 576422233/330750*ep^-1 - 780778304/225*z3 + 5268480*z5; *Fill mncnoptab(6,2,2,2) = * - 102264570285053/86821875 - 377056/225*ep^-3 - 27899296/2625*ep^-2 + * 791190703/165375*ep^-1 - 770079104/225*z3 + 5268480*z5; *Fill mncnoptab(6,3,1,2) = * - 712078941266617/2083725000 - 88616/225*ep^-3 - 65364799/23625*ep^-2 * - 76182557/220500*ep^-1 - 220289344/225*z3 + 1505280*z5; *Fill mncnoptab(6,3,2,1) = * - 71933674894463/463050000 - 88408/225*ep^-3 - 22366649/7875*ep^-2 - * 83726576/55125*ep^-1 - 109791872/225*z3 + 752640*z5; *Fill mncnoptab(6,4,1,1) = * - 2549268572811643/200037600000 - 39952/675*ep^-3 - 181234189/567000* * ep^-2 - 659982313/3969000*ep^-1 - 27943568/675*z3 + 62720*z5; *Fill mncnoptab(7,1,1,3) = * - 3723627858464321/33339600000 + 46897/1350*ep^-3 + 73683103/378000* * ep^-2 - 3880010633/15876000*ep^-1 - 195059276/675*z3 + 439040*z5; *Fill mncnoptab(7,2,1,2) = * - 122256120796157/2083725000 - 8008/675*ep^-3 - 230717/875*ep^-2 - * 984557027/992250*ep^-1 - 111467072/675*z3 + 250880*z5; *Fill mncnoptab(7,2,2,1) = * - 374471233554053/29172150000 - 352616/4725*ep^-3 - 77449193/165375* * ep^-2 + 1455586687/13891500*ep^-1 - 215345344/4725*z3 + 71680*z5; *Fill mncnoptab(7,3,1,1) = * - 886148642962981/266716800000 - 8938/675*ep^-3 - 56364883/756000*ep^-2 * - 1845718393/31752000*ep^-1 - 6977492/675*z3 + 15680*z5; *Fill mncnoptab(8,1,1,2) = * - 952067717329531/408410100000 - 305366/33075*ep^-3 - 157911017/4630500 * *ep^-2 + 15496117051/97240500*ep^-1 - 208616944/33075*z3 + 10240*z5; *Fill mncnoptab(8,2,1,1) = * - 716689569830281/3267280800000 - 51952/33075*ep^-3 - 25922261/3087000* * ep^-2 - 18220093/24310125*ep^-1 - 28039568/33075*z3 + 1280*z5; *Fill mncnoptab(9,1,1,1) = * - 1896551334050581/209105971200000 + 73249/1058400*ep^-3 + 51235081/ * 296352000*ep^-2 - 54957379097/49787136000*ep^-1 - 413312/33075*z3 + 20* * z5; Fill mncnoptab(3,3,3,2) = 427977441983/103680 - 52955/12*ep^-3 - 3917279/144*ep^-2 + 44625631/2880 *ep^-1 + 10894318111/72*ep*z3 + 15370495*ep*z4 - 99078000*ep*z5 - 452482708047761/10368000*ep + 30740990/3*z3 - 15435000*z5; Fill mncnoptab(4,2,1,4) = 492417147546743/571536000 - 22771/54*ep^-3 - 1974617/1080*ep^-2 + 915359519/151200*ep^-1 + 6081755963/180*ep*z3 + 30675106/9*ep*z4 - 67110400/3*ep*z5 - 2327268549647543977/240045120000*ep + 61350212/27*z3 - 3430000*z5; Fill mncnoptab(4,2,2,3) = 10310508922643/3888000 - 29239/18*ep^-3 - 410057/40*ep^-2 + 29037853/ 7200*ep^-1 + 18176277881/180*ep*z3 + 30621724/3*ep*z4 - 66463600*ep*z5 - 6775865580736891/233280000*ep + 61243448/9*z3 - 10290000*z5; Fill mncnoptab(4,3,1,3) = 98209093589899/127008000 - 847/12*ep^-3 - 21579/16*ep^-2 - 513470983/ 100800*ep^-1 + 1219050631/40*ep*z3 + 3045119*ep*z4 - 20286000*ep*z5 - 152753095200805831/17781120000*ep + 6090238/3*z3 - 3087000*z5; Fill mncnoptab(4,3,2,2) = 746549351657/432000 - 18823/6*ep^-3 - 2095397/120*ep^-2 + 476289437/ 21600*ep^-1 + 3674812061/60*ep*z3 + 6207586*ep*z4 - 40454400*ep*z5 - 449125235438929/25920000*ep + 12415172/3*z3 - 6174000*z5; Fill mncnoptab(4,3,3,1) = 33417478515833/70560000 - 1981/60*ep^-3 - 6027293/3600*ep^-2 - 2496913651/302400*ep^-1 + 33147300541/1800*ep*z3 + 9111137/5*ep*z4 - 12359760*ep*z5 - 1343694916819313567/266716800000*ep + 18222274/15*z3 - 1852200*z5; Fill mncnoptab(4,4,2,1) = 111808019020979/571536000 - 20419/54*ep^-3 - 7607927/3240*ep^-2 + 618574609/453600*ep^-1 + 11269028347/1620*ep*z3 + 6219724/9*ep*z4 - 14131600/3*ep*z5 - 445250532042081389/240045120000*ep + 12439448/27*z3 - 686000*z5; Fill mncnoptab(5,1,1,4) = 3404545910519813/16003008000 + 11537/216*ep^-3 + 2265673/30240*ep^-2 - 6664583011/4233600*ep^-1 + 6125595259/720*ep*z3 + 7568332/9*ep*z4 - 17149300/3*ep*z5 - 15988216912889349067/6721263360000*ep + 15136664/27* z3 - 857500*z5; Fill mncnoptab(5,2,1,3) = 94217706529879/254016000 + 1407/8*ep^-3 + 784633/1440*ep^-2 - 794391811/ 201600*ep^-1 + 11025810727/720*ep*z3 + 1515276*ep*z4 - 10304700*ep*z5 - 151196680058747123/35562240000*ep + 1010184*z3 - 1543500*z5; Fill mncnoptab(5,2,2,2) = 6657499764253/12960000 - 48041/60*ep^-3 - 17309333/3600*ep^-2 + 1298841/ 320*ep^-1 + 33499700221/1800*ep*z3 + 9286732/5*ep*z4 - 12506760*ep*z5 - 439852636788781/86400000*ep + 18573464/15*z3 - 1852200*z5; Fill mncnoptab(5,3,1,2) = 15299981746757/108864000 - 10171/72*ep^-3 - 4960199/4320*ep^-2 - 67110217/86400*ep^-1 + 2256184967/432*ep*z3 + 1537060/3*ep*z4 - 3562300* ep*z5 - 12594448880199007/9144576000*ep + 3074120/9*z3 - 514500*z5; Fill mncnoptab(5,3,2,1) = 115620267808099/1270080000 - 23387/120*ep^-3 - 1040799/800*ep^-2 + 1988123/120960*ep^-1 + 3798914129/1200*ep*z3 + 1550612/5*ep*z4 - 2172660 *ep*z5 - 433205664999625789/533433600000*ep + 3101224/15*z3 - 308700*z5; Fill mncnoptab(5,4,1,1) = 116607543852899/16003008000 - 6157/216*ep^-3 - 12443447/90720*ep^-2 + 33603169/12700800*ep^-1 + 11782494547/45360*ep*z3 + 216868/9*ep*z4 - 567700/3*ep*z5 - 56108643614351387/960180480000*ep + 433736/27*z3 - 24500*z5; Fill mncnoptab(6,1,1,3) = 2037883590668579/44452800000 + 733/200*ep^-3 + 7183069/252000*ep^-2 - 1717712057/21168000*ep^-1 + 33824122981/18000*ep*z3 + 4538676/25*ep*z4 - 1299396*ep*z5 - 9366902119661172109/18670176000000*ep + 3025784/25*z3 - 185220*z5; Fill mncnoptab(6,2,1,2) = 35390275843033/1058400000 - 16667/300*ep^-3 - 1822397/6000*ep^-2 + 682534127/1512000*ep^-1 + 1280879763/1000*ep*z3 + 3119284/25*ep*z4 - 892584*ep*z5 - 434777012367296309/1333584000000*ep + 6238568/75*z3 - 123480*z5; Fill mncnoptab(6,2,2,1) = 43705933939733/3175200000 - 51667/900*ep^-3 - 643293/2000*ep^-2 + 164162507/504000*ep^-1 + 3941599109/9000*ep*z3 + 3185084/75*ep*z4 - 309288*ep*z5 - 139189622958910043/1333584000000*ep + 6370168/225*z3 - 41160*z5; Fill mncnoptab(6,3,1,1) = 4402290724537/1646400000 - 2127/200*ep^-3 - 13081511/252000*ep^-2 + 85049863/21168000*ep^-1 + 11976922627/126000*ep*z3 + 216756/25*ep*z4 - 70476*ep*z5 - 54838846552119547/2667168000000*ep + 144504/25*z3 - 8820* z5; Fill mncnoptab(7,1,1,2) = 238117911919931/133358400000 + 29933/5400*ep^-3 + 4181741/756000*ep^-2 - 10958786353/63504000*ep^-1 + 3961449709/54000*ep*z3 + 1424992/225*ep* z4 - 54348*ep*z5 - 883201342630552501/56010528000000*ep + 2849984/675*z3 - 6860*z5; Fill mncnoptab(7,2,1,1) = 37694309069933/133358400000 - 4981/5400*ep^-3 - 3848197/756000*ep^-2 - 229928551/63504000*ep^-1 + 4150542589/378000*ep*z3 + 217456/225*ep*z4 - 8484*ep*z5 - 16503907631292229/8001504000000*ep + 434912/675*z3 - 980*z5 ; Fill mncnoptab(8,1,1,1) = 61242264325133/6534561600000 - 26581/264600*ep^-3 - 8290837/37044000* ep^-2 + 4495302041/3111696000*ep^-1 + 641079787/2646000*ep*z3 + 206656/ 11025*ep*z4 - 1452/7*ep*z5 - 152139085793242243/2744515872000000*ep + 413312/33075*z3 - 20*z5; Fill mncnoptab(3,2,2,3) = - 13078015423/40500 - 1166/3*ep^-3 - 219653/90*ep^-2 + 179359/150*ep^-1 - 621784364/45*ep*z3 - 1410728*ep*z4 + 8943600*ep*z5 + 565882214657/ 135000*ep - 2821456/3*z3 + 1440000*z5; Fill mncnoptab(3,3,2,2) = - 931159283/4320 - 800*ep^-3 - 48001/12*ep^-2 + 1417247/180*ep^-1 - 62078545/6*ep*z3 - 1038120*ep*z4 + 6768000*ep*z5 + 4000067937751/1296000 *ep - 692080*z3 + 1080000*z5; Fill mncnoptab(3,3,3,1) = - 5573732533/57600 + 175/4*ep^-3 - 9581/48*ep^-2 - 7492889/2880*ep^-1 - 94545971/24*ep*z3 - 403305*ep*z4 + 2574000*ep*z5 + 12321204871351/ 10368000*ep - 268870*z3 + 405000*z5; Fill mncnoptab(4,1,1,4) = - 2807827829/72900 - 1630/27*ep^-3 - 3245/18*ep^-2 + 34576/27*ep^-1 - 42000568/27*ep*z3 - 1383640/9*ep*z4 + 3082000/3*ep*z5 + 979385889611/ 2187000*ep - 2767280/27*z3 + 160000*z5; Fill mncnoptab(4,2,1,3) = - 28221879029/324000 + 4/3*ep^-3 - 1799/20*ep^-2 - 44113/75*ep^-1 - 35012467/10*ep*z3 - 356408*ep*z4 + 2289600*ep*z5 + 6698633885851/6480000 *ep - 712816/3*z3 + 360000*z5; Fill mncnoptab(4,2,2,2) = - 23078731723/216000 - 461*ep^-3 - 130721/60*ep^-2 + 19017283/3600* ep^-1 - 156219263/30*ep*z3 - 514644*ep*z4 + 3448800*ep*z5 + 19670240647171/12960000*ep - 343096*z3 + 540000*z5; Fill mncnoptab(4,3,1,2) = - 9262246349/324000 - 338/3*ep^-3 - 11801/20*ep^-2 + 26071/25*ep^-1 - 14061799/10*ep*z3 - 137384*ep*z4 + 946800*ep*z5 + 869340324673/2160000* ep - 274768/3*z3 + 144000*z5; Fill mncnoptab(4,3,2,1) = - 4269941147/216000 - 251/3*ep^-3 - 93673/180*ep^-2 + 3333209/10800* ep^-1 - 95416027/90*ep*z3 - 104348*ep*z4 + 717600*ep*z5 + 11837431004993/ 38880000*ep - 208696/3*z3 + 108000*z5; Fill mncnoptab(4,4,1,1) = - 3869903417/2916000 - 364/27*ep^-3 - 89387/1620*ep^-2 + 432743/8100* ep^-1 - 67431383/810*ep*z3 - 71512/9*ep*z4 + 176800/3*ep*z5 + 3785470839041/174960000*ep - 143024/27*z3 + 8000*z5; Fill mncnoptab(5,1,1,3) = - 94014346831/5184000 + 121/8*ep^-3 + 106063/1440*ep^-2 - 16207369/ 86400*ep^-1 - 482890991/720*ep*z3 - 66732*ep*z4 + 447900*ep*z5 + 59566361995607/311040000*ep - 44488*z3 + 67500*z5; Fill mncnoptab(5,2,1,2) = - 1631016859/144000 - 15/2*ep^-3 - 14459/120*ep^-2 - 80399/288*ep^-1 - 32279897/60*ep*z3 - 53352*ep*z4 + 367200*ep*z5 + 1309588517171/8640000* ep - 35568*z3 + 54000*z5; Fill mncnoptab(5,2,2,1) = - 1703250341/540000 - 201/5*ep^-3 - 28709/150*ep^-2 + 179513/450*ep^-1 - 32408209/150*ep*z3 - 99576/5*ep*z4 + 152280*ep*z5 + 1861089308173/ 32400000*ep - 66384/5*z3 + 21600*z5; Fill mncnoptab(5,3,1,1) = - 1507518839/1728000 - 49/8*ep^-3 - 37471/1440*ep^-2 + 1281373/86400* ep^-1 - 34159189/720*ep*z3 - 4452*ep*z4 + 33900*ep*z5 + 3821093000941/ 311040000*ep - 2968*z3 + 4500*z5; Fill mncnoptab(6,1,1,2) = - 8071460023/8100000 - 181/25*ep^-3 - 24496/1125*ep^-2 + 1915223/13500* ep^-1 - 99509497/2250*ep*z3 - 94056/25*ep*z4 + 32136*ep*z5 + 5141063764979/486000000*ep - 62704/25*z3 + 4320*z5; Fill mncnoptab(6,2,1,1) = - 35661097/400000 - 77/50*ep^-3 - 55603/9000*ep^-2 + 967589/108000* ep^-1 - 35320249/4500*ep*z3 - 17976/25*ep*z4 + 5856*ep*z5 + 3353461354561/1944000000*ep - 11984/25*z3 + 720*z5; Fill mncnoptab(7,1,1,1) = - 3387368219/388800000 + 469/5400*ep^-3 + 14099/108000*ep^-2 - 1960937/ 1296000*ep^-1 - 4305961/18000*ep*z3 - 4144/225*ep*z4 + 196*ep*z5 + 1489128179587/23328000000*ep - 8288/675*z3 + 20*z5; Fill mncnoptab(3,2,1,3) = 2831372533/194400 + 455/18*ep^-3 + 6319/216*ep^-2 - 4589599/6480*ep^-1 + 15385216/27*ep*z3 + 173950/3*ep*z4 - 363500*ep*z5 - 981631156921/ 5832000*ep + 347900/9*z3 - 60000*z5; Fill mncnoptab(3,2,2,2) = 145969549/3888 - 1435/9*ep^-3 - 70691/108*ep^-2 + 1431199/648*ep^-1 + 31188362/27*ep*z3 + 372740/3*ep*z4 - 721000*ep*z5 - 8538217571/23328*ep + 745480/9*z3 - 120000*z5; Fill mncnoptab(3,3,2,1) = 7510602449/777600 - 235/9*ep^-3 - 67391/432*ep^-2 + 2082899/12960*ep^-1 + 63188269/216*ep*z3 + 90710/3*ep*z4 - 187000*ep*z5 - 4047664683001/ 46656000*ep + 181420/9*z3 - 30000*z5; Fill mncnoptab(4,1,1,3) = 15081744101/2916000 + 203/54*ep^-3 + 19823/3240*ep^-2 - 11583047/97200* ep^-1 + 77945816/405*ep*z3 + 172582/9*ep*z4 - 374300/3*ep*z5 - 5068206135881/87480000*ep + 345164/27*z3 - 20000*z5; Fill mncnoptab(4,2,1,2) = 1399378579/233280 - 740/27*ep^-3 - 70421/648*ep^-2 + 1649821/3888*ep^-1 + 63915859/324*ep*z3 + 190060/9*ep*z4 - 380000/3*ep*z5 - 830598308171/ 13996800*ep + 380120/27*z3 - 20000*z5; Fill mncnoptab(4,2,2,1) = 8626579097/2332800 - 1505/54*ep^-3 - 70453/648*ep^-2 + 15165647/38880* ep^-1 + 32636837/324*ep*z3 + 97820/9*ep*z4 - 196000/3*ep*z5 - 4214387793553/139968000*ep + 195640/27*z3 - 10000*z5; Fill mncnoptab(4,3,1,1) = 7805797697/11664000 - 119/27*ep^-3 - 93743/6480*ep^-2 + 5998307/194400* ep^-1 + 65653693/3240*ep*z3 + 17638/9*ep*z4 - 42200/3*ep*z5 - 3678149914921/699840000*ep + 35276/27*z3 - 2000*z5; Fill mncnoptab(5,1,1,2) = 38410091629/46656000 + 763/216*ep^-3 - 13217/12960*ep^-2 - 88538189/ 777600*ep^-1 + 162821989/6480*ep*z3 + 19568/9*ep*z4 - 51700/3*ep*z5 - 17384289807653/2799360000*ep + 39136/27*z3 - 2500*z5; Fill mncnoptab(5,2,1,1) = 7464164057/46656000 - 193/216*ep^-3 - 42829/12960*ep^-2 + 3267047/777600 *ep^-1 + 33840689/6480*ep*z3 + 4432/9*ep*z4 - 11300/3*ep*z5 - 3355464483121/2799360000*ep + 8864/27*z3 - 500*z5; Fill mncnoptab(6,1,1,1) = 9848776457/1166400000 - 769/5400*ep^-3 - 49837/324000*ep^-2 + 8517547/ 3888000*ep^-1 + 36299969/162000*ep*z3 + 4144/225*ep*z4 - 548/3*ep*z5 - 4938159875041/69984000000*ep + 8288/675*z3 - 20*z5; Fill mncnoptab(2,2,2,2) = - 79897/27 - 64*ep^-3 - 500/3*ep^-2 + 10846/9*ep^-1 - 466976/3*ep*z3 - 14352*ep*z4 + 97440*ep*z5 + 2415263/54*ep - 9568*z3 + 17280*z5; Fill mncnoptab(3,1,1,3) = - 1209925/864 + 9/2*ep^-3 + 123/8*ep^-2 - 4087/48*ep^-1 - 123208/3*ep* z3 - 4314*ep*z4 + 25260*ep*z5 + 74575541/5184*ep - 2876*z3 + 4320*z5; Fill mncnoptab(3,2,1,2) = - 466685/648 - 4*ep^-3 - 310/9*ep^-2 + 473/108*ep^-1 - 478994/9*ep*z3 - 5712*ep*z4 + 33600*ep*z5 + 65128439/3888*ep - 3808*z3 + 5760*z5; Fill mncnoptab(3,2,2,1) = - 582479/972 - 148/9*ep^-3 - 1217/27*ep^-2 + 47689/162*ep^-1 - 955180/ 27*ep*z3 - 9328/3*ep*z4 + 22880*ep*z5 + 57290287/5832*ep - 18656/9*z3 + 3840*z5; Fill mncnoptab(3,3,1,1) = - 1518557/10368 - 5/3*ep^-3 - 565/144*ep^-2 + 11917/864*ep^-1 - 514753/ 72*ep*z3 - 710*ep*z4 + 4680*ep*z5 + 273452161/124416*ep - 1420/3*z3 + 720*z5; Fill mncnoptab(4,1,1,2) = - 1072745/2916 - 142/27*ep^-3 - 1705/162*ep^-2 + 56761/486*ep^-1 - 974044/81*ep*z3 - 8152/9*ep*z4 + 24080/3*ep*z5 + 7103453/2187*ep - 16304/ 27*z3 + 1280*z5; Fill mncnoptab(4,2,1,1) = - 471157/23328 - 40/27*ep^-3 - 1019/324*ep^-2 + 16361/972*ep^-1 - 519899/162*ep*z3 - 2920/9*ep*z4 + 6560/3*ep*z5 + 204421561/279936*ep - 5840/27*z3 + 320*z5; Fill mncnoptab(5,1,1,1) = - 2696245/373248 + 25/216*ep^-3 + 17/2592*ep^-2 - 63191/31104*ep^-1 - 286261/1296*ep*z3 - 160/9*ep*z4 + 500/3*ep*z5 + 369093769/4478976*ep - 320/27*z3 + 20*z5; Fill mncnoptab(2,2,2,1) = 50881/216 - 9*ep^-3 - 85/6*ep^-2 + 6803/36*ep^-1 + 30293/3*ep*z3 + 1476* ep*z4 - 5760*ep*z5 - 5699221/1296*ep + 984*z3 - 1080*z5; Fill mncnoptab(3,1,1,2) = 144325/432 + 3/2*ep^-3 - 15/4*ep^-2 - 377/8*ep^-1 + 30517/6*ep*z3 + 384* ep*z4 - 3000*ep*z5 - 4415225/2592*ep + 256*z3 - 540*z5; Fill mncnoptab(3,2,1,1) = 73417/1296 - 5/6*ep^-3 - 29/36*ep^-2 + 2027/216*ep^-1 + 30409/18*ep*z3 + 176*ep*z4 - 1080*ep*z5 - 4203133/7776*ep + 352/3*z3 - 180*z5; Fill mncnoptab(4,1,1,1) = 44165/11664 - 13/54*ep^-3 + 59/324*ep^-2 + 6575/1944*ep^-1 + 31733/162* ep*z3 + 160/9*ep*z4 - 440/3*ep*z5 - 6225337/69984*ep + 320/27*z3 - 20*z5 ; Fill mncnoptab(2,1,1,2) = - 677/3 - 10/3*ep^-3 + 1/3*ep^-2 + 233/3*ep^-1 - 4480/3*ep*z3 + 56*ep* z4 + 760*ep*z5 + 1567/3*ep + 112/3*z3 + 160*z5; Fill mncnoptab(2,2,1,1) = - 85/4 - 4/3*ep^-3 + 3/2*ep^-2 + 31/2*ep^-1 - 697*ep*z3 - 88*ep*z4 + 400*ep*z5 + 571/8*ep - 176/3*z3 + 80*z5; Fill mncnoptab(3,1,1,1) = - 53/16 + 1/6*ep^-3 - 5/12*ep^-2 - 47/24*ep^-1 - 1151/6*ep*z3 - 16*ep* z4 + 120*ep*z5 + 3427/32*ep - 32/3*z3 + 20*z5; Fill mncnoptab(2,1,1,1) = - 10 - 2/3*ep^-3 + 10/3*ep^-2 - 2*ep^-1 + 404/3*ep*z3 + 16*ep*z4 - 80* ep*z5 - 42*ep + 32/3*z3 - 20*z5; Fill mncnoptab(1,1,1,1) = 20*z5; *--#] notabl.h : *--#[ gtabls.h : Ctable,relax,mncT00(1:10,1:10); Ctable,relax,mncT10(-6:10,1:10); Ctable,relax,mncT20(-6:10,1:10); Ctable,relax,mncT11(-6:10,-6:10); fill mncT00(1,1) = ep^-1; fill mncT00(1,2) = 2-ep^-1; fill mncT00(1,3) = -1+2*ep; fill mncT00(1,4) = -1/3+4/3*ep^2; fill mncT00(1,5) = -1/6-1/6*ep+2/3*ep^2+2/3*ep^3; fill mncT00(1,6) = -1/10-1/6*ep+1/3*ep^2+2/3*ep^3+4/15*ep^4; fill mncT00(1,7) = -1/15-13/90*ep+1/6*ep^2+5/9*ep^3+2/5*ep^4+4/45*ep^5; fill mncT00(1,8) = -1/21-11/90*ep+7/90*ep^2+4/9*ep^3+4/9*ep^4+8/45*ep^5; fill mncT00(1,9) = -1/28-29/280*ep+1/36*ep^2+127/360*ep^3+4/9*ep^4+11/45*ep^5; fill mncT00(1,10) = -1/36-223/2520*ep-4/2835*ep^2+101/360*ep^3+229/540*ep^4+13/ 45*ep^5; fill mncT00(2,1) = 2-ep^-1; fill mncT00(2,2) = 2-2*ep^-1+4*ep; fill mncT00(2,3) = -1-2*ep^-1+8*ep+4*ep^2; fill mncT00(2,4) = -8/3-2*ep^-1+22/3*ep+32/3*ep^2+8/3*ep^3; fill mncT00(2,5) = -23/6-2*ep^-1+35/6*ep+15*ep^2+26/3*ep^3+4/3*ep^4; fill mncT00(2,6) = -71/15-2*ep^-1+62/15*ep+53/3*ep^2+46/3*ep^3+76/15*ep^4+8/ 15*ep^5; fill mncT00(2,7) = -82/15-2*ep^-1+217/90*ep+1729/90*ep^2+196/9*ep^3+476/45*ep^4 +104/45*ep^5; fill mncT00(2,8) = -213/35-2*ep^-1+229/315*ep+899/45*ep^2+1247/45*ep^3+776/45* ep^4+248/45*ep^5; fill mncT00(2,9) = -927/140-2*ep^-1-2263/2520*ep+6359/315*ep^2+3967/120*ep^3+ 1477/60*ep^4+151/15*ep^5; fill mncT00(2,10) = -4469/630-2*ep^-1-3097/1260*ep+45329/2268*ep^2+85787/2268*ep^3 +17489/540*ep^4+4273/270*ep^5; fill mncT00(3,1) = -1+2*ep; fill mncT00(3,2) = -1-2*ep^-1+8*ep+4*ep^2; fill mncT00(3,3) = -5-6*ep^-1+23*ep+20*ep^2+4*ep^3; fill mncT00(3,4) = -15-12*ep^-1+127/3*ep+178/3*ep^2+68/3*ep^3+8/3*ep^4; fill mncT00(3,5) = -97/3-20*ep^-1+371/6*ep+751/6*ep^2+217/3*ep^3+50/3*ep^4+4/ 3*ep^5; fill mncT00(3,6) = -58-30*ep^-1+2333/30*ep+6529/30*ep^2+500/3*ep^3+172/3*ep^4 +136/15*ep^5; fill mncT00(3,7) = -464/5-42*ep^-1+2603/30*ep+15089/45*ep^2+28489/90*ep^3+6416/ 45*ep^4+1508/45*ep^5; fill mncT00(3,8) = -687/5-56*ep^-1+10807/126*ep+149903/315*ep^2+1061/2*ep^3+291 *ep^4+268/3*ep^5; fill mncT00(3,9) = -6733/35-72*ep^-1+2015/28*ep+1603937/2520*ep^2+513547/630*ep^3 +62519/120*ep^4+11669/60*ep^5; fill mncT00(3,10) = -3615/14-90*ep^-1+13466/315*ep+2051033/2520*ep^2+6665453/5670* ep^3+19284803/22680*ep^4+49856/135*ep^5; fill mncT00(4,1) = -1/3+4/3*ep^2; fill mncT00(4,2) = -8/3-2*ep^-1+22/3*ep+32/3*ep^2+8/3*ep^3; fill mncT00(4,3) = -15-12*ep^-1+127/3*ep+178/3*ep^2+68/3*ep^3+8/3*ep^4; fill mncT00(4,4) = -58-40*ep^-1+1180/9*ep+226*ep^2+1036/9*ep^3+24*ep^4+16/9* ep^5; fill mncT00(4,5) = -505/3-100*ep^-1+5311/18*ep+11569/18*ep^2+3740/9*ep^3+1100/9 *ep^4+152/9*ep^5; fill mncT00(4,6) = -401-210*ep^-1+8123/15*ep+13433/9*ep^2+52729/45*ep^3+3992/9* ep^4+3976/45*ep^5; fill mncT00(4,7) = -12467/15-392*ep^-1+77009/90*ep+405461/135*ep^2+249029/90*ep^3 +57259/45*ep^4+14788/45*ep^5; fill mncT00(4,8) = -23332/15-672*ep^-1+25051/21*ep+734401/135*ep^2+5421223/945* ep^3+138649/45*ep^4+43618/45*ep^5; fill mncT00(4,9) = -18855/7-1080*ep^-1+618431/420*ep+1527913/168*ep^2+40749427/ 3780*ep^3+49720691/7560*ep^4+108841/45*ep^5; fill mncT00(4,10) = -61445/14-1650*ep^-1+1187719/756*ep+13492646/945*ep^2+ 319245677/17010*ep^3+1605965/126*ep^4+36227755/6804*ep^5; fill mncT00(5,1) = -1/6-1/6*ep+2/3*ep^2+2/3*ep^3; fill mncT00(5,2) = -23/6-2*ep^-1+35/6*ep+15*ep^2+26/3*ep^3+4/3*ep^4; fill mncT00(5,3) = -97/3-20*ep^-1+371/6*ep+751/6*ep^2+217/3*ep^3+50/3*ep^4+4/ 3*ep^5; fill mncT00(5,4) = -505/3-100*ep^-1+5311/18*ep+11569/18*ep^2+3740/9*ep^3+1100/9 *ep^4+152/9*ep^5; fill mncT00(5,5) = -3835/6-350*ep^-1+34147/36*ep+43147/18*ep^2+63929/36*ep^3+ 5720/9*ep^4+1082/9*ep^5; fill mncT00(5,6) = -11683/6-980*ep^-1+427073/180*ep+321547/45*ep^2+120747/20*ep^3 +25521/10*ep^4+9106/15*ep^5; fill mncT00(5,7) = -75782/15-2352*ep^-1+445667/90*ep+1953209/108*ep^2+465035/27* ep^3+1510033/180*ep^4+215411/90*ep^5; fill mncT00(5,8) = -11610-5040*ep^-1+5635817/630*ep+152869817/3780*ep^2+81063041/ 1890*ep^3+89139203/3780*ep^4+351502/45*ep^5; fill mncT00(5,9) = -339795/14-9900*ep^-1+7169401/504*ep+177345113/2160*ep^2+ 1450750099/15120*ep^3+177108377/3024*ep^4+66478591/3024*ep^5; fill mncT00(5,10) = -329285/7-18150*ep^-1+30067363/1512*ep+333243523/2160*ep^2+ 26798048483/136080*ep^3+2559867239/19440*ep^4+1496306639/27216*ep^5; fill mncT00(6,1) = -1/10-1/6*ep+1/3*ep^2+2/3*ep^3+4/15*ep^4; fill mncT00(6,2) = -71/15-2*ep^-1+62/15*ep+53/3*ep^2+46/3*ep^3+76/15*ep^4+8/ 15*ep^5; fill mncT00(6,3) = -58-30*ep^-1+2333/30*ep+6529/30*ep^2+500/3*ep^3+172/3*ep^4 +136/15*ep^5; fill mncT00(6,4) = -401-210*ep^-1+8123/15*ep+13433/9*ep^2+52729/45*ep^3+3992/9* ep^4+3976/45*ep^5; fill mncT00(6,5) = -11683/6-980*ep^-1+427073/180*ep+321547/45*ep^2+120747/20*ep^3 +25521/10*ep^4+9106/15*ep^5; fill mncT00(6,6) = -37009/5-3528*ep^-1+1164389/150*ep+2400553/90*ep^2+2213339/90* ep^3+23205/2*ep^4+80157/25*ep^5; fill mncT00(6,7) = -23499-10584*ep^-1+1544798/75*ep+74618423/900*ep^2+11272138/ 135*ep^3+23575927/540*ep^4+3092012/225*ep^5; fill mncT00(6,8) = -64989-27720*ep^-1+29212361/630*ep+1058350894/4725*ep^2+ 1159995587/4725*ep^3+133238803/945*ep^4+93995227/1890*ep^5; fill mncT00(6,9) = -2256507/14-65340*ep^-1+76200941/840*ep+4550075377/8400*ep^2+ 9721402571/15120*ep^3+30385900253/75600*ep^4+2369271799/15120*ep^5; fill mncT00(6,10) = -5124141/14-141570*ep^-1+97914331/630*ep+45269411767/37800*ep^2 +43425450739/28350*ep^3+43960605211/42525*ep^4+74891892349/170100* ep^5; fill mncT00(7,1) = -1/15-13/90*ep+1/6*ep^2+5/9*ep^3+2/5*ep^4+4/45*ep^5; fill mncT00(7,2) = -82/15-2*ep^-1+217/90*ep+1729/90*ep^2+196/9*ep^3+476/45*ep^4 +104/45*ep^5; fill mncT00(7,3) = -464/5-42*ep^-1+2603/30*ep+15089/45*ep^2+28489/90*ep^3+6416/ 45*ep^4+1508/45*ep^5; fill mncT00(7,4) = -12467/15-392*ep^-1+77009/90*ep+405461/135*ep^2+249029/90*ep^3 +57259/45*ep^4+14788/45*ep^5; fill mncT00(7,5) = -75782/15-2352*ep^-1+445667/90*ep+1953209/108*ep^2+465035/27* ep^3+1510033/180*ep^4+215411/90*ep^5; fill mncT00(7,6) = -23499-10584*ep^-1+1544798/75*ep+74618423/900*ep^2+11272138/ 135*ep^3+23575927/540*ep^4+3092012/225*ep^5; fill mncT00(7,7) = -89691-38808*ep^-1+15230353/225*ep+839340229/2700*ep^2+ 2703725629/8100*ep^3+33824861/180*ep^4+526025219/8100*ep^5; fill mncT00(7,8) = -293898-121968*ep^-1+583171907/3150*ep+6289238647/6300*ep^2+ 64919324111/56700*ep^3+39277798103/56700*ep^4+14806523023/56700*ep^5 ; fill mncT00(7,9) = -5970591/7-339768*ep^-1+910963763/2100*ep+1275352103/450*ep^2+ 37461814447/10800*ep^3+72796743971/32400*ep^4+5945016637/6480*ep^5; fill mncT00(7,10) = -4484337/2-858858*ep^-1+16663386827/18900*ep+825227119253/113400 *ep^2+1290630089159/136080*ep^3+2673094441009/408240*ep^4+ 1957097729129/680400*ep^5; fill mncT00(8,1) = -1/21-11/90*ep+7/90*ep^2+4/9*ep^3+4/9*ep^4+8/45*ep^5; fill mncT00(8,2) = -213/35-2*ep^-1+229/315*ep+899/45*ep^2+1247/45*ep^3+776/45* ep^4+248/45*ep^5; fill mncT00(8,3) = -687/5-56*ep^-1+10807/126*ep+149903/315*ep^2+1061/2*ep^3+291 *ep^4+268/3*ep^5; fill mncT00(8,4) = -23332/15-672*ep^-1+25051/21*ep+734401/135*ep^2+5421223/945* ep^3+138649/45*ep^4+43618/45*ep^5; fill mncT00(8,5) = -11610-5040*ep^-1+5635817/630*ep+152869817/3780*ep^2+81063041/ 1890*ep^3+89139203/3780*ep^4+351502/45*ep^5; fill mncT00(8,6) = -64989-27720*ep^-1+29212361/630*ep+1058350894/4725*ep^2+ 1159995587/4725*ep^3+133238803/945*ep^4+93995227/1890*ep^5; fill mncT00(8,7) = -293898-121968*ep^-1+583171907/3150*ep+6289238647/6300*ep^2+ 64919324111/56700*ep^3+39277798103/56700*ep^4+14806523023/56700*ep^5 ; fill mncT00(8,8) = -7885284/7-453024*ep^-1+6655456091/11025*ep+473865407/126*ep^2 +9189330217/2025*ep^3+1644373427/567*ep^4+5518157081/4725*ep^5; fill mncT00(8,9) = -26476593/7-1472328*ep^-1+73265477633/44100*ep+54627219331/4410* ep^2+3572949997297/226800*ep^3+2411251880873/226800*ep^4+ 206938354943/45360*ep^5; fill mncT00(8,10) = -22789767/2-4294290*ep^-1+528877919/135*ep+29013083864323/793800 *ep^2+116678567813779/2381400*ep^3+17786915424493/510300*ep^4+ 8105581054537/510300*ep^5; fill mncT00(9,1) = -1/28-29/280*ep+1/36*ep^2+127/360*ep^3+4/9*ep^4+11/45*ep^5; fill mncT00(9,2) = -927/140-2*ep^-1-2263/2520*ep+6359/315*ep^2+3967/120*ep^3+ 1477/60*ep^4+151/15*ep^5; fill mncT00(9,3) = -6733/35-72*ep^-1+2015/28*ep+1603937/2520*ep^2+513547/630*ep^3 +62519/120*ep^4+11669/60*ep^5; fill mncT00(9,4) = -18855/7-1080*ep^-1+618431/420*ep+1527913/168*ep^2+40749427/ 3780*ep^3+49720691/7560*ep^4+108841/45*ep^5; fill mncT00(9,5) = -339795/14-9900*ep^-1+7169401/504*ep+177345113/2160*ep^2+ 1450750099/15120*ep^3+177108377/3024*ep^4+66478591/3024*ep^5; fill mncT00(9,6) = -2256507/14-65340*ep^-1+76200941/840*ep+4550075377/8400*ep^2+ 9721402571/15120*ep^3+30385900253/75600*ep^4+2369271799/15120*ep^5; fill mncT00(9,7) = -5970591/7-339768*ep^-1+910963763/2100*ep+1275352103/450*ep^2+ 37461814447/10800*ep^3+72796743971/32400*ep^4+5945016637/6480*ep^5; fill mncT00(9,8) = -26476593/7-1472328*ep^-1+73265477633/44100*ep+54627219331/4410* ep^2+3572949997297/226800*ep^3+2411251880873/226800*ep^4+ 206938354943/45360*ep^5; fill mncT00(9,9) = -407455191/28-5521230*ep^-1+62145308573/11760*ep+8267348377283/ 176400*ep^2+26321703245023/423360*ep^3+4967716026299/113400*ep^4+ 1280830607257/64800*ep^5; fill mncT00(9,10) = -1394685435/28-18404100*ep^-1+100114668349/7056*ep+1852144738247/ 11760*ep^2+1386280258914223/6350400*ep^3+510011325931501/3175200* ep^4+62160020883013/816480*ep^5; fill mncT00(10,1) = -1/36-223/2520*ep-4/2835*ep^2+101/360*ep^3+229/540*ep^4+13/ 45*ep^5; fill mncT00(10,2) = -4469/630-2*ep^-1-3097/1260*ep+45329/2268*ep^2+85787/2268*ep^3 +17489/540*ep^4+4273/270*ep^5; fill mncT00(10,3) = -3615/14-90*ep^-1+13466/315*ep+2051033/2520*ep^2+6665453/5670* ep^3+19284803/22680*ep^4+49856/135*ep^5; fill mncT00(10,4) = -61445/14-1650*ep^-1+1187719/756*ep+13492646/945*ep^2+ 319245677/17010*ep^3+1605965/126*ep^4+36227755/6804*ep^5; fill mncT00(10,5) = -329285/7-18150*ep^-1+30067363/1512*ep+333243523/2160*ep^2+ 26798048483/136080*ep^3+2559867239/19440*ep^4+1496306639/27216*ep^5; fill mncT00(10,6) = -5124141/14-141570*ep^-1+97914331/630*ep+45269411767/37800*ep^2 +43425450739/28350*ep^3+43960605211/42525*ep^4+74891892349/170100* ep^5; fill mncT00(10,7) = -4484337/2-858858*ep^-1+16663386827/18900*ep+825227119253/113400 *ep^2+1290630089159/136080*ep^3+2673094441009/408240*ep^4+ 1957097729129/680400*ep^5; fill mncT00(10,8) = -22789767/2-4294290*ep^-1+528877919/135*ep+29013083864323/793800 *ep^2+116678567813779/2381400*ep^3+17786915424493/510300*ep^4+ 8105581054537/510300*ep^5; fill mncT00(10,9) = -1394685435/28-18404100*ep^-1+100114668349/7056*ep+1852144738247/ 11760*ep^2+1386280258914223/6350400*ep^3+510011325931501/3175200* ep^4+62160020883013/816480*ep^5; fill mncT00(10,10) = -8074989065/42-69526600*ep^-1+1350488632313/31752*ep+ 47479977496171/79380*ep^2+24566922560195171/28576800*ep^3+ 18726665340585257/28576800*ep^4+10393828589694061/32148900*ep^5; fill mncT10(-6,1) = -1/112-757/31360*ep-3727229/79027200*ep^2-596248999/7375872000* ep^3-805517926621/6195732480000*ep^4-116996591020151/578268364800000 *ep^5; fill mncT10(-6,2) = -143/140-1/2*ep^-1-317803/176400*ep-72277427/24696000*ep^2- 15809639243/3457440000*ep^3-3390537990787/484041600000*ep^4- 79974824548387/7529536000000*ep^5; fill mncT10(-6,3) = -59/20-21/2*ep^-1-24049/1200*ep-1127389/72000*ep^2-6231227/ 160000*ep^3-1260578141/28800000*ep^4-15537540689/192000000*ep^5; fill mncT10(-6,4) = 235/4-105/2*ep^-1-30433/240*ep+1041767/14400*ep^2-51977471/ 288000*ep^3+178464223/5760000*ep^4-30193341199/115200000*ep^5; fill mncT10(-6,5) = 670/3-175/2*ep^-1-60443/144*ep+100289/192*ep^2-4637557/6912*ep^3 +53277763/82944*ep^4-794249701/995328*ep^5; fill mncT10(-6,6) = 443/2-105/2*ep^-1-125593/240*ep+2499871/2880*ep^2-13702799/11520 *ep^3+7218039/5120*ep^4-174569129/110592*ep^5; fill mncT10(-6,7) = 337/5-21/2*ep^-1-260689/1200*ep+33888383/72000*ep^2-376269769/ 480000*ep^3+31338072103/28800000*ep^4-2307104628361/1728000000*ep^5; fill mncT10(-6,8) = 353/70-1/2*ep^-1-86107/3600*ep+5200903/72000*ep^2-228739987/ 1440000*ep^3+23861797469/86400000*ep^4-696292338001/1728000000*ep^5; fill mncT10(-6,9) = 1/56-463/1960*ep+7054603/4939200*ep^2-1232361283/230496000*ep^3+ 1372388471947/96808320000*ep^4-1175386471449923/40659494400000*ep^5; fill mncT10(-6,10) = 1/1344*ep-3179/376320*ep^2+38770049/948326400*ep^3-9635223953/ 88510464000*ep^4+11802258330329/74348789760000*ep^5; fill mncT10(-5,1) = -1/84-131/4410*ep-45907/823200*ep^2-32325739/345744000*ep^3- 798737439/5378240000*ep^4-172809886751/752953600000*ep^5; fill mncT10(-5,2) = -13/15-1/2*ep^-1-5267/3600*ep-55693/24000*ep^2-5155573/1440000 *ep^3-52300417/9600000*ep^4-526842293/64000000*ep^5; fill mncT10(-5,3) = 5/4-15/2*ep^-1-3119/240*ep-22373/4800*ep^2-2122051/96000*ep^3- 35026237/1920000*ep^4-543093073/12800000*ep^5; fill mncT10(-5,4) = 265/6-25*ep^-1-5579/72*ep+20767/288*ep^2-121699/1152*ep^3+ 315191/4608*ep^4-267971/2048*ep^5; fill mncT10(-5,5) = 1055/12-25*ep^-1-6547/36*ep+3175/12*ep^2-36151/108*ep^3+473935/ 1296*ep^4-391195/972*ep^5; fill mncT10(-5,6) = 173/4-15/2*ep^-1-30149/240*ep+78807/320*ep^2-4323407/11520*ep^3 +66872909/138240*ep^4-186295291/331776*ep^5; fill mncT10(-5,7) = 71/15-1/2*ep^-1-75287/3600*ep+4216483/72000*ep^2-515461421/ 4320000*ep^3+50009271427/259200000*ep^4-4105017792749/15552000000* ep^5; fill mncT10(-5,8) = 1/42-379/1260*ep+43399/25200*ep^2-9167693/1512000*ep^3+ 1366105291/90720000*ep^4-156453380117/5443200000*ep^5; fill mncT10(-5,9) = 1/784*ep-2263/164640*ep^2+1428971/23049600*ep^3-1443954119/ 9680832000*ep^4+725260343671/4065949440000*ep^5; fill mncT10(-5,10) = 1/28224*ep-5797/23708160*ep^2+2202023/6638284800*ep^3+8689170961/ 5576159232000*ep^4-31132238888473/4683973754880000*ep^5; fill mncT10(-4,1) = -1/60-17/450*ep-2441/36000*ep^2-26639/240000*ep^3-278431/ 1600000*ep^4-8544297/32000000*ep^5; fill mncT10(-4,2) = -41/60-1/2*ep^-1-1337/1200*ep-41419/24000*ep^2-1262653/480000* ep^3-12728737/3200000*ep^4-383416719/64000000*ep^5; fill mncT10(-4,3) = 11/3-5*ep^-1-211/24*ep+167/96*ep^2-4763/384*ep^3-1851/512*ep^4 -41841/2048*ep^5; fill mncT10(-4,4) = 53/2-10*ep^-1-416/9*ep+331/6*ep^2-595/9*ep^3+1505/24*ep^4- 595/8*ep^5; fill mncT10(-4,5) = 299/12-5*ep^-1-755/12*ep+3889/36*ep^2-15913/108*ep^3+225715/ 1296*ep^4-371315/1944*ep^5; fill mncT10(-4,6) = 131/30-1/2*ep^-1-845/48*ep+25747/576*ep^2-570889/6912*ep^3+ 50613671/414720*ep^4-154047985/995328*ep^5; fill mncT10(-4,7) = 1/30-179/450*ep+4253/2000*ep^2-7480199/1080000*ep^3+1025875513/ 64800000*ep^4-108169063031/3888000000*ep^5; fill mncT10(-4,8) = 1/420*ep-101/4200*ep^2+24967/252000*ep^3-1045543/5040000*ep^4+ 159617923/907200000*ep^5; fill mncT10(-4,9) = 1/11760*ep-437/823200*ep^2+150043/345744000*ep^3+198757571/ 48404160000*ep^4-812570541017/60989241600000*ep^5; fill mncT10(-4,10) = 1/141120*ep-3529/118540800*ep^2-540767/11063808000*ep^3+ 10661942293/27880796160000*ep^4-8911337124349/23419868774400000*ep^5; fill mncT10(-3,1) = -1/40-121/2400*ep-4127/48000*ep^2-43883/320000*ep^3-1357221/ 6400000*ep^4-41346027/128000000*ep^5; fill mncT10(-3,2) = -11/24-1/2*ep^-1-73/96*ep-443/384*ep^2-891/512*ep^3-5361/ 2048*ep^4-32211/8192*ep^5; fill mncT10(-3,3) = 9/2-3*ep^-1-20/3*ep+29/6*ep^2-31/4*ep^3+27/8*ep^4-159/16* ep^5; fill mncT10(-3,4) = 12-3*ep^-1-74/3*ep+35*ep^2-499/12*ep^3+89/2*ep^4-747/16*ep^5 ; fill mncT10(-3,5) = 47/12-1/2*ep^-1-167/12*ep+1111/36*ep^2-10793/216*ep^3+85315/ 1296*ep^4-594665/7776*ep^5; fill mncT10(-3,6) = 1/20-133/240*ep+2597/960*ep^2-91439/11520*ep^3+2244941/138240* ep^4-8504443/331776*ep^5; fill mncT10(-3,7) = 1/200*ep-557/12000*ep^2+40553/240000*ep^3-4125511/14400000*ep^4+ 81009257/864000000*ep^5; fill mncT10(-3,8) = 1/4200*ep-109/84000*ep^2+683/5040000*ep^3+171199/14400000*ep^4- 507092773/18144000000*ep^5; fill mncT10(-3,9) = 1/39200*ep-1439/16464000*ep^2-573283/2304960000*ep^3+1163405147/ 968083200000*ep^4-159267256723/406594944000000*ep^5; fill mncT10(-3,10) = 1/235200*ep-1723/197568000*ep^2-3323987/55319040000*ep^3+ 6428460691/46467993600000*ep^4+7694842432037/39033114624000000*ep^5; fill mncT10(-2,1) = -1/24-7/96*ep-15/128*ep^2-93/512*ep^3-567/2048*ep^4-3429/ 8192*ep^5; fill mncT10(-2,2) = -1/6-1/2*ep^-1-5/12*ep-5/8*ep^2-15/16*ep^3-45/32*ep^4-135/ 64*ep^5; fill mncT10(-2,3) = 4-3/2*ep^-1-23/4*ep+47/8*ep^2-99/16*ep^3+183/32*ep^4-411/64* ep^5; fill mncT10(-2,4) = 10/3-1/2*ep^-1-39/4*ep+421/24*ep^2-375/16*ep^3+855/32*ep^4- 1815/64*ep^5; fill mncT10(-2,5) = 1/12-5/6*ep+257/72*ep^2-3883/432*ep^3+40625/2592*ep^4-332755/ 15552*ep^5; fill mncT10(-2,6) = 1/80*ep-33/320*ep^2+239/768*ep^3-16369/46080*ep^4-28393/110592* ep^5; fill mncT10(-2,7) = 1/1200*ep-89/24000*ep^2-5057/1440000*ep^3+3402559/86400000*ep^4- 297978833/5184000000*ep^5; fill mncT10(-2,8) = 1/8400*ep-7/24000*ep^2-4979/3360000*ep^3+2574119/604800000*ep^4+ 1593769/576000000*ep^5; fill mncT10(-2,9) = 1/39200*ep-153/5488000*ep^2-303141/768320000*ep^3+446130407/ 968083200000*ep^4+235332367979/135531648000000*ep^5; fill mncT10(-2,10) = 1/141120*ep-19/39513600*ep^2-1286911/11063808000*ep^3+395635669/ 27880796160000*ep^4+4644027020161/7806622924800000*ep^5; fill mncT10(-1,1) = -1/12-1/8*ep-3/16*ep^2-9/32*ep^3-27/64*ep^4-81/128*ep^5; fill mncT10(-1,2) = 1/4-1/2*ep^-1-1/8*ep-3/16*ep^2-9/32*ep^3-27/64*ep^4-81/128* ep^5; fill mncT10(-1,3) = 5/2-1/2*ep^-1-5*ep+6*ep^2-6*ep^3+6*ep^4-6*ep^5; fill mncT10(-1,4) = 1/6-17/12*ep+39/8*ep^2-151/16*ep^3+407/32*ep^4-919/64*ep^5; fill mncT10(-1,5) = 1/24*ep-41/144*ep^2+523/864*ep^3-641/5184*ep^4-46589/31104*ep^5; fill mncT10(-1,6) = 1/240*ep-37/2880*ep^2-1301/34560*ep^3+63767/414720*ep^4-55825/ 995328*ep^5; fill mncT10(-1,7) = 1/1200*ep-67/72000*ep^2-52171/4320000*ep^3+3702677/259200000*ep^4 +700238501/15552000000*ep^5; fill mncT10(-1,8) = 1/4200*ep+13/252000*ep^2-56531/15120000*ep^3-548003/907200000*ep^4 +945051661/54432000000*ep^5; fill mncT10(-1,9) = 1/11760*ep+257/2469600*ep^2-1351993/1037232000*ep^3-679414663/ 435637440000*ep^4+1056611141567/182967724800000*ep^5; fill mncT10(-1,10) = 1/28224*ep+569/7902720*ep^2-3349369/6638284800*ep^3-6050070703/ 5576159232000*ep^4+8556135083879/4683973754880000*ep^5; fill mncT10(0,1) = -1/4-3/8*ep-9/16*ep^2-27/32*ep^3-81/64*ep^4-243/128*ep^5; fill mncT10(0,2) = 1-1/2*ep^-1; fill mncT10(0,3) = 1/2-3*ep+6*ep^2-6*ep^3+6*ep^4-6*ep^5; fill mncT10(0,4) = 1/4*ep-9/8*ep^2+9/16*ep^3+87/32*ep^4-279/64*ep^5; fill mncT10(0,5) = 1/24*ep-5/144*ep^2-449/864*ep^3+2275/5184*ep^4+37975/31104*ep^5; fill mncT10(0,6) = 1/80*ep+13/960*ep^2-1951/11520*ep^3-24083/138240*ep^4+178885/ 331776*ep^5; fill mncT10(0,7) = 1/200*ep+143/12000*ep^2-42841/720000*ep^3-6769033/43200000*ep^4+ 281515271/2592000000*ep^5; fill mncT10(0,8) = 1/420*ep+101/12600*ep^2-16957/756000*ep^3-4615741/45360000*ep^4- 69750733/2721600000*ep^5; fill mncT10(0,9) = 1/784*ep+291/54880*ep^2-196163/23049600*ep^3-616218973/9680832000* ep^4-235493357243/4065949440000*ep^5; fill mncT10(0,10) = 1/1344*ep+1349/376320*ep^2-909109/316108800*ep^3-10682456563/ 265531392000*ep^4-13079587690741/223046369280000*ep^5; fill mncT10(1,1) = 1/2*ep^-1; fill mncT10(1,2) = 3-ep^-1; fill mncT10(1,3) = -3/2+3*ep+6*ep^2-6*ep^3+6*ep^4-6*ep^5; fill mncT10(1,4) = -1/2-3/4*ep+39/8*ep^2+105/16*ep^3-105/32*ep^4+105/64*ep^5; fill mncT10(1,5) = -1/4-5/6*ep+119/72*ep^2+3299/432*ep^3+13895/2592*ep^4-19285/ 15552*ep^5; fill mncT10(1,6) = -3/20-11/16*ep+65/192*ep^2+13213/2304*ep^3+1265101/138240*ep^4 +1354885/331776*ep^5; fill mncT10(1,7) = -1/10-83/150*ep-3973/18000*ep^2+4308551/1080000*ep^3+632934263/ 64800000*ep^4+34727955719/3888000000*ep^5; fill mncT10(1,8) = -1/14-9/20*ep-559/1200*ep^2+194473/72000*ep^3+39548249/4320000 *ep^4+3093776137/259200000*ep^5; fill mncT10(1,9) = -3/56-729/1960*ep-312307/548800*ep^2+411281683/230496000*ep^3+ 789265539653/96808320000*ep^4+547737213033523/40659494400000*ep^5; fill mncT10(1,10) = -1/24-2099/6720*ep-3411341/5644800*ep^2+5367611413/4741632000* ep^3+28254903745891/3982970880000*ep^4+46982106507854437/ 3345695539200000*ep^5; fill mncT10(2,1) = 2-1/2*ep^-1-2*ep+2*ep^2-2*ep^3+2*ep^4-2*ep^5; fill mncT10(2,2) = 3-3/2*ep^-1+6*ep-6*ep^2+6*ep^3-6*ep^4+6*ep^5; fill mncT10(2,3) = -3/2-3/2*ep^-1+15*ep+12*ep^2-12*ep^3+12*ep^4-12*ep^5; fill mncT10(2,4) = -4-3/2*ep^-1+49/4*ep+295/8*ep^2+169/16*ep^3-233/32*ep^4+ 361/64*ep^5; fill mncT10(2,5) = -23/4-3/2*ep^-1+89/12*ep+457/9*ep^2+1487/27*ep^3+700/81*ep^4 -700/243*ep^5; fill mncT10(2,6) = -71/10-3/2*ep^-1+511/240*ep+164303/2880*ep^2+3505459/34560* ep^3+25651559/414720*ep^4+8078735/995328*ep^5; fill mncT10(2,7) = -41/5-3/2*ep^-1-1263/400*ep+465987/8000*ep^2+22952577/160000* ep^3+445571067/3200000*ep^4+3730168857/64000000*ep^5; fill mncT10(2,8) = -639/70-3/2*ep^-1-23221/2800*ep+9404347/168000*ep^2+1808749211/ 10080000*ep^3+139327252843/604800000*ep^4+5435434915259/36288000000* ep^5; fill mncT10(2,9) = -2781/280-3/2*ep^-1-259297/19600*ep+52749191/1029000*ep^2+ 45208808453/216090000*ep^3+3723811897181/11344725000*ep^4+ 663357839735273/2382392250000*ep^5; fill mncT10(2,10) = -4469/420-3/2*ep^-1-4223269/235200*ep+8846797177/197568000*ep^2 +38689293302239/165957120000*ep^3+59709391783310473/139403980800000* ep^4+51332799820998824911/117099343872000000*ep^5; fill mncT10(3,1) = -3/4+27/8*ep-75/16*ep^2+171/32*ep^3-363/64*ep^4+747/128*ep^5 ; fill mncT10(3,2) = 3/4-3/2*ep^-1+105/8*ep-105/16*ep^2+105/32*ep^3-105/64*ep^4+ 105/128*ep^5; fill mncT10(3,3) = -3-9/2*ep^-1+171/4*ep+201/8*ep^2-297/16*ep^3+489/32*ep^4- 873/64*ep^5; fill mncT10(3,4) = -15-9*ep^-1+159/2*ep+543/4*ep^2+105/8*ep^3-105/16*ep^4+105/ 32*ep^5; fill mncT10(3,5) = -149/4-15*ep^-1+335/3*ep+24041/72*ep^2+90941/432*ep^3+30905/ 2592*ep^4-70315/15552*ep^5; fill mncT10(3,6) = -285/4-45/2*ep^-1+10293/80*ep+196431/320*ep^2+169797/256*ep^3 +1264407/5120*ep^4+46389/4096*ep^5; fill mncT10(3,7) = -591/5-63/2*ep^-1+48357/400*ep+7699887/8000*ep^2+229927077/ 160000*ep^3+2914218567/3200000*ep^4+15233331357/64000000*ep^5; fill mncT10(3,8) = -1791/10-42*ep^-1+27859/350*ep+7153343/5250*ep^2+101471723/ 39375*ep^3+5250487699/2362500*ep^4+69188808181/70875000*ep^5; fill mncT10(3,9) = -35673/140-54*ep^-1-64347/19600*ep+153855913/85750*ep^2+ 296173542391/72030000*ep^3+33238587150539/7563150000*ep^4+ 4145231326795487/1588261500000*ep^5; fill mncT10(3,10) = -4845/14-135/2*ep^-1-2120191/15680*ep+392726021/175616*ep^2+ 893381947379/147517440*ep^3+189024874192657/24782929920*ep^4+ 23238823471233947/4163532226560*ep^5; fill mncT10(4,1) = -1/4+11/24*ep+239/144*ep^2-2989/864*ep^3+23879/5184*ep^4- 163669/31104*ep^5; fill mncT10(4,2) = -1/2-3/2*ep^-1+173/12*ep+257/72*ep^2-3187/432*ep^3+19577/ 2592*ep^4-109867/15552*ep^5; fill mncT10(4,3) = -15/2-9*ep^-1+85*ep+194/3*ep^2-302/9*ep^3+626/27*ep^4-1598/ 81*ep^5; fill mncT10(4,4) = -89/2-30*ep^-1+1607/6*ep+14399/36*ep^2+4547/216*ep^3+3623/ 1296*ep^4-92053/7776*ep^5; fill mncT10(4,5) = -625/4-75*ep^-1+3617/6*ep+100921/72*ep^2+281917/432*ep^3+ 99961/2592*ep^4-395051/15552*ep^5; fill mncT10(4,6) = -825/2-315/2*ep^-1+87101/80*ep+3474373/960*ep^2+34090769/11520 *ep^3+115905997/138240*ep^4-1176443/331776*ep^5; fill mncT10(4,7) = -9107/10-294*ep^-1+498149/300*ep+34741013/4500*ep^2+296389693/ 33750*ep^3+1083612773/253125*ep^4+3003598556/3796875*ep^5; fill mncT10(4,8) = -8891/5-504*ep^-1+4553953/2100*ep+454960141/31500*ep^2+ 4911347351/236250*ep^3+14142455467/1012500*ep^4+992017228511/ 212625000*ep^5; fill mncT10(4,9) = -88875/28-810*ep^-1+9252927/3920*ep+168366909/6860*ep^2+ 8166579979/192080*ep^3+144167672767/4033680*ep^4+562192184635/ 33882912*ep^5; fill mncT10(4,10) = -148145/28-2475/2*ep^-1+5844233/3136*ep+102041943371/2634240* ep^2+34685940027097/442552320*ep^3+5810307829273907/74348789760*ep^4 +567484189539766993/12490596679680*ep^5; fill mncT10(5,1) = -1/8+7/96*ep+1331/1152*ep^2-10697/13824*ep^3-16261/165888*ep^4 +1688527/1990656*ep^5; fill mncT10(5,2) = -11/8-3/2*ep^-1+1385/96*ep+13765/1152*ep^2-112975/13824*ep^3 +625645/165888*ep^4-3023815/1990656*ep^5; fill mncT10(5,3) = -16-15*ep^-1+3359/24*ep+40699/288*ep^2-146353/3456*ep^3+ 909331/41472*ep^4-9088057/497664*ep^5; fill mncT10(5,4) = -225/2-75*ep^-1+5331/8*ep+32337/32*ep^2+10551/128*ep^3+6201/ 512*ep^4-76569/2048*ep^5; fill mncT10(5,5) = -1025/2-525/2*ep^-1+103501/48*ep+2646365/576*ep^2+12919849/ 6912*ep^3+12547205/82944*ep^4-106259855/995328*ep^5; fill mncT10(5,6) = -1750-735*ep^-1+650707/120*ep+22250591/1440*ep^2+185708083/ 17280*ep^3+552944999/207360*ep^4-58423921/497664*ep^5; fill mncT10(5,7) = -49007/10-1764*ep^-1+850421/75*ep+760299527/18000*ep^2+ 43823276051/1080000*ep^3+1087265701763/64800000*ep^4+9074623643219/ 3888000000*ep^5; fill mncT10(5,8) = -23775/2-3780*ep^-1+2859667/140*ep+23847883/240*ep^2+ 2424900241/20160*ep^3+16526858893/241920*ep^4+7708831711/414720*ep^5 ; fill mncT10(5,9) = -1448565/56-7425*ep^-1+12607711/392*ep+68703347107/329280*ep^2 +8372383405609/27659520*ep^3+500539948415827/2323399680*ep^4+ 16253187395221297/195165573120*ep^5; fill mncT10(5,10) = -2895365/56-27225/2*ep^-1+137893873/3136*ep+351913867217/878080* ep^2+6644184374413/9834496*ep^3+1574369597037737/2753658880*ep^4+ 8634850111386637/30840979456*ep^5; fill mncT10(6,1) = -3/40-13/800*ep+35531/48000*ep^2+233003/2880000*ep^3-93186661/ 172800000*ep^4+5785099307/10368000000*ep^5; fill mncT10(6,2) = -41/20-3/2*ep^-1+16777/1200*ep+1335301/72000*ep^2-19367987/ 4320000*ep^3-196568531/259200000*ep^4+20928087997/15552000000*ep^5; fill mncT10(6,3) = -117/4-45/2*ep^-1+16461/80*ep+419211/1600*ep^2-885519/32000* ep^3+5867451/640000*ep^4-167036679/12800000*ep^5; fill mncT10(6,4) = -999/4-315/2*ep^-1+110547/80*ep+3592917/1600*ep^2+10569807/ 32000*ep^3+5651397/640000*ep^4-934558713/12800000*ep^5; fill mncT10(6,5) = -5677/4-735*ep^-1+181561/30*ep+22883293/1800*ep^2+275706917/ 54000*ep^3+823074373/1620000*ep^4-15404524363/48600000*ep^5; fill mncT10(6,6) = -120561/20-2646*ep^-1+4004489/200*ep+640164857/12000*ep^2+ 24618330341/720000*ep^3+348715791533/43200000*ep^4-1386850102771/ 2592000000*ep^5; fill mncT10(6,7) = -414603/20-7938*ep^-1+10807857/200*ep+720254637/4000*ep^2+ 12473875827/80000*ep^3+93453599817/1600000*ep^4+206943175107/ 32000000*ep^5; fill mncT10(6,8) = -243381/4-20790*ep^-1+34826081/280*ep+8670420679/16800*ep^2+ 561756327107/1008000*ep^3+17090170665691/60480000*ep^4+ 238855334385083/3628800000*ep^5; fill mncT10(6,9) = -8845353/56-49005*ep^-1+61371918/245*ep+715102622253/548800*ep^2 +128719613722761/76832000*ep^3+11393633670678117/10756480000*ep^4+ 536420721540120849/1505907200000*ep^5; fill mncT10(6,10) = -10411467/28-212355/2*ep^-1+7007897301/15680*ep+13054357748157/ 4390400*ep^2+5432640205465833/1229312000*ep^3+1141773110158691877/ 344207360000*ep^4+137203192797278262513/96378060800000*ep^5; fill mncT10(7,1) = -1/20-1/25*ep+17713/36000*ep^2+82091/240000*ep^3-48738953/ 129600000*ep^4+427746437/2592000000*ep^5; fill mncT10(7,2) = -13/5-3/2*ep^-1+16009/1200*ep+1713467/72000*ep^2+5388271/ 4320000*ep^3-914192377/259200000*ep^4+25764655399/15552000000*ep^5; fill mncT10(7,3) = -957/20-63/2*ep^-1+112243/400*ep+10355459/24000*ep^2+39466867/ 1440000*ep^3-820748029/86400000*ep^4-52688239277/5184000000*ep^5; fill mncT10(7,4) = -4991/10-294*ep^-1+760201/300*ep+40405069/9000*ep^2+276581461/ 270000*ep^3+34098109/8100000*ep^4-31522116779/243000000*ep^5; fill mncT10(7,5) = -34601/10-1764*ep^-1+2884389/200*ep+557280473/18000*ep^2+ 2372481179/180000*ep^3+25064318153/16200000*ep^4-124218058181/ 162000000*ep^5; fill mncT10(7,6) = -356391/20-7938*ep^-1+302601/5*ep+25242353/160*ep^2+189122879/ 1920*ep^3+535864919/23040*ep^4-88343129/55296*ep^5; fill mncT10(7,7) = -1470819/20-29106*ep^-1+40709357/200*ep+7693396111/12000*ep^2+ 377114820443/720000*ep^3+8039414975059/43200000*ep^4+45909374983667/ 2592000000*ep^5; fill mncT10(7,8) = -2560767/10-91476*ep^-1+403678357/700*ep+91955041481/42000*ep^2 +5533074324853/2520000*ep^3+156314232405389/151200000*ep^4+ 1952097820330957/9072000000*ep^5; fill mncT10(7,9) = -109180863/140-254826*ep^-1+27831938271/19600*ep+4471028447173/ 686000*ep^2+1110743856904309/144060000*ep^3+135627586834713397/ 30252600000*ep^4+8622826680259950451/6353046000000*ep^5; fill mncT10(7,10) = -10657361/5-1288287/2*ep^-1+104096074001/33600*ep+70010581183721/ 4032000*ep^2+11415336636644921/483840000*ep^3+941071217126100521/ 58060800000*ep^4+43764869471914228121/6967296000000*ep^5; fill mncT10(8,1) = -1/28-11/245*ep+841441/2469600*ep^2+140549527/345744000*ep^3- 78460581929/435637440000*ep^4-119057887957/6776582400000*ep^5; fill mncT10(8,2) = -429/140-3/2*ep^-1+741721/58800*ep+76963479/2744000*ep^2+ 81887763001/10372320000*ep^3-6160336923403/1452124800000*ep^4+ 1295154979900681/1829677248000000*ep^5; fill mncT10(8,3) = -723/10-42*ep^-1+190459/525*ep+3999879/6125*ep^2+1606404113/ 11576250*ep^3-18966571957/810337500*ep^4-6990546924043/510512625000* ep^5; fill mncT10(8,4) = -4583/5-504*ep^-1+2976049/700*ep+3633118901/441000*ep^2+ 26640129587/10290000*ep^3+1404226137989/19448100000*ep^4- 312289819072471/1361367000000*ep^5; fill mncT10(8,5) = -15261/2-3780*ep^-1+1708635/56*ep+160324043/2352*ep^2+ 1046272427/32928*ep^3+18358712195/4148928*ep^4-10404645445/6453888* ep^5; fill mncT10(8,6) = -187149/4-20790*ep^-1+44283219/280*ep+9735744713/23520*ep^2+ 34385651633/131712*ep^3+10575190295741/165957120*ep^4-1096338717877/ 309786624*ep^5; fill mncT10(8,7) = -2277627/10-91476*ep^-1+226386421/350*ep+584576884757/294000* ep^2+195459943419287/123480000*ep^3+28591792133478017/51861600000* ep^4+1079869635250403447/21781872000000*ep^5; fill mncT10(8,8) = -32429661/35-339768*ep^-1+10790696937/4900*ep+2046677027189/ 257250*ep^2+91578785899761/12005000*ep^3+77932951717863967/ 22689450000*ep^4+1055840020003157587/1588261500000*ep^5; fill mncT10(8,9) = -457261233/140-1104246*ep^-1+126658602561/19600*ep+ 56612672242069/2058000*ep^2+1477059000503353/48020000*ep^3+ 1532380088383876441/90757800000*ep^4+30091840120792481701/ 6353046000000*ep^5; fill mncT10(8,10) = -40973075/4-6441435/2*ep^-1+22478238109/1344*ep+476548217134259/ 5644800*ep^2+510156069130971413/4741632000*ep^3+ 275923509539915048291/3982970880000*ep^4+83099258828924445467237/ 3345695539200000*ep^5; fill mncT10(9,1) = -3/112-1371/31360*ep+6431963/26342400*ep^2+2966087647/7375872000 *ep^3-611577766213/18587197440000*ep^4-132891842895899/ 1734805094400000*ep^5; fill mncT10(9,2) = -1941/560-3/2*ep^-1+5574893/470400*ep+1384537139/43904000*ep^2 +4946688512957/331914240000*ep^3-290639078154967/92935987200000*ep^4 -134149663854043507/234198687744000000*ep^5; fill mncT10(9,3) = -3606/35-54*ep^-1+8832897/19600*ep+15295528679/16464000*ep^2+ 1480090671851/4609920000*ep^3-216275657823529/11616998400000*ep^4- 79790911767110501/3252759552000000*ep^5; fill mncT10(9,4) = -11007/7-810*ep^-1+5227599/784*ep+619210523/43904*ep^2+ 41651662777/7375872*ep^3+489208925459/1239146496*ep^4-81859576744847/ 208176611328*ep^5; fill mncT10(9,5) = -108615/7-7425*ep^-1+92424603/1568*ep+36431450201/263424*ep^2+ 1051649748017/14751744*ep^3+88092329320049/7434878976*ep^4- 414528826232413/138784407552*ep^5; fill mncT10(9,6) = -3127311/28-49005*ep^-1+2898678549/7840*ep+433169530321/439040* ep^2+47397954971827/73758720*ep^3+2054240925109729/12391464960*ep^4 -2252571502338001/416353222656*ep^5; fill mncT10(9,7) = -22145607/35-254826*ep^-1+35373882351/19600*ep+30313548935039/ 5488000*ep^2+20203931885697673/4609920000*ep^3+5933616533636271311/ 3872332800000*ep^4+462091977884877380377/3252759552000000*ep^5; fill mncT10(9,8) = -103963002/35-1104246*ep^-1+20313977223/2800*ep+8587525177223/ 336000*ep^2+107219196240447/4480000*ep^3+50977876717066823/ 4838400000*ep^4+380601667803088541/193536000000*ep^5; fill mncT10(9,9) = -47947185/4-8281845/2*ep^-1+78174883767/3136*ep+445278263627459/ 4390400*ep^2+403289285860381253/3687936000*ep^3+ 179134080933423547571/3097866240000*ep^4+40107079404902794050197/ 2602207641600000*ep^5; fill mncT10(9,10) = -85433205/2-13803075*ep^-1+117761275265/1568*ep+467167231082219/ 1317120*ep^2+95619206829958873/221276160*ep^3+9875467238318703923/ 37174394880*ep^4+561612840013743600337/6245298339840*ep^5; fill mncT10(10,1) = -1/48-4913/120960*ep+54821267/304819200*ep^2+287421825007/ 768144384000*ep^3+129457437294347/1935723847680000*ep^4- 380383365844061513/4878024096153600000*ep^5; fill mncT10(10,2) = -3209/840-3/2*ep^-1+23449001/2116800*ep+183663936121/5334336000* ep^2+295519349213141/13442526720000*ep^3-16723146461182439/ 33875167334400000*ep^4-139225311874684347619/85365421682688000000*ep^5 ; fill mncT10(10,3) = -7863/56-135/2*ep^-1+5105869/9408*ep+5979475273/4741632*ep^2+ 1404672849793/2389782528*ep^3+25182200308273/1204450394112*ep^4- 24400676646773807/607042998632448*ep^5; fill mncT10(10,4) = -142895/56-2475/2*ep^-1+279921139/28224*ep+324527671543/14224896 *ep^2+79228822515679/7169347584*ep^3+4736815497678319/3613351182336* ep^4-1128953117831145521/1821128995897344*ep^5; fill mncT10(10,5) = -1652695/56-27225/2*ep^-1+2991229469/28224*ep+3731016922625/ 14224896*ep^2+1070807836572329/7169347584*ep^3+106428276085837625/ 3613351182336*ep^4-8696857836147578215/1821128995897344*ep^5; fill mncT10(10,6) = -13805781/56-212355/2*ep^-1+37220066537/47040*ep+51518379298877/ 23708160*ep^2+17681366933446277/11948912640*ep^3+2462941888380796757/ 6022251970560*ep^4-1155889915078838159/607042998632448*ep^5; fill mncT10(10,7) = -64298663/40-1288287/2*ep^-1+65399895179/14400*ep+72673731308677/ 5184000*ep^2+21008503589356631/1866240000*ep^3+2699732995940530693/ 671846400000*ep^4+98615194279443444479/241864704000000*ep^5; fill mncT10(10,8) = -68961035/8-6441435/2*ep^-1+85716427777/4032*ep+538624877659483/ 7257600*ep^2+180099386375368169/2612736000*ep^3+28379320048858941307/ 940584960000*ep^4+1897053674504596395521/338610585600000*ep^5; fill mncT10(10,9) = -315660345/8-13803075*ep^-1+99248819645/1176*ep+991879090289449/ 2963520*ep^2+263813554159185809/746807040*ep^3+34403361676341944641/ 188195374080*ep^4+2243502897931080551873/47425234268160*ep^5; fill mncT10(10,10) = -3802934135/24-52144950*ep^-1+12362003265215/42336*ep+ 141030167154691039/106686720*ep^2+16799338215122256935/10754021376* ep^3+25215345288750461743819/27100133867520*ep^4+ 826552886737401492355103/2731693493846016*ep^5; fill mncT20(-6,1) = -1/84-23/980*ep-5843/154350*ep^2-453806/8103375*ep^3-67430704/ 850854375*ep^4-9775819136/89339709375*ep^5; fill mncT20(-6,2) = -73/105-2/3*ep^-1-11492/11025*ep-1677703/1157625*ep^2- 240693302/121550625*ep^3-34187537368/12762815625*ep^4-4827576638912/ 1340095640625*ep^5; fill mncT20(-6,3) = 72/5-14*ep^-1-3697/150*ep+30361/2250*ep^2-484709/16875*ep^3+ 2108492/253125*ep^4-135135596/3796875*ep^5; fill mncT20(-6,4) = 587/3-70*ep^-1-5104/15*ep+95062/225*ep^2-3304937/6750*ep^3+ 100310887/202500*ep^4-3255229337/6075000*ep^5; fill mncT20(-6,5) = 3275/6-350/3*ep^-1-47683/36*ep+79933/36*ep^2-968071/324*ep^3+ 757925/216*ep^4-44696575/11664*ep^5; fill mncT20(-6,6) = 485-70*ep^-1-49229/30*ep+439127/120*ep^2-26640239/4320*ep^3+ 49332629/5760*ep^4-1299375595/124416*ep^5; fill mncT20(-6,7) = 2092/15-14*ep^-1-16473/25*ep+17887891/9000*ep^2-2354883317/ 540000*ep^3+244404539179/32400000*ep^4-21223511520773/1944000000* ep^5; fill mncT20(-6,8) = 353/35-2/3*ep^-1-31619/450*ep+303089/1000*ep^2-1489855661/ 1620000*ep^3+68644660769/32400000*ep^4-22832247383309/5832000000* ep^5; fill mncT20(-6,9) = 1/28-1349/1960*ep+2479361/411600*ep^2-1852848323/57624000*ep^3+ 8626260284921/72606240000*ep^4-3329436346797163/10164873600000*ep^5; fill mncT20(-6,10) = 1/504*ep-4591/141120*ep^2+26553911/118540800*ep^3-26897921381/ 33191424000*ep^4+112312437169799/83642388480000*ep^5; fill mncT20(-5,1) = -1/63-379/13230*ep-30823/694575*ep^2-4683932/72930375*ep^3- 687208288/7657689375*ep^4-98880776192/804057384375*ep^5; fill mncT20(-5,2) = -22/45-2/3*ep^-1-1033/1350*ep-10573/10125*ep^2-214376/151875* ep^3-4322512/2278125*ep^4-86870144/34171875*ep^5; fill mncT20(-5,3) = 46/3-10*ep^-1-1937/90*ep+11788/675*ep^2-236794/10125*ep^3+ 2350972/151875*ep^4-59300836/2278125*ep^5; fill mncT20(-5,4) = 1075/9-100/3*ep^-1-12457/54*ep+25549/81*ep^2-179305/486*ep^3+ 1142575/2916*ep^4-7163485/17496*ep^5; fill mncT20(-5,5) = 1775/9-100/3*ep^-1-30707/54*ep+175897/162*ep^2-773903/486*ep^3 +5761805/2916*ep^4-38852975/17496*ep^5; fill mncT20(-5,6) = 90-10*ep^-1-5711/15*ep+368137/360*ep^2-8629087/4320*ep^3+ 160556317/51840*ep^4-507053099/124416*ep^5; fill mncT20(-5,7) = 142/15-2/3*ep^-1-13787/225*ep+6570173/27000*ep^2-1093489951/ 1620000*ep^3+137668367537/97200000*ep^4-13917130212319/5832000000* ep^5; fill mncT20(-5,8) = 1/21-551/630*ep+136597/18900*ep^2-40929769/1134000*ep^3+ 8420292103/68040000*ep^4-1284520788361/4082400000*ep^5; fill mncT20(-5,9) = 1/294*ep-3257/61740*ep^2+4361053/12965400*ep^3-5867075167/ 5445468000*ep^4+2880118282903/2287096560000*ep^5; fill mncT20(-5,10) = 1/10584*ep-8513/8890560*ep^2+14714953/7468070400*ep^3+77922221551/ 6273179136000*ep^4-395835392153543/5269470474240000*ep^5; fill mncT20(-4,1) = -1/45-49/1350*ep-544/10125*ep^2-11528/151875*ep^3-238336/ 2278125*ep^4-4860032/34171875*ep^5; fill mncT20(-4,2) = -11/45-2/3*ep^-1-337/675*ep-6794/10125*ep^2-136528/151875*ep^3 -2738336/2278125*ep^4-54860032/34171875*ep^5; fill mncT20(-4,3) = 131/9-20/3*ep^-1-1067/54*ep+1565/81*ep^2-5080/243*ep^3+13700/ 729*ep^4-47260/2187*ep^5; fill mncT20(-4,4) = 562/9-40/3*ep^-1-3842/27*ep+17653/81*ep^2-130045/486*ep^3+ 856255/2916*ep^4-5371645/17496*ep^5; fill mncT20(-4,5) = 157/3-20/3*ep^-1-3427/18*ep+23569/54*ep^2-59156/81*ep^3+479815/ 486*ep^4-3400565/2916*ep^5; fill mncT20(-4,6) = 131/15-2/3*ep^-1-925/18*ep+39547/216*ep^2-1169689/2592*ep^3+ 130416407/155520*ep^4-469580545/373248*ep^5; fill mncT20(-4,7) = 1/15-173/150*ep+39883/4500*ep^2-10971971/270000*ep^3+2049129277/ 16200000*ep^4-281553155699/972000000*ep^5; fill mncT20(-4,8) = 2/315*ep-62/675*ep^2+75109/141750*ep^3-12130183/8505000*ep^4+ 49117903/72900000*ep^5; fill mncT20(-4,9) = 1/4410*ep-1913/926100*ep^2+493441/194481000*ep^3+2703618881/ 81682020000*ep^4-5052527519129/34306448400000*ep^5; fill mncT20(-4,10) = 1/52920*ep-5237/44452800*ep^2-9426899/37340352000*ep^3+96602667307/ 31365895680000*ep^4-104343711700451/26347352371200000*ep^5; fill mncT20(-3,1) = -1/30-11/225*ep-232/3375*ep^2-4784/50625*ep^3-97408/759375* ep^4-1968896/11390625*ep^5; fill mncT20(-3,2) = 1/18-2/3*ep^-1-7/27*ep-28/81*ep^2-112/243*ep^3-448/729*ep^4- 1792/2187*ep^5; fill mncT20(-3,3) = 37/3-4*ep^-1-167/9*ep+538/27*ep^2-1628/81*ep^3+4828/243*ep^4 -14708/729*ep^5; fill mncT20(-3,4) = 77/3-4*ep^-1-223/3*ep+403/3*ep^2-1085/6*ep^3+2485/12*ep^4- 5285/24*ep^5; fill mncT20(-3,5) = 47/6-2/3*ep^-1-727/18*ep+6667/54*ep^2-83453/324*ep^3+788095/ 1944*ep^4-6126365/11664*ep^5; fill mncT20(-3,6) = 1/10-8/5*ep+1339/120*ep^2-65581/1440*ep^3+2144431/17280*ep^4- 10217753/41472*ep^5; fill mncT20(-3,7) = 1/75*ep-22/125*ep^2+19867/22500*ep^3-2410529/1350000*ep^4- 106376777/81000000*ep^5; fill mncT20(-3,8) = 1/1575*ep-118/23625*ep^2+841/1417500*ep^3+8151533/85050000*ep^4- 1499687771/5103000000*ep^5; fill mncT20(-3,9) = 1/14700*ep-263/771750*ep^2-879791/648270000*ep^3+2609273819/ 272273400000*ep^4-219838700171/114354828000000*ep^5; fill mncT20(-3,10) = 1/88200*ep-2563/74088000*ep^2-20465941/62233920000*ep^3+ 58042373213/52276492800000*ep^4+116022719392091/43912253952000000*ep^5 ; fill mncT20(-2,1) = -1/18-2/27*ep-8/81*ep^2-32/243*ep^3-128/729*ep^4-512/2187* ep^5; fill mncT20(-2,2) = 4/9-2/3*ep^-1-2/27*ep-8/81*ep^2-32/243*ep^3-128/729*ep^4-512/ 2187*ep^5; fill mncT20(-2,3) = 9-2*ep^-1-17*ep+20*ep^2-20*ep^3+20*ep^4-20*ep^5; fill mncT20(-2,4) = 20/3-2/3*ep^-1-28*ep+67*ep^2-215/2*ep^3+535/4*ep^4-1175/8* ep^5; fill mncT20(-2,5) = 1/6-43/18*ep+781/54*ep^2-16061/324*ep^3+214615/1944*ep^4- 2073125/11664*ep^5; fill mncT20(-2,6) = 1/30*ep-139/360*ep^2+6721/4320*ep^3-84259/51840*ep^4-902827/ 124416*ep^5; fill mncT20(-2,7) = 1/450*ep-377/27000*ep^2-35201/1620000*ep^3+30326287/97200000*ep^4 -3031593569/5832000000*ep^5; fill mncT20(-2,8) = 1/3150*ep-23/21000*ep^2-93791/11340000*ep^3+7404539/226800000*ep^4 +1951554721/40824000000*ep^5; fill mncT20(-2,9) = 1/14700*ep-317/3087000*ep^2-2824597/1296540000*ep^3+1840664773/ 544546800000*ep^4+5160486513443/228709656000000*ep^5; fill mncT20(-2,10) = 1/52920*ep-29/44452800*ep^2-23874563/37340352000*ep^3+1050578059/ 31365895680000*ep^4+195040341925213/26347352371200000*ep^5; fill mncT20(-1,1) = -1/9-4/27*ep-16/81*ep^2-64/243*ep^3-256/729*ep^4-1024/2187* ep^5; fill mncT20(-1,2) = 1-2/3*ep^-1; fill mncT20(-1,3) = 5-2/3*ep^-1-14*ep+20*ep^2-20*ep^3+20*ep^4-20*ep^5; fill mncT20(-1,4) = 1/3-4*ep+19*ep^2-95/2*ep^3+295/4*ep^4-695/8*ep^5; fill mncT20(-1,5) = 1/9*ep-28/27*ep^2+217/81*ep^3+1105/486*ep^4-69035/2916*ep^5; fill mncT20(-1,6) = 1/90*ep-49/1080*ep^2-2909/12960*ep^3+176471/155520*ep^4+77183/ 373248*ep^5; fill mncT20(-1,7) = 1/450*ep-77/27000*ep^2-108701/1620000*ep^3+8508787/97200000*ep^4 +3586068931/5832000000*ep^5; fill mncT20(-1,8) = 1/1575*ep+19/47250*ep^2-57553/2835000*ep^3-2102489/170100000*ep^4 +2150196743/10206000000*ep^5; fill mncT20(-1,9) = 1/4410*ep+439/926100*ep^2-2704141/388962000*ep^3-2439933731/ 163364040000*ep^4+4525924032779/68612896800000*ep^5; fill mncT20(-1,10) = 1/10584*ep+2743/8890560*ep^2-19721351/7468070400*ep^3-60095960177/ 6273179136000*ep^4+102403388672761/5269470474240000*ep^5; fill mncT20(0,1) = -1/3-2/3*ep-4/3*ep^2-8/3*ep^3-16/3*ep^4-32/3*ep^5; fill mncT20(0,2) = 2-2/3*ep^-1; fill mncT20(0,3) = 1-8*ep+20*ep^2-20*ep^3+20*ep^4-20*ep^5; fill mncT20(0,4) = 2/3*ep-11/3*ep^2-5/6*ep^3+325/12*ep^4-965/24*ep^5; fill mncT20(0,5) = 1/9*ep-1/27*ep^2-457/162*ep^3+995/972*ep^4+98855/5832*ep^5; fill mncT20(0,6) = 1/30*ep+29/360*ep^2-3599/4320*ep^3-106051/51840*ep^4+600341/ 124416*ep^5; fill mncT20(0,7) = 1/75*ep+43/750*ep^2-11891/45000*ep^3-3854183/2700000*ep^4+ 28768321/162000000*ep^5; fill mncT20(0,8) = 2/315*ep+172/4725*ep^2-23929/283500*ep^3-14469227/17010000*ep^4- 956061151/1020600000*ep^5; fill mncT20(0,9) = 1/294*ep+1447/61740*ep^2-566677/25930800*ep^3-5484186467/ 10890936000*ep^4-4758952611397/4574193120000*ep^5; fill mncT20(0,10) = 1/504*ep+2201/141120*ep^2+99943/118540800*ep^3-10086927493/ 33191424000*ep^4-74798499514553/83642388480000*ep^5; fill mncT20(1,1) = 1/3*ep^-1; fill mncT20(1,2) = 4-ep^-1; fill mncT20(1,3) = -2+4*ep+20*ep^2-20*ep^3+20*ep^4-20*ep^5; fill mncT20(1,4) = -2/3-2*ep+11*ep^2+65/2*ep^3-25/4*ep^4-55/8*ep^5; fill mncT20(1,5) = -1/3-17/9*ep+133/54*ep^2+9697/324*ep^3+90685/1944*ep^4+48265/ 11664*ep^5; fill mncT20(1,6) = -1/5-3/2*ep-17/24*ep^2+5783/288*ep^3+1068911/17280*ep^4+ 2624615/41472*ep^5; fill mncT20(1,7) = -2/15-89/75*ep-8617/4500*ep^2+3351779/270000*ep^3+970238027/ 16200000*ep^4+101308463051/972000000*ep^5; fill mncT20(1,8) = -2/21-43/45*ep-6341/2700*ep^2+1156907/162000*ep^3+510974491/ 9720000*ep^4+72810365483/583200000*ep^5; fill mncT20(1,9) = -1/14-769/980*ep-1010321/411600*ep^2+205879523/57624000*ep^3+ 3214970899279/72606240000*ep^4+1341980656664563/10164873600000*ep^5; fill mncT20(1,10) = -1/18-551/840*ep-5115629/2116800*ep^2+75291971/65856000*ep^3+ 54543220808719/1493614080000*ep^4+54914876768924611/418211942400000* ep^5; fill mncT20(2,1) = 2-1/3*ep^-1-4*ep+8*ep^2-16*ep^3+32*ep^4-64*ep^5; fill mncT20(2,2) = 4-4/3*ep^-1+8*ep-16*ep^2+32*ep^3-64*ep^4+128*ep^5; fill mncT20(2,3) = -2-4/3*ep^-1+24*ep+28*ep^2-36*ep^3+52*ep^4-84*ep^5; fill mncT20(2,4) = -16/3-4/3*ep^-1+18*ep+87*ep^2+105/2*ep^3-105/4*ep^4+105/8* ep^5; fill mncT20(2,5) = -23/3-4/3*ep^-1+73/9*ep+6289/54*ep^2+68989/324*ep^3+192745/ 1944*ep^4-257915/11664*ep^5; fill mncT20(2,6) = -142/15-4/3*ep^-1-233/90*ep+135527/1080*ep^2+4831027/12960* ep^3+64777463/155520*ep^4+59776703/373248*ep^5; fill mncT20(2,7) = -164/15-4/3*ep^-1-5959/450*ep+3266573/27000*ep^2+827279549/ 1620000*ep^3+82540045037/97200000*ep^4+3971016625181/5832000000*ep^5 ; fill mncT20(2,8) = -426/35-4/3*ep^-1-74243/3150*ep+2252989/21000*ep^2+7047906613/ 11340000*ep^3+303789722423/226800000*ep^4+62608258173397/40824000000 *ep^5; fill mncT20(2,9) = -927/70-4/3*ep^-1-1476577/44100*ep+179362247/2058000*ep^2+ 5488605605993/7779240000*ep^3+2014683523898821/1089093600000*ep^4+ 3664245722376390233/1372257936000000*ep^5; fill mncT20(2,10) = -4469/315-4/3*ep^-1-3789689/88200*ep+4624227637/74088000*ep^2+ 47595938660059/62233920000*ep^3+123202774990297213/52276492800000*ep^4 +177176618299181880091/43912253952000000*ep^5; fill mncT20(3,1) = -2/3+14/3*ep-38/3*ep^2+86/3*ep^3-182/3*ep^4+374/3*ep^5; fill mncT20(3,2) = 2-4/3*ep^-1+18*ep-26*ep^2+42*ep^3-74*ep^4+138*ep^5; fill mncT20(3,3) = -2-4*ep^-1+66*ep+30*ep^2-30*ep^3+30*ep^4-30*ep^5; fill mncT20(3,4) = -50/3-8*ep^-1+124*ep+269*ep^2+125/2*ep^3-145/4*ep^4+185/8* ep^5; fill mncT20(3,5) = -134/3-40/3*ep^-1+1522/9*ep+19061/27*ep^2+115049/162*ep^3+ 134645/972*ep^4-243775/5832*ep^5; fill mncT20(3,6) = -88-20*ep^-1+5417/30*ep+474037/360*ep^2+9565217/4320*ep^3+ 75824797/51840*ep^4+33326293/124416*ep^5; fill mncT20(3,7) = -2224/15-28*ep^-1+20927/150*ep+18515191/9000*ep^2+2581018183/ 540000*ep^3+162439806679/32400000*ep^4+4861399866727/1944000000*ep^5 ; fill mncT20(3,8) = -1134/5-112/3*ep^-1+45233/1575*ep+4307843/1500*ep^2+ 48365901917/5670000*ep^3+1347457264207/113400000*ep^4+26378646127739/ 2916000000*ep^5; fill mncT20(3,9) = -11366/35-48*ep^-1-205412/1225*ep+1902910333/514500*ep^2+ 2921999991203/216090000*ep^3+2096541650905573/90757800000*ep^4+ 872516058420356243/38118276000000*ep^5; fill mncT20(3,10) = -9305/21-60*ep^-1-1638433/3528*ep+7361205209/1646400*ep^2+ 81972708321109/4148928000*ep^3+138028550387269363/3485099520000*ep^4 +138795980231409673141/2927483596800000*ep^5; fill mncT20(4,1) = -2/9+22/27*ep+118/81*ep^2-2018/243*ep^3+17158/729*ep^4- 120338/2187*ep^5; fill mncT20(4,2) = 8/9-4/3*ep^-1+560/27*ep-1120/81*ep^2+2240/243*ep^3-4480/729* ep^4+8960/2187*ep^5; fill mncT20(4,3) = -10/3-8*ep^-1+1178/9*ep+1370/27*ep^2-3550/81*ep^3+9530/243* ep^4-26350/729*ep^5; fill mncT20(4,4) = -364/9-80/3*ep^-1+11414/27*ep+52583/81*ep^2+29995/486*ep^3- 94465/2916*ep^4+301315/17496*ep^5; fill mncT20(4,5) = -1490/9-200/3*ep^-1+25756/27*ep+213712/81*ep^2+439192/243*ep^3 +121240/729*ep^4-122360/2187*ep^5; fill mncT20(4,6) = -466-140*ep^-1+50969/30*ep+2595829/360*ep^2+37296929/4320*ep^3 +203776669/51840*ep^4+45626581/124416*ep^5; fill mncT20(4,7) = -15974/15-784/3*ep^-1+563653/225*ep+212948149/13500*ep^2+ 21367432837/810000*ep^3+981651206581/48600000*ep^4+20536825751653/ 2916000000*ep^5; fill mncT20(4,8) = -31864/15-448*ep^-1+4807756/1575*ep+704184707/23625*ep^2+ 90017249191/1417500*ep^3+5633202721583/85050000*ep^4+190987510132879/ 5103000000*ep^5; fill mncT20(4,9) = -26930/7-720*ep^-1+414236/147*ep+15650506589/308700*ep^2+ 17001990837739/129654000*ep^3+9261629868042749/54454680000*ep^4+ 2943607325873278459/22870965600000*ep^5; fill mncT20(4,10) = -408245/63-1100*ep^-1+11019805/10584*ep+707513577751/8890560* ep^2+1814527882945273/7468070400*ep^3+2338002817201507471/ 6273179136000*ep^4+1826951548514338306297/5269470474240000*ep^5; fill mncT20(5,1) = -1/9+13/54*ep+461/324*ep^2-6623/1944*ep^3+60269/11664*ep^4- 459047/69984*ep^5; fill mncT20(5,2) = 1/9-4/3*ep^-1+1175/54*ep-785/324*ep^2-11845/1944*ep^3+111775/ 11664*ep^4-756925/69984*ep^5; fill mncT20(5,3) = -62/9-40/3*ep^-1+5893/27*ep+17225/162*ep^2-73355/972*ep^3+ 345665/5832*ep^4-1772675/34992*ep^5; fill mncT20(5,4) = -790/9-200/3*ep^-1+28721/27*ep+227557/162*ep^2+46625/972*ep^3 -32195/5832*ep^4-567415/34992*ep^5; fill mncT20(5,5) = -485-700/3*ep^-1+62669/18*ep+836537/108*ep^2+2614229/648*ep^3 +872705/3888*ep^4-2444035/23328*ep^5; fill mncT20(5,6) = -1813-1960/3*ep^-1+394943/45*ep+30703469/1080*ep^2+347378191/ 12960*ep^3+1441025999/155520*ep^4+151385327/373248*ep^5; fill mncT20(5,7) = -80164/15-1568*ep^-1+1368386/75*ep+20352181/250*ep^2+542082151/ 5000*ep^3+6553417021/100000*ep^4+34239683791/2000000*ep^5; fill mncT20(5,8) = -40180/3-3360*ep^-1+2038402/63*ep+1858182677/9450*ep^2+ 189734040541/567000*ep^3+9555153067133/34020000*ep^4+255951484910029/ 2041200000*ep^5; fill mncT20(5,9) = -625915/21-6600*ep^-1+43566575/882*ep+155241292369/370440*ep^2 +134457514968671/155584800*ep^3+59632498889714041/65345616000*ep^4 +15336180514258890431/27445158720000*ep^5; fill mncT20(5,10) = -3815020/63-12100*ep^-1+672043865/10584*ep+7209932656511/8890560 *ep^2+14657572049878313/7468070400*ep^3+15493420641913630511/ 6273179136000*ep^4+9940372453388210088377/5269470474240000*ep^5; fill mncT20(6,1) = -1/15+37/450*ep+13681/13500*ep^2-531047/405000*ep^3+10925689/ 12150000*ep^4-58905143/364500000*ep^5; fill mncT20(6,2) = -22/45-4/3*ep^-1+14917/675*ep+145621/20250*ep^2-7176827/607500 *ep^3+178762549/18225000*ep^4-3758759963/546750000*ep^5; fill mncT20(6,3) = -40/3-20*ep^-1+14728/45*ep+140792/675*ep^2-1143752/10125*ep^3 +11067512/151875*ep^4-126680072/2278125*ep^5; fill mncT20(6,4) = -530/3-140*ep^-1+33557/15*ep+423607/150*ep^2+76397/1500*ep^3 +536287/15000*ep^4-11154523/150000*ep^5; fill mncT20(6,5) = -1225-1960/3*ep^-1+893521/90*ep+52848593/2700*ep^2+682276609/ 81000*ep^3+991720817/2430000*ep^4-19991371679/72900000*ep^5; fill mncT20(6,6) = -5782-2352*ep^-1+1655967/50*ep+91233989/1000*ep^2+1443847463/ 20000*ep^3+8173903421/400000*ep^4+1458637007/8000000*ep^5; fill mncT20(6,7) = -105938/5-7056*ep^-1+13461241/150*ep+196444423/600*ep^2+ 22085957393/60000*ep^3+222489175979/1200000*ep^4+911520869801/ 24000000*ep^5; fill mncT20(6,8) = -194530/3-18480*ep^-1+26018777/126*ep+36860355869/37800*ep^2+ 3184378641517/2268000*ep^3+135220583203421/136080000*ep^4+ 2985861528034573/8164800000*ep^5; fill mncT20(6,9) = -1213465/7-43560*ep^-1+60822598/147*ep+194807431393/77175*ep^2 +71368977411709/16206750*ep^3+13453624222021897/3403417500*ep^4+ 1454776080000749701/714717675000*ep^5; fill mncT20(6,10) = -8757815/21-94380*ep^-1+285953499/392*ep+86753994798313/14817600 *ep^2+148907578338425071/12446784000*ep^3+134583634360736251897/ 10455298560000*ep^4+73478148911479794387679/8782450790400000*ep^5; fill mncT20(7,1) = -2/45+17/675*ep+14621/20250*ep^2-266827/607500*ep^3-2337451/ 18225000*ep^4+292240037/546750000*ep^5; fill mncT20(7,2) = -44/45-4/3*ep^-1+14924/675*ep+154756/10125*ep^2-1870036/151875 *ep^3+13127716/2278125*ep^4-60303796/34171875*ep^5; fill mncT20(7,3) = -116/5-28*ep^-1+34276/75*ep+412444/1125*ep^2-2379164/16875* ep^3+17847484/253125*ep^4-185697404/3796875*ep^5; fill mncT20(7,4) = -1666/5-784/3*ep^-1+938503/225*ep+35955539/6750*ep^2+35076907/ 202500*ep^3+360336491/6075000*ep^4-26477428517/182250000*ep^5; fill mncT20(7,5) = -13916/5-1568*ep^-1+1802036/75*ep+50033084/1125*ep^2+287204996/ 16875*ep^3+221622524/253125*ep^4-2634047644/3796875*ep^5; fill mncT20(7,6) = -80066/5-7056*ep^-1+5093047/50*ep+760464367/3000*ep^2+ 31791539167/180000*ep^3+469636512367/10800000*ep^4-549658402433/ 648000000*ep^5; fill mncT20(7,7) = -1064182/15-25872*ep^-1+17267879/50*ep+9947129741/9000*ep^2+ 589989515933/540000*ep^3+15486776900429/32400000*ep^4+ 153970495460477/1944000000*ep^5; fill mncT20(7,8) = -3889732/15-81312*ep^-1+1550451076/1575*ep+93444165512/23625* ep^2+1773570582514/354375*ep^3+16430603243333/5315625*ep^4+ 154326257660627/159468750*ep^5; fill mncT20(7,9) = -28622858/35-226512*ep^-1+8945694844/3675*ep+4693005624746/ 385875*ep^2+754866033770809/40516875*ep^3+124746450400539397/ 8508543750*ep^4+11669819549415577201/1786794187500*ep^5; fill mncT20(7,10) = -103252721/45-572572*ep^-1+201215003399/37800*ep+ 1052670739682273/31752000*ep^2+1584389477988125111/26671680000*ep^3+ 1260115013745961428977/22404211200000*ep^4+600882741173995469811239/ 18819537408000000*ep^5; fill mncT20(8,1) = -2/63+11/6615*ep+735761/1389150*ep^2-15307249/291721500*ep^3- 20069423959/61261515000*ep^4+5172990804431/12864918150000*ep^5; fill mncT20(8,2) = -146/105-4/3*ep^-1+241897/11025*ep+51352127/2315250*ep^2- 4773167543/486202500*ep^3+121383985487/102102525000*ep^4+ 32097376872217/21441530250000*ep^5; fill mncT20(8,3) = -554/15-112/3*ep^-1+955123/1575*ep+194381393/330750*ep^2- 9944115137/69457500*ep^3+720242324633/14586075000*ep^4- 106786845347297/3063075750000*ep^5; fill mncT20(8,4) = -8888/15-448*ep^-1+1247644/175*ep+58053334/6125*ep^2+135651199/ 214375*ep^3+298200803/15006250*ep^4-231974825609/1050437500*ep^5; fill mncT20(8,5) = -17476/3-3360*ep^-1+5423872/105*ep+1026210586/11025*ep^2+ 39090448813/1157625*ep^3+462912373583/243101250*ep^4-78990538402847/ 51051262500*ep^5; fill mncT20(8,6) = -119554/3-18480*ep^-1+56805143/210*ep+11147568661/17640*ep^2+ 597336826967/1481760*ep^3+11261910805309/124467840*ep^4- 7996110736781/2091059712*ep^5; fill mncT20(8,7) = -3134692/15-81312*ep^-1+586429352/525*ep+180345975898/55125*ep^2 +16981787031817/5788125*ep^3+1400937773650811/1215506250*ep^4+ 40384500100087813/255256312500*ep^5; fill mncT20(8,8) = -94105352/105-302016*ep^-1+42304774636/11025*ep+15966836211554/ 1157625*ep^2+1917150465063091/121550625*ep^3+222944364852849553/ 25525631250*ep^4+12784984115109386899/5360382562500*ep^5; fill mncT20(8,9) = -344915714/105-981552*ep^-1+125188224652/11025*ep+57327608405708/ 1157625*ep^2+169691073788368/2480625*ep^3+616775730790589453/ 12762815625*ep^4+25521414100086000862/1340095640625*ep^5; fill mncT20(8,10) = -95522999/9-2862860*ep^-1+223988205851/7560*ep+198479962759177/ 1270080*ep^2+53777209618419011/213373440*ep^3+7693053960436534657/ 35846737920*ep^4+653914768896638272619/6022251970560*ep^5; fill mncT20(9,1) = -1/42-17/1960*ep+988423/2469600*ep^2+130080361/1037232000*ep^3 -132124778273/435637440000*ep^4+39081330520489/182967724800000*ep^5; fill mncT20(9,2) = -367/210-4/3*ep^-1+1911101/88200*ep+1042101407/37044000*ep^2- 86110890751/15558480000*ep^3-17042462394457/6534561600000*ep^4+ 7907446988034401/2744515872000000*ep^5; fill mncT20(9,3) = -1922/35-48*ep^-1+1897591/2450*ep+301069579/343000*ep^2- 4948522049/48020000*ep^3+80071131619/6722800000*ep^4-18482489761289/ 941192000000*ep^5; fill mncT20(9,4) = -6998/7-720*ep^-1+16770571/1470*ep+3293023879/205800*ep^2+ 51986235451/28812000*ep^3-478953480881/4033680000*ep^4- 174098181323789/564715200000*ep^5; fill mncT20(9,5) = -239485/21-6600*ep^-1+59678963/588*ep+8999125993/49392*ep^2+ 273368291219/4148928*ep^3+1420652321425/348509952*ep^4- 91124037255205/29274835968*ep^5; fill mncT20(9,6) = -637747/7-43560*ep^-1+629646273/980*ep+119042517491/82320*ep^2 +6030757537057/6914880*ep^3+107478921385259/580849920*ep^4- 105005045961691/9758278656*ep^5; fill mncT20(9,7) = -19467998/35-226512*ep^-1+23281533403/7350*ep+2995897232957/ 343000*ep^2+349928274306329/48020000*ep^3+17758196394663413/ 6722800000*ep^4+289303778474762561/941192000000*ep^5; fill mncT20(9,8) = -41386202/15-981552*ep^-1+283630630979/22050*ep+395546421637189/ 9261000*ep^2+175501506642798899/3889620000*ep^3+37418073001064553109/ 1633640400000*ep^4+3822672350863462613219/686128968000000*ep^5; fill mncT20(9,9) = -162519643/14-3680820*ep^-1+262595305811/5880*ep+87238249360337/ 493920*ep^2+9315219944358107/41489280*ep^3+101175453391617973/ 697019904*ep^4+15089495884566992579/292748359680*ep^5; fill mncT20(9,10) = -1794820885/42-12269400*ep^-1+239935332475/1764*ep+ 629668364238581/987840*ep^2+156590334768924257/165957120*ep^3+ 20499084628777351687/27880796160*ep^4+315771825523270174417/ 936794750976*ep^5; fill mncT20(10,1) = -1/54-899/68040*ep+26608661/85730400*ep^2+22301027281/ 108020304000*ep^3-30764322105499/136105583040000*ep^4+ 13987748932332121/171493034630400000*ep^5; fill mncT20(10,2) = -1949/945-4/3*ep^-1+25400111/1190700*ep+50002245931/1500282000* ep^2-307591759849/1890355320000*ep^3-12413937459889229/ 2381847703200000*ep^4+8738028774226905791/3001128106032000000*ep^5; fill mncT20(10,3) = -1627/21-60*ep^-1+25410289/26460*ep+41398021589/33339600*ep^2- 190296782231/42007896000*ep^3-1878209166342451/52929948960000*ep^4- 604812037282539071/66691735689600000*ep^5; fill mncT20(10,4) = -101455/63-1100*ep^-1+275221241/15876*ep+103162952009/4000752* ep^2+4293929585705/1008189504*ep^3-89566560900055/254063755008*ep^4 -27959241939151255/64024066262016*ep^5; fill mncT20(10,5) = -1329680/63-12100*ep^-1+737272054/3969*ep+84298599661/250047* ep^2+3965429329817/31505922*ep^3+34545751893985/3969746172*ep^4- 2913598743696175/500188017672*ep^5; fill mncT20(10,6) = -4079713/21-94380*ep^-1+36973908163/26460*ep+20570227539667/ 6667920*ep^2+3033514159050163/1680315840*ep^3+157783074769647667/ 423439591680*ep^4-528901375770096745/21341355420672*ep^5; fill mncT20(10,7) = -61332271/45-572572*ep^-1+459094453861/56700*ep+1531948229048633/ 71442000*ep^2+1529532469520022109/90016920000*ep^3+ 659328793858498496657/113421319200000*ep^4+84193338407945687943061/ 142910862192000000*ep^5; fill mncT20(10,8) = -69552769/9-2862860*ep^-1+434310052219/11340*ep+7004672898859/ 58320*ep^2+350749945127471/2939328*ep^3+5985907366175321/105815808* ep^4+33984285466122253/2720977920*ep^5; fill mncT20(10,9) = -1551477785/42-12269400*ep^-1+1627394154415/10584*ep+ 7543699807403531/13335840*ep^2+2260333080623120459/3360631680*ep^3+ 68488673475056100559/169375836672*ep^4+5610227992150949456143/ 42682710841344*ep^5; fill mncT20(10,10) = -29016110695/189-139053200/3*ep^-1+51295527403105/95256*ep+ 554800602494906533/240045120*ep^2+385811958544034384741/120982740480* ep^3+140661160501409433770533/60975301201920*ep^4+ 5972748132827112581530465/6146310361153536*ep^5; fill mncT11(-6,-6) = 1/25971865920*ep+54143/374368864117248*ep^2+1461092694913/ 3372689096832287232000*ep^3+1521012295134409487/ 1215382242934483026923520000*ep^4+144702912918207566541491/ 39815922278533663962014515200000*ep^5; fill mncT11(-6,-5) = 1/5194373184*ep+191897/267406331512320*ep^2+1446714588313/ 674537819366457446400*ep^3+215051810762400977/ 34725206940985229340672000*ep^4+143219674905396635366459/ 7963184455706732792402903040000*ep^5; fill mncT11(-6,-4) = 1/856215360*ep+1349351/308545767129600*ep^2+291188566637/ 22237510528564531200*ep^3+1515740361197464559/ 40067546470367572316160000*ep^4+144212179045019487639827/ 1312612822369241669077401600000*ep^5; fill mncT11(-6,-3) = 1/109771200*ep+21271/608571532800*ep^2+1781801717/16869602889216000* ep^3+715217051621027/2338126960445337600000*ep^4+5235259582269107603/ 5892079940322250752000000*ep^5; fill mncT11(-6,-2) = 1/9979200*ep+22531/55324684800*ep^2+1933272617/1533600262656000*ep^3 +781840739076527/212556996404121600000*ep^4+63017127138305883733/ 5892079940322250752000000*ep^5; fill mncT11(-6,-1) = 1/544320*ep+11509/1371686400*ep^2+19034489/691329945600*ep^3+ 716347562557/8710757314560000*ep^4+5281738326720781/ 21951108432691200000*ep^5; fill mncT11(-6,0) = 1/12096*ep+14701/30481920*ep^2+142493173/76814438400*ep^3+ 1175022146197/193572384768000*ep^4+362229416590381/19512096384614400* ep^5; fill mncT11(-6,1) = -1/168-491/11760*ep-2809459/14817600*ep^2-164251523/230496000* ep^3-9394096633/3872332800*ep^4-953372760821057/121978483200000*ep^5 ; fill mncT11(-6,2) = -89/105-1/6*ep^-1-1805329/529200*ep-97649753/8232000*ep^2- 2971437071/76832000*ep^3-528741075088307/4356374400000*ep^4- 683016375960851521/1829677248000000*ep^5; fill mncT11(-6,3) = -53/10-7/2*ep^-1-132547/3600*ep-5766373/72000*ep^2-94663519/ 288000*ep^3-73265935007/86400000*ep^4-14991092330803/5184000000*ep^5 ; fill mncT11(-6,4) = 19-35/2*ep^-1-127459/720*ep+746551/14400*ep^2-117119053/96000* ep^3-12251704507/17280000*ep^4-2900897885237/345600000*ep^5; fill mncT11(-6,5) = 1865/18-175/6*ep^-1-65051/144*ep+552703/576*ep^2-21762941/6912* ep^3+393823703/82944*ep^4-17125296709/995328*ep^5; fill mncT11(-6,6) = 1313/12-35/2*ep^-1-117053/240*ep+7250177/4800*ep^2-1244217599/ 288000*ep^3+174112515313/17280000*ep^4-25434137985631/1036800000* ep^5; fill mncT11(-6,7) = 2027/60-7/2*ep^-1-74183/400*ep+5800583/8000*ep^2-222102029/96000 *ep^3+546926396573/86400000*ep^4-81787562480723/5184000000*ep^5; fill mncT11(-6,8) = 353/140-1/6*ep^-1-373727/19600*ep+800940667/8232000*ep^2- 29289691863/76832000*ep^3+5385992171933273/4356374400000*ep^4- 709521618026979929/203297472000000*ep^5; fill mncT11(-6,9) = 1/112-5471/31360*ep+14340133/8780800*ep^2-24494628927/2458624000* ep^3+6237727760217/137682944000*ep^4-864838163864034797/ 5204415283200000*ep^5; fill mncT11(-6,10) = 1/2016*ep-42589/5080320*ep^2+827883523/12802406400*ep^3- 9821121950233/32262064128000*ep^4+15684812553506807/16260080320512000* ep^5; fill mncT11(-5,-6) = 1/5194373184*ep+191897/267406331512320*ep^2+1446714588313/ 674537819366457446400*ep^3+215051810762400977/ 34725206940985229340672000*ep^4+143219674905396635366459/ 7963184455706732792402903040000*ep^5; fill mncT11(-5,-5) = 1/1198701504*ep+188597/61709153425920*ep^2+1414297457413/ 155662573699951718400*ep^3+209999513637846077/ 8013509294073514463232000*ep^4+139865314491088852726559/ 1837657951316938336708362240000*ep^5; fill mncT11(-5,-4) = 1/230519520*ep+14411/912857299200*ep^2+1659590243/35426166067353600* ep^3+94747430653571/701438088133601280000*ep^4+4854449588337788357/ 12373367874676726579200000*ep^5; fill mncT11(-5,-3) = 1/34927200*ep+2917/27662342400*ep^2+1687155977/5367600919296000*ep^3 +96432007853561/106278498202060800000*ep^4+54350675476108434613/ 20622279791127877632000000*ep^5; fill mncT11(-5,-2) = 1/3810240*ep+1387/1371686400*ep^2+14843729/4839309619200*ep^3+ 77510868451/8710757314560000*ep^4+3973230536370181/ 153657759028838400000*ep^5; fill mncT11(-5,-1) = 1/254016*ep+1543/91445760*ep^2+86761273/1613103206400*ep^3+ 92265059071/580717154304000*ep^4+189942040247089/409754024076902400* ep^5; fill mncT11(-5,0) = 1/7056*ep+41/52920*ep^2+198451/69148800*ep^3+38167517/4148928000* ep^4+13589568749/487913932800*ep^5; fill mncT11(-5,1) = -1/126-1373/26460*ep-278951/1234800*ep^2-428917169/518616000* ep^3-24133350683/8712748800*ep^4-808252068538657/91483862400000*ep^5 ; fill mncT11(-5,2) = -67/90-1/6*ep^-1-10367/3600*ep-699593/72000*ep^2-26955169/ 864000*ep^3-25135874401/259200000*ep^4-4614144435149/15552000000* ep^5; fill mncT11(-5,3) = -7/4-5/2*ep^-1-16687/720*ep-515657/14400*ep^2-54125287/288000* ep^3-7162742651/17280000*ep^4-1628632766623/1036800000*ep^5; fill mncT11(-5,4) = 655/36-25/3*ep^-1-3409/36*ep+3161/27*ep^2-49598/81*ep^3+ 1147271/3888*ep^4-2667887/729*ep^5; fill mncT11(-5,5) = 85/2-25/3*ep^-1-12743/72*ep+414557/864*ep^2-14012279/10368*ep^3 +347829317/124416*ep^4-10748954831/1492992*ep^5; fill mncT11(-5,6) = 259/12-5/2*ep^-1-26179/240*ep+5674733/14400*ep^2-1023344371/ 864000*ep^3+158892462077/51840000*ep^4-22936759409299/3110400000* ep^5; fill mncT11(-5,7) = 71/30-1/6*ep^-1-60467/3600*ep+17415031/216000*ep^2-773765929/ 2592000*ep^3+715830606667/777600000*ep^4-116118457957877/46656000000 *ep^5; fill mncT11(-5,8) = 1/84-1961/8820*ep+14678609/7408800*ep^2-35755774219/3111696000* ep^3+13000149370291/261382464000*ep^4-95609558172939007/ 548903174400000*ep^5; fill mncT11(-5,9) = 1/1176*ep-13513/987840*ep^2+11790271/118540800*ep^3-304304606929/ 697019904000*ep^4+148251273664517/117099343872000*ep^5; fill mncT11(-5,10) = 1/42336*ep-27589/106686720*ep^2+34849789/38407219200*ep^3+ 317044794767/677503346688000*ep^4-5172935456652193/341461686730752000* ep^5; fill mncT11(-4,-6) = 1/856215360*ep+1349351/308545767129600*ep^2+291188566637/ 22237510528564531200*ep^3+1515740361197464559/ 40067546470367572316160000*ep^4+144212179045019487639827/ 1312612822369241669077401600000*ep^5; fill mncT11(-4,-5) = 1/230519520*ep+14411/912857299200*ep^2+1659590243/35426166067353600* ep^3+94747430653571/701438088133601280000*ep^4+4854449588337788357/ 12373367874676726579200000*ep^5; fill mncT11(-4,-4) = 1/52390800*ep+14123/207467568000*ep^2+8083406479/40257006894720000* ep^3+92187701272739/159417747303091200000*ep^4+51962531752521149719/ 30933419686691816448000000*ep^5; fill mncT11(-4,-3) = 1/9525600*ep+1279/3429216000*ep^2+66497617/60491370240000*ep^3+ 2757573631/871075731456000*ep^4+3532802670886561/384144397572096000000 *ep^5; fill mncT11(-4,-2) = 1/1270080*ep+263/91445760*ep^2+69071293/8065516032000*ep^3+ 71796516667/2903585771520000*ep^4+3679611959381101/ 51219253009612800000*ep^5; fill mncT11(-4,-1) = 1/105840*ep+1/26460*ep^2+364073/3111696000*ep^3+63883327/ 186701760000*ep^4+546850483751/548903174400000*ep^5; fill mncT11(-4,0) = 1/3780*ep+71/52920*ep^2+529973/111132000*ep^3+698334139/ 46675440000*ep^4+879324400001/19603684800000*ep^5; fill mncT11(-4,1) = -1/90-1/15*ep-14927/54000*ep^2-3184063/3240000*ep^3-628561811/ 194400000*ep^4-23803415627/2332800000*ep^5; fill mncT11(-4,2) = -28/45-1/6*ep^-1-2789/1200*ep-1633991/216000*ep^2-310028443/ 12960000*ep^3-57229724639/777600000*ep^4-10450629954547/46656000000* ep^5; fill mncT11(-4,3) = 19/36-5/3*ep^-1-57/4*ep-223/27*ep^2-8182/81*ep^3-582373/3888* ep^4-2237203/2916*ep^5; fill mncT11(-4,4) = 73/6-10/3*ep^-1-883/18*ep+926/9*ep^2-25784/81*ep^3+103267/216* ep^4-4865789/2916*ep^5; fill mncT11(-4,5) = 37/3-5/3*ep^-1-449/8*ep+157679/864*ep^2-1769167/3456*ep^3+ 153246119/124416*ep^4-476712269/165888*ep^5; fill mncT11(-4,6) = 131/60-1/6*ep^-1-17149/1200*ep+13715489/216000*ep^2-946662581/ 4320000*ep^3+494298681041/777600000*ep^4-8467731288263/5184000000* ep^5; fill mncT11(-4,7) = 1/60-53/180*ep+266561/108000*ep^2-87124181/6480000*ep^3+ 21293362823/388800000*ep^4-6769202801/37324800*ep^5; fill mncT11(-4,8) = 1/630*ep-53/2205*ep^2+9018689/55566000*ep^3-5067714581/7779240000* ep^4+16436907354443/9801842400000*ep^5; fill mncT11(-4,9) = 1/17640*ep-563/987840*ep^2+2929291/1778112000*ep^3+9789209929/ 3485099520000*ep^4-303031735346099/8782450790400000*ep^5; fill mncT11(-4,10) = 1/211680*ep-3737/106686720*ep^2+3220069/192036096000*ep^3+ 1849098148199/3387516733440000*ep^4-17893832061607469/ 8536542168268800000*ep^5; fill mncT11(-3,-6) = 1/109771200*ep+21271/608571532800*ep^2+1781801717/16869602889216000* ep^3+715217051621027/2338126960445337600000*ep^4+5235259582269107603/ 5892079940322250752000000*ep^5; fill mncT11(-3,-5) = 1/34927200*ep+2917/27662342400*ep^2+1687155977/5367600919296000*ep^3 +96432007853561/106278498202060800000*ep^4+54350675476108434613/ 20622279791127877632000000*ep^5; fill mncT11(-3,-4) = 1/9525600*ep+1279/3429216000*ep^2+66497617/60491370240000*ep^3+ 2757573631/871075731456000*ep^4+3532802670886561/384144397572096000000 *ep^5; fill mncT11(-3,-3) = 1/2116800*ep+1249/762048000*ep^2+64485187/13442526720000*ep^3+ 13352658713/967861923840000*ep^4+3421865471751211/85365421682688000000 *ep^5; fill mncT11(-3,-2) = 1/352800*ep+209/21168000*ep^2+600599/20744640000*ep^3+829559/ 9957427200*ep^4+885842668847/3659354496000000*ep^5; fill mncT11(-3,-1) = 1/37800*ep+521/5292000*ep^2+658699/2222640000*ep^3+32087681/ 37340352000*ep^4+979800893347/392073696000000*ep^5; fill mncT11(-3,0) = 1/1800*ep+31/12000*ep^2+18961/2160000*ep^3+698329/25920000*ep^4+ 622296697/7776000000*ep^5; fill mncT11(-3,1) = -1/60-323/3600*ep-8431/24000*ep^2-5219689/4320000*ep^3- 1010598197/259200000*ep^4-189197104081/15552000000*ep^5; fill mncT11(-3,2) = -17/36-1/6*ep^-1-7/4*ep-293/54*ep^2-10979/648*ep^3-200341/ 3888*ep^4-3640769/23328*ep^5; fill mncT11(-3,3) = 5/3-ep^-1-9*ep+58/9*ep^2-5849/108*ep^3-3065/324*ep^4-1329407/ 3888*ep^5; fill mncT11(-3,4) = 35/6-ep^-1-139/6*ep+578/9*ep^2-18179/108*ep^3+233215/648*ep^4 -3293897/3888*ep^5; fill mncT11(-3,5) = 47/24-1/6*ep^-1-1103/96*ep+159143/3456*ep^2-2004967/13824*ep^3 +193964447/497664*ep^4-625422901/663552*ep^5; fill mncT11(-3,6) = 1/40-329/800*ep+50941/16000*ep^2-46047001/2880000*ep^3+ 3470853629/57600000*ep^4-1929124683769/10368000000*ep^5; fill mncT11(-3,7) = 1/300*ep-841/18000*ep^2+309163/1080000*ep^3-13185257/12960000*ep^4 +8539596691/3888000000*ep^5; fill mncT11(-3,8) = 1/6300*ep-1259/882000*ep^2+3355417/1111320000*ep^3+367419121/ 31116960000*ep^4-16828556763959/196036848000000*ep^5; fill mncT11(-3,9) = 1/58800*ep-1793/16464000*ep^2-338951/5927040000*ep^3+1515706901/ 774466560000*ep^4-162680266832969/29274835968000000*ep^5; fill mncT11(-3,10) = 1/352800*ep-11797/889056000*ep^2-12737699/320060160000*ep^3+ 342043914019/1129172244480000*ep^4-5184963405893189/ 14227570280448000000*ep^5; fill mncT11(-2,-6) = 1/9979200*ep+22531/55324684800*ep^2+1933272617/1533600262656000*ep^3 +781840739076527/212556996404121600000*ep^4+63017127138305883733/ 5892079940322250752000000*ep^5; fill mncT11(-2,-5) = 1/3810240*ep+1387/1371686400*ep^2+14843729/4839309619200*ep^3+ 77510868451/8710757314560000*ep^4+3973230536370181/ 153657759028838400000*ep^5; fill mncT11(-2,-4) = 1/1270080*ep+263/91445760*ep^2+69071293/8065516032000*ep^3+ 71796516667/2903585771520000*ep^4+3679611959381101/ 51219253009612800000*ep^5; fill mncT11(-2,-3) = 1/352800*ep+209/21168000*ep^2+600599/20744640000*ep^3+829559/ 9957427200*ep^4+885842668847/3659354496000000*ep^5; fill mncT11(-2,-2) = 1/75600*ep+1423/31752000*ep^2+1737677/13335840000*ep^3+419308739/ 1120210560000*ep^4+2559077496341/2352442176000000*ep^5; fill mncT11(-2,-1) = 1/10800*ep+209/648000*ep^2+36853/38880000*ep^3+10193/3732480*ep^4 +1111096141/139968000000*ep^5; fill mncT11(-2,0) = 1/720*ep+253/43200*ep^2+49169/2592000*ep^3+8860237/155520000*ep^4 +1566217001/9331200000*ep^5; fill mncT11(-2,1) = -1/36-7/54*ep-307/648*ep^2-6101/3888*ep^3-115633/23328*ep^4- 2138849/139968*ep^5; fill mncT11(-2,2) = -5/18-1/6*ep^-1-127/108*ep-2159/648*ep^2-40519/3888*ep^3- 727775/23328*ep^4-13187287/139968*ep^5; fill mncT11(-2,3) = 11/6-1/2*ep^-1-25/4*ep+97/8*ep^2-545/16*ep^3+1537/32*ep^4- 10625/64*ep^5; fill mncT11(-2,4) = 5/3-1/6*ep^-1-299/36*ep+6187/216*ep^2-103013/1296*ep^3+1504375/ 7776*ep^4-20294069/46656*ep^5; fill mncT11(-2,5) = 1/24-179/288*ep+14881/3456*ep^2-800819/41472*ep^3+32595961/ 497664*ep^4-1102859819/5971968*ep^5; fill mncT11(-2,6) = 1/120*ep-757/7200*ep^2+242359/432000*ep^3-43044433/25920000*ep^4 +4074665071/1555200000*ep^5; fill mncT11(-2,7) = 1/1800*ep-461/108000*ep^2+3287/720000*ep^3+3937531/77760000*ep^4 -5571523609/23328000000*ep^5; fill mncT11(-2,8) = 1/12600*ep-2167/5292000*ep^2-1838653/2222640000*ep^3+1565353577/ 186701760000*ep^4-1969039700503/130691232000000*ep^5; fill mncT11(-2,9) = 1/58800*ep-2929/49392000*ep^2-210289/658560000*ep^3+10265988779/ 6970199040000*ep^4-7503545288719/29274835968000000*ep^5; fill mncT11(-2,10) = 1/211680*ep-1133/106686720*ep^2-20839151/192036096000*ep^3+ 1005421668539/3387516733440000*ep^4+3636684674926231/ 8536542168268800000*ep^5; fill mncT11(-1,-6) = 1/544320*ep+11509/1371686400*ep^2+19034489/691329945600*ep^3+ 716347562557/8710757314560000*ep^4+5281738326720781/ 21951108432691200000*ep^5; fill mncT11(-1,-5) = 1/254016*ep+1543/91445760*ep^2+86761273/1613103206400*ep^3+ 92265059071/580717154304000*ep^4+189942040247089/409754024076902400* ep^5; fill mncT11(-1,-4) = 1/105840*ep+1/26460*ep^2+364073/3111696000*ep^3+63883327/ 186701760000*ep^4+546850483751/548903174400000*ep^5; fill mncT11(-1,-3) = 1/37800*ep+521/5292000*ep^2+658699/2222640000*ep^3+32087681/ 37340352000*ep^4+979800893347/392073696000000*ep^5; fill mncT11(-1,-2) = 1/10800*ep+209/648000*ep^2+36853/38880000*ep^3+10193/3732480*ep^4 +1111096141/139968000000*ep^5; fill mncT11(-1,-1) = 1/2160*ep+203/129600*ep^2+35419/7776000*ep^3+6106487/466560000* ep^4+1064948251/27993600000*ep^5; fill mncT11(-1,0) = 1/216*ep+23/1296*ep^2+427/7776*ep^3+7547/46656*ep^4+132547/ 279936*ep^5; fill mncT11(-1,1) = -1/18-23/108*ep-463/648*ep^2-8807/3888*ep^3-163039/23328*ep^4 -2977367/139968*ep^5; fill mncT11(-1,2) = -1/6*ep^-1-2/3*ep-4/3*ep^2-14/3*ep^3-40/3*ep^4-122/3*ep^5; fill mncT11(-1,3) = 5/4-1/6*ep^-1-37/8*ep+197/16*ep^2-901/32*ep^3+3845/64*ep^4- 15877/128*ep^5; fill mncT11(-1,4) = 1/12-77/72*ep+2683/432*ep^2-60473/2592*ep^3+1053499/15552*ep^4 -15759953/93312*ep^5; fill mncT11(-1,5) = 1/36*ep-43/144*ep^2+6583/5184*ep^3-55583/20736*ep^4+1116007/ 746496*ep^5; fill mncT11(-1,6) = 1/360*ep-119/7200*ep^2-12041/1296000*ep^3+6722789/25920000*ep^4- 3468808529/4665600000*ep^5; fill mncT11(-1,7) = 1/1800*ep-211/108000*ep^2-62167/6480000*ep^3+3518981/77760000*ep^4 -169501453/7776000000*ep^5; fill mncT11(-1,8) = 1/6300*ep-401/1323000*ep^2-2005079/555660000*ep^3+391786789/ 46675440000*ep^4+154028720287/10890936000000*ep^5; fill mncT11(-1,9) = 1/17640*ep-121/2963520*ep^2-2512789/1778112000*ep^3+15188895707/ 10455298560000*ep^4+2773974518263/325275955200000*ep^5; fill mncT11(-1,10) = 1/42336*ep+551/106686720*ep^2-23198471/38407219200*ep^3+ 34557361427/677503346688000*ep^4+1401049384583171/341461686730752000* ep^5; fill mncT11(0,-6) = 1/12096*ep+14701/30481920*ep^2+142493173/76814438400*ep^3+ 1175022146197/193572384768000*ep^4+362229416590381/19512096384614400* ep^5; fill mncT11(0,-5) = 1/7056*ep+41/52920*ep^2+198451/69148800*ep^3+38167517/4148928000* ep^4+13589568749/487913932800*ep^5; fill mncT11(0,-4) = 1/3780*ep+71/52920*ep^2+529973/111132000*ep^3+698334139/ 46675440000*ep^4+879324400001/19603684800000*ep^5; fill mncT11(0,-3) = 1/1800*ep+31/12000*ep^2+18961/2160000*ep^3+698329/25920000*ep^4+ 622296697/7776000000*ep^5; fill mncT11(0,-2) = 1/720*ep+253/43200*ep^2+49169/2592000*ep^3+8860237/155520000*ep^4 +1566217001/9331200000*ep^5; fill mncT11(0,-1) = 1/216*ep+23/1296*ep^2+427/7776*ep^3+7547/46656*ep^4+132547/ 279936*ep^5; fill mncT11(0,0) = 1/36*ep+23/216*ep^2+427/1296*ep^3+7547/7776*ep^4+132547/46656* ep^5; fill mncT11(0,1) = -1/6-1/2*ep-3/2*ep^2-9/2*ep^3-27/2*ep^4-81/2*ep^5; fill mncT11(0,2) = 1/2-1/6*ep^-1-1/2*ep+1/2*ep^2-1/2*ep^3+1/2*ep^4-1/2*ep^5; fill mncT11(0,3) = 1/4-19/8*ep+151/16*ep^2-799/32*ep^3+3631/64*ep^4-15439/128* ep^5; fill mncT11(0,4) = 1/6*ep-47/36*ep^2+697/216*ep^3-2123/1296*ep^4-85583/7776*ep^5; fill mncT11(0,5) = 1/36*ep-13/144*ep^2-2147/5184*ep^3+36787/20736*ep^4-1243883/ 746496*ep^5; fill mncT11(0,6) = 1/120*ep-19/2400*ep^2-79541/432000*ep^3+676763/2880000*ep^4+ 1092053971/1555200000*ep^5; fill mncT11(0,7) = 1/300*ep+17/9000*ep^2-14077/180000*ep^3-119341/6480000*ep^4+ 813955783/1944000000*ep^5; fill mncT11(0,8) = 1/630*ep+71/26460*ep^2-2011631/55566000*ep^3-1183313023/ 23337720000*ep^4+68567159309/363031200000*ep^5; fill mncT11(0,9) = 1/1176*ep+2167/987840*ep^2-2147569/118540800*ep^3-30974065249/ 697019904000*ep^4+1001999162669/13011038208000*ep^5; fill mncT11(0,10) = 1/2016*ep+1193/725760*ep^2-123315497/12802406400*ep^3- 1087179659173/32262064128000*ep^4+60277238568413/2322868617216000*ep^5 ; fill mncT11(1,-6) = -1/168-491/11760*ep-2809459/14817600*ep^2-164251523/230496000* ep^3-9394096633/3872332800*ep^4-953372760821057/121978483200000*ep^5 ; fill mncT11(1,-5) = -1/126-1373/26460*ep-278951/1234800*ep^2-428917169/518616000* ep^3-24133350683/8712748800*ep^4-808252068538657/91483862400000*ep^5 ; fill mncT11(1,-4) = -1/90-1/15*ep-14927/54000*ep^2-3184063/3240000*ep^3-628561811/ 194400000*ep^4-23803415627/2332800000*ep^5; fill mncT11(1,-3) = -1/60-323/3600*ep-8431/24000*ep^2-5219689/4320000*ep^3- 1010598197/259200000*ep^4-189197104081/15552000000*ep^5; fill mncT11(1,-2) = -1/36-7/54*ep-307/648*ep^2-6101/3888*ep^3-115633/23328*ep^4- 2138849/139968*ep^5; fill mncT11(1,-1) = -1/18-23/108*ep-463/648*ep^2-8807/3888*ep^3-163039/23328*ep^4 -2977367/139968*ep^5; fill mncT11(1,0) = -1/6-1/2*ep-3/2*ep^2-9/2*ep^3-27/2*ep^4-81/2*ep^5; fill mncT11(1,1) = 1/3*ep^-1; fill mncT11(1,2) = 5/2-1/2*ep^-1-5/2*ep+5/2*ep^2-5/2*ep^3+5/2*ep^4-5/2*ep^5; fill mncT11(1,3) = -1+9/2*ep-1/4*ep^2-111/8*ep^3+719/16*ep^4-3471/32*ep^5; fill mncT11(1,4) = -1/3+1/9*ep+331/54*ep^2-1391/324*ep^3-14147/1944*ep^4+345409/ 11664*ep^5; fill mncT11(1,5) = -1/6-7/24*ep+2759/864*ep^2+4931/1152*ep^3-1045681/124416*ep^4 +3278833/497664*ep^5; fill mncT11(1,6) = -1/10-47/150*ep+30253/18000*ep^2+5658839/1080000*ep^3- 104471693/64800000*ep^4-13141480309/3888000000*ep^5; fill mncT11(1,7) = -1/15-5/18*ep+8173/9000*ep^2+7556441/1620000*ep^3+241319777/ 97200000*ep^4-1397739257/388800000*ep^5; fill mncT11(1,8) = -1/21-524/2205*ep+902201/1852200*ep^2+3014463589/777924000*ep^3 +1208942969/268912000*ep^4-57410968341421/45741931200000*ep^5; fill mncT11(1,9) = -1/28-227/1120*ep+4829183/19756800*ep^2+17493523283/5531904000* ep^3+2131548126517/398297088000*ep^4+1653666696353377/ 1301103820800000*ep^5; fill mncT11(1,10) = -1/36-493/2835*ep+11263261/114307200*ep^2+741728374799/ 288054144000*ep^3+812764988352467/145179288576000*ep^4+ 6149677687096924787/1829259036057600000*ep^5; fill mncT11(2,-6) = -89/105-1/6*ep^-1-1805329/529200*ep-97649753/8232000*ep^2- 2971437071/76832000*ep^3-528741075088307/4356374400000*ep^4- 683016375960851521/1829677248000000*ep^5; fill mncT11(2,-5) = -67/90-1/6*ep^-1-10367/3600*ep-699593/72000*ep^2-26955169/ 864000*ep^3-25135874401/259200000*ep^4-4614144435149/15552000000* ep^5; fill mncT11(2,-4) = -28/45-1/6*ep^-1-2789/1200*ep-1633991/216000*ep^2-310028443/ 12960000*ep^3-57229724639/777600000*ep^4-10450629954547/46656000000* ep^5; fill mncT11(2,-3) = -17/36-1/6*ep^-1-7/4*ep-293/54*ep^2-10979/648*ep^3-200341/ 3888*ep^4-3640769/23328*ep^5; fill mncT11(2,-2) = -5/18-1/6*ep^-1-127/108*ep-2159/648*ep^2-40519/3888*ep^3- 727775/23328*ep^4-13187287/139968*ep^5; fill mncT11(2,-1) = -1/6*ep^-1-2/3*ep-4/3*ep^2-14/3*ep^3-40/3*ep^4-122/3*ep^5; fill mncT11(2,0) = 1/2-1/6*ep^-1-1/2*ep+1/2*ep^2-1/2*ep^3+1/2*ep^4-1/2*ep^5; fill mncT11(2,1) = 5/2-1/2*ep^-1-5/2*ep+5/2*ep^2-5/2*ep^3+5/2*ep^4-5/2*ep^5; fill mncT11(2,2) = 3-ep^-1+7*ep-17*ep^2+27*ep^3-37*ep^4+47*ep^5; fill mncT11(2,3) = -ep^-1+37/2*ep-27/4*ep^2-209/8*ep^3+1305/16*ep^4-5513/32* ep^5; fill mncT11(2,4) = -5/3-ep^-1+343/18*ep+2581/108*ep^2-30839/648*ep^3+175645/ 3888*ep^4-564887/23328*ep^5; fill mncT11(2,5) = -17/6-ep^-1+1249/72*ep+40177/864*ep^2-251579/10368*ep^3- 1938527/124416*ep^4+60671869/1492992*ep^5; fill mncT11(2,6) = -56/15-ep^-1+26869/1800*ep+6747947/108000*ep^2+99246511/ 6480000*ep^3-16902461257/388800000*ep^4+700982831959/23328000000* ep^5; fill mncT11(2,7) = -67/15-ep^-1+7363/600*ep+7963583/108000*ep^2+77642911/1296000* ep^3-4851581503/129600000*ep^4-72804350141/23328000000*ep^5; fill mncT11(2,8) = -178/35-ep^-1+843481/88200*ep+1007464943/12348000*ep^2+ 326316812099/3111696000*ep^3-3321224463607/726062400000*ep^4- 81840394319902889/2744515872000000*ep^5; fill mncT11(2,9) = -787/140-ep^-1+2427349/352800*ep+8586842269/98784000*ep^2+ 7377872489189/49787136000*ep^3+373227039620317/7744665600000*ep^4- 6457306438212806471/175649015808000000*ep^5; fill mncT11(2,10) = -3839/630-ep^-1+13517821/3175200*ep+722967654779/8001504000*ep^2 +762299414847911/4032758016000*ep^3+5863782749601411287/ 50812751001600000*ep^4-2410867506661744804829/128048132524032000000* ep^5; fill mncT11(3,-6) = -53/10-7/2*ep^-1-132547/3600*ep-5766373/72000*ep^2-94663519/ 288000*ep^3-73265935007/86400000*ep^4-14991092330803/5184000000*ep^5 ; fill mncT11(3,-5) = -7/4-5/2*ep^-1-16687/720*ep-515657/14400*ep^2-54125287/288000* ep^3-7162742651/17280000*ep^4-1628632766623/1036800000*ep^5; fill mncT11(3,-4) = 19/36-5/3*ep^-1-57/4*ep-223/27*ep^2-8182/81*ep^3-582373/3888* ep^4-2237203/2916*ep^5; fill mncT11(3,-3) = 5/3-ep^-1-9*ep+58/9*ep^2-5849/108*ep^3-3065/324*ep^4-1329407/ 3888*ep^5; fill mncT11(3,-2) = 11/6-1/2*ep^-1-25/4*ep+97/8*ep^2-545/16*ep^3+1537/32*ep^4- 10625/64*ep^5; fill mncT11(3,-1) = 5/4-1/6*ep^-1-37/8*ep+197/16*ep^2-901/32*ep^3+3845/64*ep^4- 15877/128*ep^5; fill mncT11(3,0) = 1/4-19/8*ep+151/16*ep^2-799/32*ep^3+3631/64*ep^4-15439/128* ep^5; fill mncT11(3,1) = -1+9/2*ep-1/4*ep^2-111/8*ep^3+719/16*ep^4-3471/32*ep^5; fill mncT11(3,2) = -ep^-1+37/2*ep-27/4*ep^2-209/8*ep^3+1305/16*ep^4-5513/32* ep^5; fill mncT11(3,3) = -3/2-3*ep^-1+225/4*ep+57/8*ep^2-1635/16*ep^3+6957/32*ep^4- 24375/64*ep^5; fill mncT11(3,4) = -15/2-6*ep^-1+449/4*ep+2363/24*ep^2-33247/144*ep^3+257735/ 864*ep^4-1975171/5184*ep^5; fill mncT11(3,5) = -58/3-10*ep^-1+6497/36*ep+126887/432*ep^2-1603513/5184*ep^3+ 13345907/62208*ep^4-160892713/746496*ep^5; fill mncT11(3,6) = -38-15*ep^-1+30613/120*ep+4364099/7200*ep^2-100543913/432000* ep^3-73359169/25920000*ep^4-101532208097/1555200000*ep^5; fill mncT11(3,7) = -643/10-21*ep^-1+198433/600*ep+37491071/36000*ep^2+40354283/ 432000*ep^3-31200286513/129600000*ep^4-456002246177/7776000000*ep^5; fill mncT11(3,8) = -989/10-28*ep^-1+2534177/6300*ep+1411806601/882000*ep^2+ 167103911539/222264000*ep^3-5874194518813/17287200000*ep^4- 44948630072541313/196036848000000*ep^5; fill mncT11(3,9) = -4983/35-36*ep^-1+4556749/9800*ep+18784846207/8232000*ep^2+ 2508753664829/1382976000*ep^3-667379229950441/5808499200000*ep^4- 2514512912366469071/4879139328000000*ep^5; fill mncT11(3,10) = -2733/14-45*ep^-1+12100511/23520*ep+36522506621/11854080*ep^2+ 499108024384793/149361408000*ep^3+238057627322242549/376390748160000* ep^4-730345405419777932839/948504685363200000*ep^5; fill mncT11(4,-6) = 19-35/2*ep^-1-127459/720*ep+746551/14400*ep^2-117119053/96000* ep^3-12251704507/17280000*ep^4-2900897885237/345600000*ep^5; fill mncT11(4,-5) = 655/36-25/3*ep^-1-3409/36*ep+3161/27*ep^2-49598/81*ep^3+ 1147271/3888*ep^4-2667887/729*ep^5; fill mncT11(4,-4) = 73/6-10/3*ep^-1-883/18*ep+926/9*ep^2-25784/81*ep^3+103267/216* ep^4-4865789/2916*ep^5; fill mncT11(4,-3) = 35/6-ep^-1-139/6*ep+578/9*ep^2-18179/108*ep^3+233215/648*ep^4 -3293897/3888*ep^5; fill mncT11(4,-2) = 5/3-1/6*ep^-1-299/36*ep+6187/216*ep^2-103013/1296*ep^3+1504375/ 7776*ep^4-20294069/46656*ep^5; fill mncT11(4,-1) = 1/12-77/72*ep+2683/432*ep^2-60473/2592*ep^3+1053499/15552*ep^4 -15759953/93312*ep^5; fill mncT11(4,0) = 1/6*ep-47/36*ep^2+697/216*ep^3-2123/1296*ep^4-85583/7776*ep^5; fill mncT11(4,1) = -1/3+1/9*ep+331/54*ep^2-1391/324*ep^3-14147/1944*ep^4+345409/ 11664*ep^5; fill mncT11(4,2) = -5/3-ep^-1+343/18*ep+2581/108*ep^2-30839/648*ep^3+175645/ 3888*ep^4-564887/23328*ep^5; fill mncT11(4,3) = -15/2-6*ep^-1+449/4*ep+2363/24*ep^2-33247/144*ep^3+257735/ 864*ep^4-1975171/5184*ep^5; fill mncT11(4,4) = -91/3-20*ep^-1+6647/18*ep+46397/108*ep^2-463897/648*ep^3+ 2998481/3888*ep^4-21706837/23328*ep^5; fill mncT11(4,5) = -95-50*ep^-1+32401/36*ep+206587/144*ep^2-7720667/5184*ep^3+ 23993707/20736*ep^4-1006400483/746496*ep^5; fill mncT11(4,6) = -241-105*ep^-1+218491/120*ep+27182593/7200*ep^2-912704891/ 432000*ep^3+25055078317/25920000*ep^4-2377547244179/1555200000*ep^5; fill mncT11(4,7) = -5243/10-196*ep^-1+2917037/900*ep+150586423/18000*ep^2- 973581653/648000*ep^3-2685625673/21600000*ep^4-21233987539753/ 11664000000*ep^5; fill mncT11(4,8) = -5094/5-336*ep^-1+2757512/525*ep+1203147311/73500*ep^2+ 41798420893/18522000*ep^3-23640276255767/12965400000*ep^4- 48468564911944603/16336404000000*ep^5; fill mncT11(4,9) = -12723/7-540*ep^-1+15515811/1960*ep+9610794797/329280*ep^2+ 5562667894709/460992000*ep^3-3161052127785863/1161699840000*ep^4- 1879943028022084523/325275955200000*ep^5; fill mncT11(4,10) = -42475/14-825*ep^-1+158826085/14112*ep+1722812465123/35562240* ep^2+2862905548098763/89616844800*ep^3+51383427764068223/ 225834448896000*ep^4-6023904889151281594517/569102811217920000*ep^5; fill mncT11(5,-6) = 1865/18-175/6*ep^-1-65051/144*ep+552703/576*ep^2-21762941/6912* ep^3+393823703/82944*ep^4-17125296709/995328*ep^5; fill mncT11(5,-5) = 85/2-25/3*ep^-1-12743/72*ep+414557/864*ep^2-14012279/10368*ep^3 +347829317/124416*ep^4-10748954831/1492992*ep^5; fill mncT11(5,-4) = 37/3-5/3*ep^-1-449/8*ep+157679/864*ep^2-1769167/3456*ep^3+ 153246119/124416*ep^4-476712269/165888*ep^5; fill mncT11(5,-3) = 47/24-1/6*ep^-1-1103/96*ep+159143/3456*ep^2-2004967/13824*ep^3 +193964447/497664*ep^4-625422901/663552*ep^5; fill mncT11(5,-2) = 1/24-179/288*ep+14881/3456*ep^2-800819/41472*ep^3+32595961/ 497664*ep^4-1102859819/5971968*ep^5; fill mncT11(5,-1) = 1/36*ep-43/144*ep^2+6583/5184*ep^3-55583/20736*ep^4+1116007/ 746496*ep^5; fill mncT11(5,0) = 1/36*ep-13/144*ep^2-2147/5184*ep^3+36787/20736*ep^4-1243883/ 746496*ep^5; fill mncT11(5,1) = -1/6-7/24*ep+2759/864*ep^2+4931/1152*ep^3-1045681/124416*ep^4 +3278833/497664*ep^5; fill mncT11(5,2) = -17/6-ep^-1+1249/72*ep+40177/864*ep^2-251579/10368*ep^3- 1938527/124416*ep^4+60671869/1492992*ep^5; fill mncT11(5,3) = -58/3-10*ep^-1+6497/36*ep+126887/432*ep^2-1603513/5184*ep^3+ 13345907/62208*ep^4-160892713/746496*ep^5; fill mncT11(5,4) = -95-50*ep^-1+32401/36*ep+206587/144*ep^2-7720667/5184*ep^3+ 23993707/20736*ep^4-1006400483/746496*ep^5; fill mncT11(5,5) = -1455/4-175*ep^-1+446189/144*ep+1074551/192*ep^2-92479423/ 20736*ep^3+81031771/27648*ep^4-11094823867/2985984*ep^5; fill mncT11(5,6) = -4557/4-490*ep^-1+6086473/720*ep+28575877/1600*ep^2- 23703069623/2592000*ep^3+75358338539/17280000*ep^4-69528709761587/ 9331200000*ep^5; fill mncT11(5,7) = -15239/5-1176*ep^-1+1961923/100*ep+871210943/18000*ep^2- 2501501699/216000*ep^3+57388478537/21600000*ep^4-52691121964811/ 3888000000*ep^5; fill mncT11(5,8) = -7207-2520*ep^-1+16965961/420*ep+4066003721/35280*ep^2+ 88549370213/74088000*ep^3-51961797853837/10372320000*ep^4- 112317791140034653/4356374400000*ep^5; fill mncT11(5,9) = -108175/7-4950*ep^-1+178300085/2352*ep+489246542041/1975680*ep^2 +97721162938507/1659571200*ep^3-7710456819734617/464679936000*ep^4 -20412668993201052719/390331146240000*ep^5; fill mncT11(5,10) = -428725/14-9075*ep^-1+1863930935/14112*ep+17420500082353/ 35562240*ep^2+19591470539173193/89616844800*ep^3-3490364875570682747/ 225834448896000*ep^4-59881195837843542836887/569102811217920000*ep^5; fill mncT11(6,-6) = 1313/12-35/2*ep^-1-117053/240*ep+7250177/4800*ep^2-1244217599/ 288000*ep^3+174112515313/17280000*ep^4-25434137985631/1036800000* ep^5; fill mncT11(6,-5) = 259/12-5/2*ep^-1-26179/240*ep+5674733/14400*ep^2-1023344371/ 864000*ep^3+158892462077/51840000*ep^4-22936759409299/3110400000* ep^5; fill mncT11(6,-4) = 131/60-1/6*ep^-1-17149/1200*ep+13715489/216000*ep^2-946662581/ 4320000*ep^3+494298681041/777600000*ep^4-8467731288263/5184000000* ep^5; fill mncT11(6,-3) = 1/40-329/800*ep+50941/16000*ep^2-46047001/2880000*ep^3+ 3470853629/57600000*ep^4-1929124683769/10368000000*ep^5; fill mncT11(6,-2) = 1/120*ep-757/7200*ep^2+242359/432000*ep^3-43044433/25920000*ep^4 +4074665071/1555200000*ep^5; fill mncT11(6,-1) = 1/360*ep-119/7200*ep^2-12041/1296000*ep^3+6722789/25920000*ep^4- 3468808529/4665600000*ep^5; fill mncT11(6,0) = 1/120*ep-19/2400*ep^2-79541/432000*ep^3+676763/2880000*ep^4+ 1092053971/1555200000*ep^5; fill mncT11(6,1) = -1/10-47/150*ep+30253/18000*ep^2+5658839/1080000*ep^3- 104471693/64800000*ep^4-13141480309/3888000000*ep^5; fill mncT11(6,2) = -56/15-ep^-1+26869/1800*ep+6747947/108000*ep^2+99246511/ 6480000*ep^3-16902461257/388800000*ep^4+700982831959/23328000000* ep^5; fill mncT11(6,3) = -38-15*ep^-1+30613/120*ep+4364099/7200*ep^2-100543913/432000* ep^3-73359169/25920000*ep^4-101532208097/1555200000*ep^5; fill mncT11(6,4) = -241-105*ep^-1+218491/120*ep+27182593/7200*ep^2-912704891/ 432000*ep^3+25055078317/25920000*ep^4-2377547244179/1555200000*ep^5; fill mncT11(6,5) = -4557/4-490*ep^-1+6086473/720*ep+28575877/1600*ep^2- 23703069623/2592000*ep^3+75358338539/17280000*ep^4-69528709761587/ 9331200000*ep^5; fill mncT11(6,6) = -8673/2-1764*ep^-1+5986513/200*ep+821439983/12000*ep^2- 18129375839/720000*ep^3+421716164459/43200000*ep^4-2440992111923/ 103680000*ep^5; fill mncT11(6,7) = -139503/10-5292*ep^-1+17533043/200*ep+886911423/4000*ep^2- 30367486541/720000*ep^3+82520804861/8640000*ep^4-17712342624601/ 288000000*ep^5; fill mncT11(6,8) = -78521/2-13860*ep^-1+187205549/840*ep+221181512717/352800*ep^2 -115715020399/29635200*ep^3-289203450863189/20744640000*ep^4- 1302317090554369133/8712748800000*ep^5; fill mncT11(6,9) = -1388409/14-32670*ep^-1+1989252439/3920*ep+5225117077949/3292800 *ep^2+152407746348439/553190400*ep^3-57305585470090057/774466560000* ep^4-229501098284133484783/650551910400000*ep^5; fill mncT11(6,10) = -1604691/7-70785*ep^-1+24874620107/23520*ep+217302808748161/ 59270400*ep^2+37867626431250733/29872281600*ep^3- 44685664886587404371/376390748160000*ep^4-759955588865113975328047/ 948504685363200000*ep^5; fill mncT11(7,-6) = 2027/60-7/2*ep^-1-74183/400*ep+5800583/8000*ep^2-222102029/96000 *ep^3+546926396573/86400000*ep^4-81787562480723/5184000000*ep^5; fill mncT11(7,-5) = 71/30-1/6*ep^-1-60467/3600*ep+17415031/216000*ep^2-773765929/ 2592000*ep^3+715830606667/777600000*ep^4-116118457957877/46656000000 *ep^5; fill mncT11(7,-4) = 1/60-53/180*ep+266561/108000*ep^2-87124181/6480000*ep^3+ 21293362823/388800000*ep^4-6769202801/37324800*ep^5; fill mncT11(7,-3) = 1/300*ep-841/18000*ep^2+309163/1080000*ep^3-13185257/12960000*ep^4 +8539596691/3888000000*ep^5; fill mncT11(7,-2) = 1/1800*ep-461/108000*ep^2+3287/720000*ep^3+3937531/77760000*ep^4 -5571523609/23328000000*ep^5; fill mncT11(7,-1) = 1/1800*ep-211/108000*ep^2-62167/6480000*ep^3+3518981/77760000*ep^4 -169501453/7776000000*ep^5; fill mncT11(7,0) = 1/300*ep+17/9000*ep^2-14077/180000*ep^3-119341/6480000*ep^4+ 813955783/1944000000*ep^5; fill mncT11(7,1) = -1/15-5/18*ep+8173/9000*ep^2+7556441/1620000*ep^3+241319777/ 97200000*ep^4-1397739257/388800000*ep^5; fill mncT11(7,2) = -67/15-ep^-1+7363/600*ep+7963583/108000*ep^2+77642911/1296000* ep^3-4851581503/129600000*ep^4-72804350141/23328000000*ep^5; fill mncT11(7,3) = -643/10-21*ep^-1+198433/600*ep+37491071/36000*ep^2+40354283/ 432000*ep^3-31200286513/129600000*ep^4-456002246177/7776000000*ep^5; fill mncT11(7,4) = -5243/10-196*ep^-1+2917037/900*ep+150586423/18000*ep^2- 973581653/648000*ep^3-2685625673/21600000*ep^4-21233987539753/ 11664000000*ep^5; fill mncT11(7,5) = -15239/5-1176*ep^-1+1961923/100*ep+871210943/18000*ep^2- 2501501699/216000*ep^3+57388478537/21600000*ep^4-52691121964811/ 3888000000*ep^5; fill mncT11(7,6) = -139503/10-5292*ep^-1+17533043/200*ep+886911423/4000*ep^2- 30367486541/720000*ep^3+82520804861/8640000*ep^4-17712342624601/ 288000000*ep^5; fill mncT11(7,7) = -532091/10-19404*ep^-1+63271401/200*ep+3391764741/4000*ep^2- 160369010221/2160000*ep^3+45079119479/8640000*ep^4-562005021127483/ 2592000000*ep^5; fill mncT11(7,8) = -878053/5-60984*ep^-1+1021262989/1050*ep+1237038993709/441000* ep^2+6809609127931/61740000*ep^3-366227813869447/5186160000*ep^4- 2411323300828693423/3630312000000*ep^5; fill mncT11(7,9) = -18034071/35-169884*ep^-1+25853745639/9800*ep+22610051516631/ 2744000*ep^2+9993527473165147/6914880000*ep^3-120104412190290221/ 387233280000*ep^4-3028135184250064568279/1626379776000000*ep^5; fill mncT11(7,10) = -6857708/5-429429*ep^-1+325970190527/50400*ep+2784773997117157/ 127008000*ep^2+314001610292351747/45722880000*ep^3- 95626190195515256131/161310320640000*ep^4-9860721257991817665174811/ 2032510040064000000*ep^5; fill mncT11(8,-6) = 353/140-1/6*ep^-1-373727/19600*ep+800940667/8232000*ep^2- 29289691863/76832000*ep^3+5385992171933273/4356374400000*ep^4- 709521618026979929/203297472000000*ep^5; fill mncT11(8,-5) = 1/84-1961/8820*ep+14678609/7408800*ep^2-35755774219/3111696000* ep^3+13000149370291/261382464000*ep^4-95609558172939007/ 548903174400000*ep^5; fill mncT11(8,-4) = 1/630*ep-53/2205*ep^2+9018689/55566000*ep^3-5067714581/7779240000* ep^4+16436907354443/9801842400000*ep^5; fill mncT11(8,-3) = 1/6300*ep-1259/882000*ep^2+3355417/1111320000*ep^3+367419121/ 31116960000*ep^4-16828556763959/196036848000000*ep^5; fill mncT11(8,-2) = 1/12600*ep-2167/5292000*ep^2-1838653/2222640000*ep^3+1565353577/ 186701760000*ep^4-1969039700503/130691232000000*ep^5; fill mncT11(8,-1) = 1/6300*ep-401/1323000*ep^2-2005079/555660000*ep^3+391786789/ 46675440000*ep^4+154028720287/10890936000000*ep^5; fill mncT11(8,0) = 1/630*ep+71/26460*ep^2-2011631/55566000*ep^3-1183313023/ 23337720000*ep^4+68567159309/363031200000*ep^5; fill mncT11(8,1) = -1/21-524/2205*ep+902201/1852200*ep^2+3014463589/777924000*ep^3 +1208942969/268912000*ep^4-57410968341421/45741931200000*ep^5; fill mncT11(8,2) = -178/35-ep^-1+843481/88200*ep+1007464943/12348000*ep^2+ 326316812099/3111696000*ep^3-3321224463607/726062400000*ep^4- 81840394319902889/2744515872000000*ep^5; fill mncT11(8,3) = -989/10-28*ep^-1+2534177/6300*ep+1411806601/882000*ep^2+ 167103911539/222264000*ep^3-5874194518813/17287200000*ep^4- 44948630072541313/196036848000000*ep^5; fill mncT11(8,4) = -5094/5-336*ep^-1+2757512/525*ep+1203147311/73500*ep^2+ 41798420893/18522000*ep^3-23640276255767/12965400000*ep^4- 48468564911944603/16336404000000*ep^5; fill mncT11(8,5) = -7207-2520*ep^-1+16965961/420*ep+4066003721/35280*ep^2+ 88549370213/74088000*ep^3-51961797853837/10372320000*ep^4- 112317791140034653/4356374400000*ep^5; fill mncT11(8,6) = -78521/2-13860*ep^-1+187205549/840*ep+221181512717/352800*ep^2 -115715020399/29635200*ep^3-289203450863189/20744640000*ep^4- 1302317090554369133/8712748800000*ep^5; fill mncT11(8,7) = -878053/5-60984*ep^-1+1021262989/1050*ep+1237038993709/441000* ep^2+6809609127931/61740000*ep^3-366227813869447/5186160000*ep^4- 2411323300828693423/3630312000000*ep^5; fill mncT11(8,8) = -23526338/35-226512*ep^-1+13076140537/3675*ep+2369104264591/ 220500*ep^2+276406698978143/216090000*ep^3-1272364093560383/ 3630312000*ep^4-10493366424372887233/4235364000000*ep^5; fill mncT11(8,9) = -79327391/35-736164*ep^-1+333168518807/29400*ep+894920683392109/ 24696000*ep^2+54340449286415137/6914880000*ep^3-1380763360930866373/ 1161699840000*ep^4-4426483375360648100903/542126592000000*ep^5; fill mncT11(8,10) = -6878157-2147145*ep^-1+325203879839/10080*ep+558376514581289/ 5080320*ep^2+2276261966505252557/64012032000*ep^3- 353006015772044616599/161310320640000*ep^4-1416153373047555093193573/ 58071715430400000*ep^5; fill mncT11(9,-6) = 1/112-5471/31360*ep+14340133/8780800*ep^2-24494628927/2458624000* ep^3+6237727760217/137682944000*ep^4-864838163864034797/ 5204415283200000*ep^5; fill mncT11(9,-5) = 1/1176*ep-13513/987840*ep^2+11790271/118540800*ep^3-304304606929/ 697019904000*ep^4+148251273664517/117099343872000*ep^5; fill mncT11(9,-4) = 1/17640*ep-563/987840*ep^2+2929291/1778112000*ep^3+9789209929/ 3485099520000*ep^4-303031735346099/8782450790400000*ep^5; fill mncT11(9,-3) = 1/58800*ep-1793/16464000*ep^2-338951/5927040000*ep^3+1515706901/ 774466560000*ep^4-162680266832969/29274835968000000*ep^5; fill mncT11(9,-2) = 1/58800*ep-2929/49392000*ep^2-210289/658560000*ep^3+10265988779/ 6970199040000*ep^4-7503545288719/29274835968000000*ep^5; fill mncT11(9,-1) = 1/17640*ep-121/2963520*ep^2-2512789/1778112000*ep^3+15188895707/ 10455298560000*ep^4+2773974518263/325275955200000*ep^5; fill mncT11(9,0) = 1/1176*ep+2167/987840*ep^2-2147569/118540800*ep^3-30974065249/ 697019904000*ep^4+1001999162669/13011038208000*ep^5; fill mncT11(9,1) = -1/28-227/1120*ep+4829183/19756800*ep^2+17493523283/5531904000* ep^3+2131548126517/398297088000*ep^4+1653666696353377/ 1301103820800000*ep^5; fill mncT11(9,2) = -787/140-ep^-1+2427349/352800*ep+8586842269/98784000*ep^2+ 7377872489189/49787136000*ep^3+373227039620317/7744665600000*ep^4- 6457306438212806471/175649015808000000*ep^5; fill mncT11(9,3) = -4983/35-36*ep^-1+4556749/9800*ep+18784846207/8232000*ep^2+ 2508753664829/1382976000*ep^3-667379229950441/5808499200000*ep^4- 2514512912366469071/4879139328000000*ep^5; fill mncT11(9,4) = -12723/7-540*ep^-1+15515811/1960*ep+9610794797/329280*ep^2+ 5562667894709/460992000*ep^3-3161052127785863/1161699840000*ep^4- 1879943028022084523/325275955200000*ep^5; fill mncT11(9,5) = -108175/7-4950*ep^-1+178300085/2352*ep+489246542041/1975680*ep^2 +97721162938507/1659571200*ep^3-7710456819734617/464679936000*ep^4 -20412668993201052719/390331146240000*ep^5; fill mncT11(9,6) = -1388409/14-32670*ep^-1+1989252439/3920*ep+5225117077949/3292800 *ep^2+152407746348439/553190400*ep^3-57305585470090057/774466560000* ep^4-229501098284133484783/650551910400000*ep^5; fill mncT11(9,7) = -18034071/35-169884*ep^-1+25853745639/9800*ep+22610051516631/ 2744000*ep^2+9993527473165147/6914880000*ep^3-120104412190290221/ 387233280000*ep^4-3028135184250064568279/1626379776000000*ep^5; fill mncT11(9,8) = -79327391/35-736164*ep^-1+333168518807/29400*ep+894920683392109/ 24696000*ep^2+54340449286415137/6914880000*ep^3-1380763360930866373/ 1161699840000*ep^4-4426483375360648100903/542126592000000*ep^5; fill mncT11(9,9) = -487558929/56-2760615*ep^-1+656747596753/15680*ep+ 366565498288861/2634240*ep^2+144763052912195807/3687936000*ep^3- 10749363204853737433/3097866240000*ep^4-8985300007371764321381/ 289134182400000*ep^5; fill mncT11(9,10) = -1673149335/56-9202050*ep^-1+1289073256967/9408*ep+ 11312477611942837/23708160*ep^2+10298545085451680663/59744563200*ep^3 -134009329612247902531/30111259852800*ep^4- 40019532931754029975386181/379401874145280000*ep^5; fill mncT11(10,-6) = 1/2016*ep-42589/5080320*ep^2+827883523/12802406400*ep^3- 9821121950233/32262064128000*ep^4+15684812553506807/16260080320512000* ep^5; fill mncT11(10,-5) = 1/42336*ep-27589/106686720*ep^2+34849789/38407219200*ep^3+ 317044794767/677503346688000*ep^4-5172935456652193/341461686730752000* ep^5; fill mncT11(10,-4) = 1/211680*ep-3737/106686720*ep^2+3220069/192036096000*ep^3+ 1849098148199/3387516733440000*ep^4-17893832061607469/ 8536542168268800000*ep^5; fill mncT11(10,-3) = 1/352800*ep-11797/889056000*ep^2-12737699/320060160000*ep^3+ 342043914019/1129172244480000*ep^4-5184963405893189/ 14227570280448000000*ep^5; fill mncT11(10,-2) = 1/211680*ep-1133/106686720*ep^2-20839151/192036096000*ep^3+ 1005421668539/3387516733440000*ep^4+3636684674926231/ 8536542168268800000*ep^5; fill mncT11(10,-1) = 1/42336*ep+551/106686720*ep^2-23198471/38407219200*ep^3+ 34557361427/677503346688000*ep^4+1401049384583171/341461686730752000* ep^5; fill mncT11(10,0) = 1/2016*ep+1193/725760*ep^2-123315497/12802406400*ep^3- 1087179659173/32262064128000*ep^4+60277238568413/2322868617216000*ep^5 ; fill mncT11(10,1) = -1/36-493/2835*ep+11263261/114307200*ep^2+741728374799/ 288054144000*ep^3+812764988352467/145179288576000*ep^4+ 6149677687096924787/1829259036057600000*ep^5; fill mncT11(10,2) = -3839/630-ep^-1+13517821/3175200*ep+722967654779/8001504000*ep^2 +762299414847911/4032758016000*ep^3+5863782749601411287/ 50812751001600000*ep^4-2410867506661744804829/128048132524032000000* ep^5; fill mncT11(10,3) = -2733/14-45*ep^-1+12100511/23520*ep+36522506621/11854080*ep^2+ 499108024384793/149361408000*ep^3+238057627322242549/376390748160000* ep^4-730345405419777932839/948504685363200000*ep^5; fill mncT11(10,4) = -42475/14-825*ep^-1+158826085/14112*ep+1722812465123/35562240* ep^2+2862905548098763/89616844800*ep^3+51383427764068223/ 225834448896000*ep^4-6023904889151281594517/569102811217920000*ep^5; fill mncT11(10,5) = -428725/14-9075*ep^-1+1863930935/14112*ep+17420500082353/ 35562240*ep^2+19591470539173193/89616844800*ep^3-3490364875570682747/ 225834448896000*ep^4-59881195837843542836887/569102811217920000*ep^5; fill mncT11(10,6) = -1604691/7-70785*ep^-1+24874620107/23520*ep+217302808748161/ 59270400*ep^2+37867626431250733/29872281600*ep^3- 44685664886587404371/376390748160000*ep^4-759955588865113975328047/ 948504685363200000*ep^5; fill mncT11(10,7) = -6857708/5-429429*ep^-1+325970190527/50400*ep+2784773997117157/ 127008000*ep^2+314001610292351747/45722880000*ep^3- 95626190195515256131/161310320640000*ep^4-9860721257991817665174811/ 2032510040064000000*ep^5; fill mncT11(10,8) = -6878157-2147145*ep^-1+325203879839/10080*ep+558376514581289/ 5080320*ep^2+2276261966505252557/64012032000*ep^3- 353006015772044616599/161310320640000*ep^4-1416153373047555093193573/ 58071715430400000*ep^5; fill mncT11(10,9) = -1673149335/56-9202050*ep^-1+1289073256967/9408*ep+ 11312477611942837/23708160*ep^2+10298545085451680663/59744563200*ep^3 -134009329612247902531/30111259852800*ep^4- 40019532931754029975386181/379401874145280000*ep^5; fill mncT11(10,10) = -29016110695/252-34763300*ep^-1+64837836509717/127008*ep+ 588017945454375487/320060160*ep^2+617147766869674120613/806551603200* ep^3+5319449752682429703959/406502008012800*ep^4- 2063640067151239842477253231/5121925300961280000*ep^5; *--#] gtabls.h : *--#[ poch.h : * * Table can be extended with the procedure makepochs * CTable,relax,mncpoch(0:27,0:26); Fill mncpoch(0,0) = 1; Fill mncpoch(1,0) = 1; Fill mncpoch(2,0) = 1; Fill mncpoch(3,0) = 1; Fill mncpoch(3,1) = 1/2+1/4*ep+1/8*ep^2+1/16*ep^3+1/32*ep^4+1/64*ep^5+1/128* ep^6; Fill mncpoch(4,0) = 1; Fill mncpoch(4,1) = 1/3+1/9*ep+1/27*ep^2+1/81*ep^3+1/243*ep^4+1/729*ep^5+1/2187 *ep^6; Fill mncpoch(4,2) = 1/12+5/72*ep+19/432*ep^2+65/2592*ep^3+211/15552*ep^4+665/ 93312*ep^5+2059/559872*ep^6; Fill mncpoch(5,0) = 1; Fill mncpoch(5,1) = 1/4+1/16*ep+1/64*ep^2+1/256*ep^3+1/1024*ep^4+1/4096*ep^5+1/ 16384*ep^6; Fill mncpoch(5,2) = 1/24+7/288*ep+37/3456*ep^2+175/41472*ep^3+781/497664*ep^4+ 3367/5971968*ep^5+14197/71663616*ep^6; Fill mncpoch(5,3) = 1/144+13/1728*ep+115/20736*ep^2+865/248832*ep^3+5971/ 2985984*ep^4+39193/35831808*ep^5+249355/429981696*ep^6; Fill mncpoch(6,0) = 1; Fill mncpoch(6,1) = 1/5+1/25*ep+1/125*ep^2+1/625*ep^3+1/3125*ep^4+1/15625*ep^5+ 1/78125*ep^6; Fill mncpoch(6,2) = 1/40+9/800*ep+61/16000*ep^2+369/320000*ep^3+2101/6400000* ep^4+11529/128000000*ep^5+61741/2560000000*ep^6; Fill mncpoch(6,3) = 1/360+47/21600*ep+1489/1296000*ep^2+39743/77760000*ep^3+ 965041/4665600000*ep^4+22102367/279936000000*ep^5+487056529/ 16796160000000*ep^6; Fill mncpoch(6,4) = 1/2880+77/172800*ep+3799/10368000*ep^2+153713/622080000* ep^3+5576431/37324800000*ep^4+189395297/2239488000000*ep^5+6168915439/ 134369280000000*ep^6; Fill mncpoch(7,0) = 1; Fill mncpoch(7,1) = 1/6+1/36*ep+1/216*ep^2+1/1296*ep^3+1/7776*ep^4+1/46656*ep^5 +1/279936*ep^6; Fill mncpoch(7,2) = 1/60+11/1800*ep+91/54000*ep^2+671/1620000*ep^3+4651/ 48600000*ep^4+31031/1458000000*ep^5+201811/43740000000*ep^6; Fill mncpoch(7,3) = 1/720+37/43200*ep+919/2592000*ep^2+19153/155520000*ep^3+ 361711/9331200000*ep^4+6418657/559872000000*ep^5+109195759/33592320000000 *ep^6; Fill mncpoch(7,4) = 1/8640+19/172800*ep+2059/31104000*ep^2+20111/622080000*ep^3 +1568371/111974400000*ep^4+4198453/746496000000*ep^5+864917299/ 403107840000000*ep^6; Fill mncpoch(7,5) = 1/86400+29/1728000*ep+4669/311040000*ep^2+22267/2073600000* ep^3+7580461/1119744000000*ep^4+88399969/22394880000000*ep^5+8820914509/ 4031078400000000*ep^6; Fill mncpoch(8,0) = 1; Fill mncpoch(8,1) = 1/7+1/49*ep+1/343*ep^2+1/2401*ep^3+1/16807*ep^4+1/117649* ep^5+1/823543*ep^6; Fill mncpoch(8,2) = 1/84+13/3528*ep+127/148176*ep^2+1105/6223392*ep^3+9031/ 261382464*ep^4+70993/10978063488*ep^5+543607/461078666496*ep^6; Fill mncpoch(8,3) = 1/1260+107/264600*ep+7669/55566000*ep^2+460223/11668860000* ep^3+24973741/2450460600000*ep^4+1270750247/514596726000000*ep^5+ 61865369749/108065312460000000*ep^6; Fill mncpoch(8,4) = 1/20160+319/8467200*ep+64171/3556224000*ep^2+10419739/ 1493614080000*ep^3+1493652451/627317913600000*ep^4+197497515259/ 263473523712000000*ep^5+24696622766131/110658879959040000000*ep^6; Fill mncpoch(8,5) = 1/302400+17/4704000*ep+128431/53343360000*ep^2+9466693/ 7468070400000*ep^3+5469663511/9409768704000000*ep^4+321083468933/ 1317367618560000000*ep^5+159551679717991/1659883199385600000000*ep^6; Fill mncpoch(8,6) = 1/3628800+223/508032000*ep+268921/640120320000*ep^2+ 28291163/89616844800000*ep^3+23293096201/112917224448000000*ep^4+ 650533401001/5269470474240000000*ep^5+1389059807609881/ 19918598392627200000000*ep^6; Fill mncpoch(9,0) = 1; Fill mncpoch(9,1) = 1/8+1/64*ep+1/512*ep^2+1/4096*ep^3+1/32768*ep^4+1/262144* ep^5+1/2097152*ep^6; Fill mncpoch(9,2) = 1/112+15/6272*ep+169/351232*ep^2+1695/19668992*ep^3+15961/ 1101463552*ep^4+144495/61681958912*ep^5+1273609/3454189699072*ep^6; Fill mncpoch(9,3) = 1/2016+73/338688*ep+3565/56899584*ep^2+145585/9559130112* ep^3+5369221/1605933858816*ep^4+185450473/269796888281088*ep^5+6121074205/ 45325877231222784*ep^6; Fill mncpoch(9,4) = 1/40320+533/33868800*ep+178669/28449792000*ep^2+48214517/ 23897825280000*ep^3+11455801981/20074173235200000*ep^4+2504107460933/ 16862305517568000000*ep^5+516331837889869/14164336634757120000000*ep^6; Fill mncpoch(9,5) = 1/806400+743/677376000*ep+334699/568995840000*ep^2+ 118501307/477956505600000*ep^3+36341076451/401483464704000000*ep^4+ 10135733515643/337246110351360000000*ep^5+2644835876174899/ 283286732695142400000000*ep^6; Fill mncpoch(9,6) = 1/14515200+341/4064256000*ep+621139/10241925120000*ep^2+ 97473409/2867739033600000*ep^3+118218740011/7226702364672000000*ep^4+ 1601369656249/224830740234240000000*ep^5+14751190477417339/ 5099161188512563200000000*ep^6; Fill mncpoch(9,7) = 1/203212800+481/56899584000*ep+1227199/143386951680000*ep^2 +29920141/4460927385600000*ep^3+457513138951/101173833105408000000*ep^4+ 78464166359381/28328673269514240000000*ep^5+113616040090237399/ 71388256639175884800000000*ep^6; Fill mncpoch(10,0) = 1; Fill mncpoch(10,1) = 1/9+1/81*ep+1/729*ep^2+1/6561*ep^3+1/59049*ep^4+1/531441* ep^5+1/4782969*ep^6; Fill mncpoch(10,2) = 1/144+17/10368*ep+217/746496*ep^2+2465/53747712*ep^3+26281/ 3869835264*ep^4+269297/278628139008*ep^5+2685817/20061226008576*ep^6; Fill mncpoch(10,3) = 1/3024+191/1524096*ep+24385/768144384*ep^2+2601215/ 387144769536*ep^3+250388161/195120963846144*ep^4+22554022271/ 98340965778456576*ep^5+1939873287745/49563846752342114304*ep^6; Fill mncpoch(10,4) = 1/72576+275/36578304*ep+47485/18435465216*ep^2+6589955/ 9291474468864*ep^3+803944381/4682903132307456*ep^4+90085350275/ 2360183178682957824*ep^5+9507042710845/1189532322056210743296*ep^6; Fill mncpoch(10,5) = 1/1814400+1879/4572288000*ep+2134141/11522165760000*ep^2+ 1899351439/29035857715200000*ep^3+1459738363381/73170361442304000000*ep^4 +1017224854753399/184389310834606080000000*ep^5+661228869152666221/ 464661063303207321600000000*ep^6; Fill mncpoch(10,6) = 1/43545600+2509/109734912000*ep+3714811/276531978240000* ep^2+4239682369/696860585164800000*ep^3+4130738255851/ 1756088674615296000000*ep^4+3619589955939529/4425343460030545920000000* ep^5+2941570541394569491/11151865519276975718400000000*ep^6; Fill mncpoch(10,7) = 1/914457600+3349/2304433152000*ep+6527971/5807171543040000 *ep^2+9723178009/14634072288460800000*ep^3+12298207783411/ 36877862166921216000000*ep^4+13950084494004769/92932212660641464320000000 *ep^5+14659641516358575451/234189175904816490086400000000*ep^6; Fill mncpoch(10,8) = 1/14631321600+4609/36870930432000*ep+12335311/ 92914744688640000*ep^2+25265669869/234145156615372800000*ep^3+ 44132951818351/590045794670739456000000*ep^4+69557603785127029/ 1486915402570263429120000000*ep^5+102302222285618631991/ 3747026814477063841382400000000*ep^6; Fill mncpoch(11,0) = 1; Fill mncpoch(11,1) = 1/10+1/100*ep+1/1000*ep^2+1/10000*ep^3+1/100000*ep^4+1/ 1000000*ep^5+1/10000000*ep^6; Fill mncpoch(11,2) = 1/180+19/16200*ep+271/1458000*ep^2+3439/131220000*ep^3+ 40951/11809800000*ep^4+468559/1062882000000*ep^5+5217031/95659380000000* ep^6; Fill mncpoch(11,3) = 1/4320+121/1555200*ep+9781/559872000*ep^2+660241/ 201553920000*ep^3+40194301/72559411200000*ep^4+2288547961/ 26121388032000000*ep^5+124353617221/9403699691520000000*ep^6; Fill mncpoch(11,4) = 1/120960+1207/304819200*ep+913789/768144384000*ep^2+ 555426703/1935723847680000*ep^3+296460129781/4878024096153600000*ep^4+ 145189272301687/12292620722307072000000*ep^5+66898216741040749/ 30977404220213821440000000*ep^6; Fill mncpoch(11,5) = 1/3628800+1627/9144576000*ep+1597129/23044331520000*ep^2+ 1226220883/58071715430400000*ep^3+811472900641/146340722884608000000*ep^4 +486007890570907/368778621669212160000000*ep^5+271021530780821689/ 929322126606414643200000000*ep^6; Fill mncpoch(11,6) = 1/108864000+2131/274337280000*ep+2671153/691329945600000* ep^2+514496399/348430292582400000*ep^3+2108003826121/ 4390221686538240000000*ep^4+1548441818935891/11063358650076364800000000* ep^5+1051436207524510753/27879663798192439296000000000*ep^6; Fill mncpoch(11,7) = 1/3048192000+2761/7681443840000*ep+4410583/ 19357238476800000*ep^2+1070229857/9756048192307200000*ep^3+5479227875671/ 122926207223070720000000*ep^4+5000355380608621/ 309774042202138214400000000*ep^5+4201660097307941983/ 780630586349388300288000000000*ep^6; Fill mncpoch(11,8) = 1/73156608000+3601/184354652160000*ep+7435423/ 464573723443200000*ep^2+2319380921/234145156615372800000*ep^3+ 15220627743871/2950228973353697280000000*ep^4+17785682685460261/ 7434577012851317145600000000*ep^5+19141633553094561223/ 18735134072385319206912000000000*ep^6; Fill mncpoch(11,9) = 1/1316818944000+4861/3318383738880000*ep+13560283/ 8362327021977600000*ep^2+5736572237/4214612819076710400000*ep^3+ 51361032836971/53104121520366551040000000*ep^4+82500584060043721/ 133822386231323708620800000000*ep^5+123092369468749649683/ 337232413302935745724416000000000*ep^6; Fill mncpoch(12,0) = 1; Fill mncpoch(12,1) = 1/11+1/121*ep+1/1331*ep^2+1/14641*ep^3+1/161051*ep^4+1/ 1771561*ep^5+1/19487171*ep^6; Fill mncpoch(12,2) = 1/220+21/24200*ep+331/2662000*ep^2+4641/292820000*ep^3+ 61051/32210200000*ep^4+771561/3543122000000*ep^5+9487171/389743420000000* ep^6; Fill mncpoch(12,3) = 1/5940+299/5880600*ep+59701/5821794000*ep^2+9950399/ 5763576060000*ep^3+1495099501/5705940299400000*ep^4+210020850599/ 5648880896406000000*ep^5+28144165209301/5592392087441940000000*ep^6; Fill mncpoch(12,4) = 1/190080+1691/752716800*ep+1792261/2980758528000*ep^2+ 1523994731/11803803770880000*ep^3+1137122864101/46743062932684800000*ep^4 +777937168743371/185102529213431808000000*ep^5+500357399225265541/ 733006015685189959680000000*ep^6; Fill mncpoch(12,5) = 1/6652800+15797/184415616000*ep+150376909/5112000875520000 *ep^2+1118222752373/141704664269414400000*ep^3+7158394096103581/ 3928053293548167168000000*ep^4+41422030615640017157/ 108885637297155193896960000000*ep^5+222897788899387733574829/ 3018309865877141974823731200000000*ep^6; Fill mncpoch(12,6) = 1/239500800+20417/6638962176000*ep+244703449/ 184032031518720000*ep^2+2248752686753/5101367913698918400000*ep^3+ 17547631508902441/141409918567734018048000000*ep^4+122492088186769294577/ 3919882942697586980290560000000*ep^5+788811236322261874520569/ 108659155171577111093654323200000000*ep^6; Fill mncpoch(12,7) = 1/8382528000+25961/232363676160000*ep+388631233/ 6441121103155200000*ep^2+880664848501/35709575395892428800000*ep^3+ 41959661109350161/4949347149870690631680000000*ep^4+355116449377006587161/ 137195902994415544310169600000000*ep^5+2757576831668386393741153/38030704\ 31005198888277901312000000000*ep^6; Fill mncpoch(12,8) = 1/268240896000+32891/7435637637120000*ep+616565863/ 206115875300966400000*ep^2+1735225134619/1142706412668557721600000*ep^3+ 102085212023898511/158379108795862100213760000000*ep^4+ 1062566968702623268391/4390268895821297417925427200000000*ep^5+ 10121165924777565643690783/121698253792166364424892841984000000000*ep^6; Fill mncpoch(12,9) = 1/7242504192000+42131/200762216202240000*ep+1005856303/ 5565128633126092800000*ep^2+3594047582563/30853073142051058483200000*ep^3 +268130210338309111/4276235937488276705771520000000*ep^4+ 3540090112228599454031/118537260187175030283986534400000000*ep^5+ 42831598561769824598937223/3285852852388491839472106733568000000000*ep^6; Fill mncpoch(12,10) = 1/144850083840000+55991/4015244324044800000*ep+1781891563/ 111302572662521856000000*ep^2+8533450995199/617061462841021169664000000* ep^3+859498364305599811/85524718749765534115430400000000*ep^4+ 15452737441504212834491/2370745203743500605679730688000000000*ep^5+ 257006539501018214484982483/65717057047769836789442134671360000000000* ep^6; Fill mncpoch(13,0) = 1; Fill mncpoch(13,1) = 1/12+1/144*ep+1/1728*ep^2+1/20736*ep^3+1/248832*ep^4+1/ 2985984*ep^5+1/35831808*ep^6; Fill mncpoch(13,2) = 1/264+23/34848*ep+397/4599936*ep^2+6095/607191552*ep^3+ 87781/80149284864*ep^4+1214423/10579705602048*ep^5+16344637/ 1396521139470336*ep^6; Fill mncpoch(13,3) = 1/7920+181/5227200*ep+21871/3449952000*ep^2+2205361/ 2276968320000*ep^3+200416951/1502799091200000*ep^4+17022590641/ 991847400192000000*ep^5+1378875935431/654619284126720000000*ep^6; Fill mncpoch(13,4) = 1/285120+763/564537600*ep+364699/1117784448000*ep^2+ 139778527/2213213207040000*ep^3+46985048971/4382162149939200000*ep^4+ 14473200299383/8676681056879616000000*ep^5+4189304622793459/ 17179828492621639680000000*ep^6; Fill mncpoch(13,5) = 1/11404800+2021/45163008000*ep+2459191/178845511680000* ep^2+2335527761/708228226252800000*ep^3+1907847025231/ 2804583775961088000000*ep^4+1407526687069601/11106151752805908480000000* ep^5+964841205958233871/43980360941111397580800000000*ep^6; Fill mncpoch(13,6) = 1/479001600+18107/13277924352000*ep+192204079/ 368064063037440000*ep^2+1562214174863/10202735827397836800000*ep^3+ 10767108840037111/282819837135468036096000000*ep^4+66294052036125743567/ 7839765885395173960581120000000*ep^5+376037049102838201214599/ 217318310343154222187308646400000000*ep^6; Fill mncpoch(13,7) = 1/20118067200+22727/557672822784000*ep+297202819/ 15458690647572480000*ep^2+2935291198643/428514904750709145600000*ep^3+ 24328154177767771/11878433159689657516032000000*ep^4+ 178690124337412845587/329270167186597306344407040000000*ep^5+ 1201585423541685547826539/9127369034412477331866963148800000000*ep^6; Fill mncpoch(13,8) = 1/804722688000+28271/22306912911360000*ep+453937243/ 618347625902899200000*ep^2+1090383854767/3428119238005673164800000*ep^3+ 54553594631909011/475137326387586300641280000000*ep^4+ 481135252976716402571/13170806687463892253776281600000000*ep^5+ 3868999266044601283680163/365094761376499093274678525952000000000*ep^6; Fill mncpoch(13,9) = 1/28970016768000+35201/803048864808960000*ep+697880173/ 22260514532504371200000*ep^2+411529154909/24682458513640846786560000*ep^3 +125851020719893261/17104943749953106823086080000000*ep^4+ 1353282826565576701301/474149040748700121135946137600000000*ep^5+ 13247249254144047823696093/13143411409553967357888426934272000000000*ep^6 ; Fill mncpoch(13,10) = 1/869100503040000+44441/24091465944268800000*ep+ 1108515013/667815435975131136000000*ep^2+4106181518569/ 3702368777046127017984000000*ep^3+315556606877781061/ 513148312498593204692582400000000*ep^4+4269025874116273704941/14224471222\ 461003634078384128000000000*ep^5+52693048330978416857350933/3943023422866\ 19020736652808028160000000000*ep^6; Fill mncpoch(13,11) = 1/19120211066880000+58301/530012250773913600000*ep+ 1916566873/14691939591452884992000000*ep^2+376756195621/ 3258084523800591775825920000*ep^3+968286715791163561/ 11289262874969050503236812800000000*ep^4+17689479754981800660401/31293836\ 6894142079949724450816000000000*ep^5+297869237735026174010508793/ 8674651530305618456206361776619520000000000*ep^6; Fill mncpoch(14,0) = 1; Fill mncpoch(14,1) = 1/13+1/169*ep+1/2197*ep^2+1/28561*ep^3+1/371293*ep^4+1/ 4826809*ep^5+1/62748517*ep^6; Fill mncpoch(14,2) = 1/312+25/48672*ep+469/7592832*ep^2+7825/1184481792*ep^3+ 122461/184779159552*ep^4+1840825/28825548890112*ep^5+26916709/ 4496785626857472*ep^6; Fill mncpoch(14,3) = 1/10296+431/17667936*ep+123985/30318178176*ep^2+29756735/ 52025993750016*ep^3+6435002161/89276605275027456*ep^4+1300327044191/ 153198654651947114496*ep^5+250535610806545/262888891382741248475136*ep^6; Fill mncpoch(14,4) = 1/411840+3013/3533587200*ep+5684779/30318178176000*ep^2+ 8597132257/260129968750080000*ep^3+11398215827131/2231915131875686400000* ep^4+13843191192775273/19149831831493389312000000*ep^5+ 15792076962253449859/164305557114213280296960000000*ep^6; Fill mncpoch(14,5) = 1/18532800+11899/477034272000*ep+85194151/ 12278862161280000*ep^2+475777842799/316057912031347200000*ep^3+ 2283980112402751/8135330655686876928000000*ep^4+9896078581316259199/ 209403411077380212126720000000*ep^5+39815208848047266256351/ 5390043801131766660141772800000000*ep^6; Fill mncpoch(14,6) = 1/889574400+30233/45795290112000*ep+535325959/ 2357541534965760000*ep^2+7251045288557/121366238220037324800000*ep^3+ 83204158230308311/6247933943567521480704000000*ep^4+852093272814154275653/ 321643639414856005826641920000000*ep^5+8031393576834107804233519/16558214\ 557076787179955526041600000000*ep^6; Fill mncpoch(14,7) = 1/43589145600+263111/15707784508416000*ep+39775926271/ 5660457225452789760000*ep^2+4534773218406131/2039802365764167317913600000 *ep^3+433223309194517878591/735063180526775334683344896000000*ep^4+ 36623467593521271300764651/264887367734628759606490166722560000000*ep^5+ 2830261534635430995623633510311/95454811836850819811794796480141721600000\ 000*ep^6; Fill mncpoch(14,8) = 1/2092278988800+323171/753973656403968000*ep+59185576531/ 271701946821733908480000*ep^2+8089458944857991/ 97910513556680031259852800000*ep^3+919076213422688818051/ 35283032665285216064800555008000000*ep^4+91823184971687961712907711/ 12714593651262180461111528002682880000000*ep^5+ 8345162024035009976100870632971/45818309681688393509661502310468026368000\ 00000*ep^6; Fill mncpoch(14,9) = 1/94152554496000+395243/33928814538178560000*ep+ 87671530027/12226587606978025881600000*ep^2+2881624291392787/ 881194622010120281338675200000*ep^3+1957498343068993541371/15877364699378\ 34722916024975360000000*ep^4+232904005553356464226598423/5721567143067981\ 20750018760120729600000000*ep^5+25131019512276517065840272175427/ 206182393567597770793476760397106118656000000000*ep^6; Fill mncpoch(14,10) = 1/3766102179840000+485333/1357152581527142400000*ep+ 131395179997/489063504279121035264000000*ep^2+5249102644578733/ 35247784880404811253547008000000*ep^3+4321956629319483821221/635094587975\ 13388916640999014400000000*ep^4+622269078288748761680398313/2288626857227\ 1924830000750404829184000000000*ep^5+81191240775309893005627356193597/ 8247295742703910831739070415884244746240000000000*ep^6; Fill mncpoch(14,11) = 1/124281371934720000+605453/44786035190395699200000*ep+ 204122194357/16139095641210994163712000000*ep^2+10152934241811301/ 1163176901053358771367051264000000*ep^3+10419808934951351201821/209581214\ 0317941834249152967475200000000*ep^4+1873896527555105068043136833/ 755246862884973519390024763359363072000000000*ep^5+ 306283691665229113778968952573557/272160759509229057447389323724180076625\ 920000000000*ep^6; Fill mncpoch(14,12) = 1/2982752926433280000+785633/1074864844569496780800000*ep +345677548297/387338295389063859929088000000*ep^2+22609770372241993/ 27916245625280610512809230336000000*ep^3+30788951063304162695521/ 50299491367630604021979671219404800000000*ep^4+ 7421449730141249102522110613/18125924709239364465360594320624713728000000\ 000*ep^5+1643480504042079377071402842823897/65318582282214973787373437693\ 80321839022080000000000*ep^6; Fill mncpoch(15,0) = 1; Fill mncpoch(15,1) = 1/14+1/196*ep+1/2744*ep^2+1/38416*ep^3+1/537824*ep^4+1/ 7529536*ep^5+1/105413504*ep^6; Fill mncpoch(15,2) = 1/364+27/66248*ep+547/12057136*ep^2+9855/2194398752*ep^3+ 166531/399380572864*ep^4+2702727/72687264261248*ep^5+42664987/ 13229082095547136*ep^6; Fill mncpoch(15,3) = 1/13104+253/14309568*ep+42715/15626048256*ep^2+6015745/ 17063644695552*ep^3+763256971/18633500007542784*ep^4+90472789513/ 20347782008236720128*ep^5+10223601479155/22219777952994498379776*ep^6; Fill mncpoch(15,4) = 1/576576+3875/6925830912*ep+9400015/83193080914944*ep^2+ 18271772975/999315287950307328*ep^3+31127621401111/ 12003775238859091623936*ep^4+48562095793871375/ 144189348169175408586719232*ep^5+71141542266920852455/ 1732002450208135007943671414784*ep^6; Fill mncpoch(15,5) = 1/28828800+25381/1731457728000*ep+387438661/ 103991351143680000*ep^2+4610928219841/6245720549689420800000*ep^3+ 47147998264059421/375117976214346613248000000*ep^4+434927426929788929401/ 22529585651433657591674880000000*ep^5+3723760724060950629591781/135312691\ 4225105474955993292800000000*ep^6; Fill mncpoch(15,6) = 1/1556755200+96163/280496151936000*ep+5412131209/ 50539796655828480000*ep^2+232845928739887/9106260561447175526400000*ep^3+ 8480563352761350841/1640766027961552086346752000000*ep^4+ 275468243066220953681263/295633222918112454917957775360000000*ep^5+ 8229495794026176501671293609/53267194105385502127117631964364800000000* ep^6; Fill mncpoch(15,7) = 1/87178291200+237371/31415569016832000*ep+32340901531/ 11320914450905579520000*ep^2+3319563339382991/ 4079604731528334635827200000*ep^3+285218744266688443051/ 1470126361053550669366689792000000*ep^4+21662662113612051435032711/ 529774735469257519212980333445120000000*ep^5+ 1502482345725330152998011257971/19090962367370163962358959296028344320000\ 0000*ep^6; Fill mncpoch(15,8) = 1/4881984307200+288851/1759271864942592000*ep+6744421573/ 90567315607244636160000*ep^2+5749983097429271/ 228457864965586739606323200000*ep^3+581227874122347314131/ 82327076218998837484534628352000000*ep^4+7369181867632927309499513/ 4238197883754060153703842667560960000000*ep^5+ 4158040723545531838249255762651/10690938925727291818921017205775872819200\ 000000*ep^6; Fill mncpoch(15,9) = 1/263627152588800+348911/95000680706899968000*ep+ 9738077953/4890635042791210352640000*ep^2+9844065830429531/ 12336724708141683938741452800000*ep^3+1172462467897944945991/444566211582\ 5937224164869931008000000*ep^4+17428909842197294946102293/228862685722719\ 248300007504048291840000000*ep^5+11485502999402118579489581785711/ 577310701989273758221734929111897132236800000000*ep^6; Fill mncpoch(15,10) = 1/13181357629440000+420983/4750034035344998400000*ep+ 14072518921/244531752139560517632000000*ep^2+3388741583229943/ 123367247081416839387414528000000*ep^3+2393629384830687205471/22228310579\ 1296861208243496550400000000*ep^4+6010531141202007201947387/1634733469447\ 994630714339314630656000000000*ep^5+32711862019428960669368433503047/ 28865535099463687911086746455594856611840000000000*ep^6; Fill mncpoch(15,11) = 1/579979735695360000+511073/209001497555179929600000*ep+ 20650028431/10759397094140662775808000000*ep^2+5993247069118249/ 5428158871582340933046239232000000*ep^3+5093287527115002467521/9780456654\ 817061893162713848217600000000*ep^4+107624328462384132170626979/ 503497908589982346260016508906242048000000000*ep^5+ 100582992277662265940130925269817/127008354437640226808781684404617369092\ 0960000000000*ep^6; Fill mncpoch(15,12) = 1/20879270485032960000+631193/7524053911986477465600000* ep+31481300311/387338295389063859929088000000*ep^2+11287394379818497/ 195413719376964273589664612352000000*ep^3+11872496591633991765721/ 352096439573414228153857698535833600000000*ep^4+ 44479481424974775838628477/2589417815605623495051513474374959104000000000 *ep^5+362383882407292799553197505474577/457230075975504816511614063856622\ 52873154560000000000*ep^6; Fill mncpoch(15,13) = 1/542861032610856960000+811373/ 195625401711648414105600000*ep+52366041331/ 10070795680115660358156288000000*ep^2+24496833037645909/50807567038010711\ 13331279921152000000*ep^3+33941693475249191183821/91545074289087699320003\ 00161931673600000000*ep^4+1185015560027737611941951879/471274042440223476\ 099375452336242556928000000000*ep^5+1856996607647877139991103732382117/ 1188798197536312522930196566027218574702018560000000000*ep^6; Fill mncpoch(16,0) = 1; Fill mncpoch(16,1) = 1/15+1/225*ep+1/3375*ep^2+1/50625*ep^3+1/759375*ep^4+1/ 11390625*ep^5+1/170859375*ep^6; Fill mncpoch(16,2) = 1/420+29/88200*ep+631/18522000*ep^2+12209/3889620000*ep^3+ 221551/816820200000*ep^4+3861089/171532242000000*ep^5+65445871/ 36021770820000000*ep^6; Fill mncpoch(16,3) = 1/16380+587/44717400*ep+229909/122078502000*ep^2+75104063/ 333274310460000*ep^3+22099571341/909838867555800000*ep^4+6074505299687/ 2483860108427334000000*ep^5+1591540832089909/6780938096006621820000000* ep^6; Fill mncpoch(16,4) = 1/786240+181/476985600*ep+1660831/23439072384000*ep^2+ 150723401/14219703912960000*ep^3+970805468551/698756250282854400000*ep^4+ 23559283621507/141304041723866112000000*ep^5+391284412543967671/ 20831041830932342231040000000*ep^6; Fill mncpoch(16,5) = 1/43243200+7793/865728864000*ep+328609891/ 155987026715520000*ep^2+1199908541813/3122860274844710400000*ep^3+ 33868064779952131/562676964321519919872000000*ep^4+95788093578258793133/ 11264792825716828795837440000000*ep^5+2262193177982682942722971/202969037\ 1337658212433989939200000000*ep^6; Fill mncpoch(16,6) = 1/2594592000+653/3462915456000*ep+505096201/ 9359221602931200000*ep^2+16378601009/1387937899930982400000*ep^3+ 73707865232274001/33760617859291195192320000000*ep^4+16223415984884756209/ 45059171302867315183349760000000*ep^5+6646895816217486003329401/121781422\ 280259492746039396352000000000*ep^6; Fill mncpoch(16,7) = 1/163459296000+4327/1178083838131200*ep+6711529309/ 5306678648861990400000*ep^2+62692963759919/191231471790390686054400000* ep^3+12245902756182085981/172280432935962969066408960000000*ep^4+ 84513205394696034097007/6208297681280361553277113282560000000*ep^5+ 13305358910031620309537534029/5593055381065477723347351356258304000000000 *ep^6; Fill mncpoch(16,8) = 1/10461394944000+52279/753973656403968000*ep+38620655011/ 1358509734108669542400000*ep^2+849477191073451/ 97910513556680031259852800000*ep^3+387257944458431377171/ 176415163326426080324002775040000000*ep^4+6193229394256281368037763/ 12714593651262180461111528002682880000000*ep^5+ 2246413060563394670926707349531/22909154840844196754830751155234013184000\ 000000*ep^6; Fill mncpoch(16,9) = 1/659067881472000+2503/1900013614137999360*ep+22793611/ 35646028008682291200000*ep^2+1412951119346707/ 6168362354070841969370726400000*ep^3+750951562578273758971/11114155289564\ 843060412174827520000000*ep^4+1989289526080312570057597/11443134286135962\ 4150003752024145920000000*ep^5+5830714928654901859656485624131/ 1443276754973184395554337322779742830592000000000*ep^6; Fill mncpoch(16,10) = 1/39544072888320000+74587/2850020421206999040000*ep+ 11017990873/733595256418681552896000000*ep^2+2339387863912039/ 370101741244250518162243584000000*ep^3+1453469738111059070671/66684931737\ 3890583624730489651200000000*ep^4+4483443596678889935329033/6865880571681\ 577449000225121448755200000000*ep^5+15255361713233596392711645893431/ 86596605298391063733260239366784569835520000000000*ep^6; Fill mncpoch(16,11) = 1/2174924008857600000+445007/783755615831924736000000*ep+ 3119956589/8069547820605497081856000000*ep^2+782683688577779/ 4071119153686755699784679424000000*ep^3+2863709208190501272871/3667671245\ 5563982099360176930816000000000*ep^4+51901967990923850782124981/ 1888117157212433798475061908398407680000000000*ep^5+ 8288022434505328561539365461571/95256265828230170106586263303463026819072\ 0000000000*ep^6; Fill mncpoch(16,12) = 1/104396352425164800000+535097/37620269559932387328000000 *ep+4497296267/387338295389063859929088000000*ep^2+1349909677549421/ 195413719376964273589664612352000000*ep^3+5904043279451184720121/ 1760482197867071140769288492679168000000000*ep^4+ 127887004997460598130082251/906296235461968223268029716031235686400000000\ 00*ep^5+24417898826815043961294119451197/45723007597550481651161406385662\ 252873154560000000000*ep^6; Fill mncpoch(16,13) = 1/4071457744581427200000+655217/ 1467190512837363105792000000*ep+6746001011/ 15106193520173490537234432000000*ep^2+2484371175567269/762113505570160666\ 9996919881728000000*ep^3+13364609919679693527121/686588057168157744900022\ 51214487552000000000*ep^4+357223711219164139055478611/3534555318301676070\ 745315892521819176960000000000*ep^5+16898299179023887779595169301169/ 356639459260893756879058969808165572410605568000000000*ep^6; Fill mncpoch(16,14) = 1/114000816848279961600000+835397/ 41081334359446166962176000000*ep+11046624767/ 422973418564857735042564096000000*ep^2+5270904366292553/21339178155964498\ 6759913756688384000000*ep^3+37107398637644498515621/192244656007084168572\ 0063034005651456000000000*ep^4+1312368152152133530847563151/9896754891244\ 6929980868844990610936954880000000000*ep^5+ 415538987011799426321335346471897/499295242965251259630682557731431801374\ 84779520000000000*ep^6; Fill mncpoch(17,0) = 1; Fill mncpoch(17,1) = 1/16+1/256*ep+1/4096*ep^2+1/65536*ep^3+1/1048576*ep^4+1/ 16777216*ep^5+1/268435456*ep^6; Fill mncpoch(17,2) = 1/480+31/115200*ep+721/27648000*ep^2+14911/6635520000*ep^3 +289201/1592524800000*ep^4+5386591/382205952000000*ep^5+97576081/ 91729428480000000*ep^6; Fill mncpoch(17,3) = 1/20160+337/33868800*ep+75769/56899584000*ep^2+14206753/ 95591301120000*ep^3+2399181961/160593385881600000*ep^4+378434270257/ 269796888281088000000*ep^5+56891840784409/453258772312227840000000*ep^6; Fill mncpoch(17,4) = 1/1048320+6061/22895308800*ep+22987441/500033544192000* ep^2+69831137221/10920732605153280000*ep^3+185839346519401/ 238508800096547635200000*ep^4+452720097659125981/ 5209032194108600352768000000*ep^5+1035175813192084068961/ 113765263119331831704453120000000*ep^6; Fill mncpoch(17,5) = 1/62899200+2627/457906176000*ep+37330861/30002012651520000 *ep^2+45924434747/218414652103065600000*ep^3+436586760238021/ 14310528005792858112000000*ep^4+415769333764108067/ 104180643882172007055360000000*ep^5+3305276375544114114781/ 6825915787159909902267187200000000*ep^6; Fill mncpoch(17,6) = 1/4151347200+12059/110813294592000*ep+6887351221/ 239596073035038720000*ep^2+37088446512379/6395617842881966899200000*ep^3+ 13682171803118081701/13828349075165673550774272000000*ep^4+ 18507364188749222564633/123041577104363015327333744640000000*ep^5+ 16768921235956947907208330581/798106729055908611660443787932467200000000* ep^6; Fill mncpoch(17,7) = 1/290594304000+8837/4654158372864000*ep+10071852541/ 16771725112452710400000*ep^2+38384146937093/268615949401042609766400000* ep^3+27514282993368915181/967984435261597148554199040000000*ep^4+ 77380131181928255170229/15503238715149739931244051824640000000*ep^5+ 44653625308676613940352053021/55867471033913602816231065155272704000000000 *ep^6; Fill mncpoch(17,8) = 1/20922789888000+95549/3015894625615872000*ep+128904492469/ 10868077872869356339200000*ep^2+5173650253288037/ 1566568216906880500157644800000*ep^3+4300186483879412144461/5645285226445\ 634570368088801280000000*ep^4+125281902357438362924784317/813733993680779\ 549511137792171704320000000*ep^5+82715366553943572077600287179109/ 2932371819628057184618336147869953687552000000000*ep^6; Fill mncpoch(17,9) = 1/1506440871936000+113567/217144413044342784000*ep+ 180060747619/782501606846593656422400000*ep^2+8417984803887179/ 112792911617295396011350425600000*ep^3+8092067738790391925011/40646053630\ 4085689066502393692160000000*ep^4+54216955774992728925926503/117177695090\ 03225512960384207272542208000000*ep^5+204825505198170945801018253560859/ 211130771013220117292520202646636665503744000000000*ep^6; Fill mncpoch(17,10) = 1/105450861035520000+134159/15200108913103994880000*ep+ 35589400117/7825016068465936564224000000*ep^2+13547983294352027/ 7895503813210677720794529792000000*ep^3+15066569538722815424611/284522375\ 41285998234655167558451200000000*ep^4+83047939830906265693317461/ 585888475450161275648019210363627110400000000*ep^5+ 504097061172824764853457056020459/147791539709254082104764141852645665852\ 62080000000000*ep^6; Fill mncpoch(17,11) = 1/6959756828344320000+158183/1003207188264863662080000*ep +49161501517/516451060518751813238784000000*ep^2+21815374681462883/ 521103251671904729572438966272000000*ep^3+28168883572409422954411/ 1877847677724875883487241058857779200000000*ep^4+ 179723548251415405272856013/386686393797106441927692678839993892864000000\ 00*ep^5+1259690802731425411701598305875059/975424162081076941891443336227\ 461394627297280000000000*ep^6; Fill mncpoch(17,12) = 1/417585409700659200000+935059/ 300962156479459098624000000*ep+13683247289/ 6197412726225021758865408000000*ep^2+7124376132408439/6253239020062856754\ 869267595264000000*ep^3+53842285403156473734811/1126708606634925530092344\ 63531466752000000000*ep^4+2007338082278875133511508177/116005918139131932\ 57830780365199816785920000000000*ep^5+131404439458218746096631125941339/ 2341017988994584660539464006945907347105513472000000000*ep^6; Fill mncpoch(17,13) = 1/21714441304434278400000+1115239/ 15650032136931873128448000000*ep+19424497661/ 322265461763701131461001216000000*ep^2+12024244516391011/3251684290432685\ 51253201914953728000000*ep^3+108005494827239782784311/5858884754501612756\ 480192103636271104000000000*ep^4+683914217018861020339953331/861758249033\ 55149915314368427198638981120000000000*ep^5+ 1864653300791185841202712983266579/60866467713859201174026064180593591024\ 7433502720000000000*ep^6; Fill mncpoch(17,14) = 1/912006534786239692800000+1355479/ 657301349751138671394816000000*ep+28728505517/ 13535149394075447521362051072000000*ep^2+21686675147956723/13657074019817\ 279152634480428056576000000*ep^3+238255665765867861122311/246073159689067\ 735772168068352723386368000000000*ep^4+12964333968216612136097386837/ 25335692521586414075102424317596399860449280000000000*ep^5+ 6225025530325288300609163682475811/25563916439820864493090946955849308230\ 392207114240000000000*ep^6; Fill mncpoch(17,15) = 1/27360196043587190784000000+1715839/ 19719040492534160141844480000000*ep+46394783861/ 406054481822263425640861532160000000*ep^2+45093029184966667/4097122205945\ 18374579034412841697280000000*ep^3+644498765693232564125311/7382194790672\ 032073165042050581701591040000000000*ep^4+46143130426104224537268397117/ 760070775647592422253072729527891995813478400000000000*ep^5+ 29504419402816573996559219101590779/7669174931946259347927284086754792469\ 11766213427200000000000*ep^6; Fill mncpoch(18,0) = 1; Fill mncpoch(18,1) = 1/17+1/289*ep+1/4913*ep^2+1/83521*ep^3+1/1419857*ep^4+1/ 24137569*ep^5+1/410338673*ep^6; Fill mncpoch(18,2) = 1/544+33/147968*ep+817/40247296*ep^2+17985/10947264512* ep^3+371281/2977655947264*ep^4+7360353/809922417655808*ep^5+141903217/ 220298897602379776*ep^6; Fill mncpoch(18,3) = 1/24480+767/99878400*ep+392449/407503872000*ep^2+167445503/ 1662615797760000*ep^3+64341277441/6783472454860800000*ep^4+23090095523327/ 27676567615832064000000*ep^5+7896872313485569/112920395872594821120000000 *ep^6; Fill mncpoch(18,4) = 1/1370880+7409/39152332800*ep+34344361/1118190624768000* ep^2+127496303969/31935524243374080000*ep^3+414575867232601/ 912078572390763724800000*ep^4+1233810004615062929/ 26048964027480211980288000000*ep^5+3446031540223992082441/ 743958412624834854157025280000000*ep^6; Fill mncpoch(18,5) = 1/89107200+124877/33083721216000*ep+9370684129/ 12283324013076480000*ep^2+547736118544133/4560552539575035494400000*ep^3+ 27484044889650755641/1693241946893419178360832000000*ep^4+ 1243049340091966141204157/628666870042588672541809704960000000*ep^5+ 52134825205663579992245684689/233411435509412322341323107257548800000000* ep^6; Fill mncpoch(18,6) = 1/6415718400+5771/88223256576000*ep+14191662109/ 884399328941506560000*ep^2+109647349355177/36484420316600283955200000* ep^3+58016445791093343061/121913420176326180841979904000000*ep^4+ 337564241429821575056833/5029334960340709380334477639680000000*ep^5+ 146132963874211695782571401869/168056233566776872085752637225435136000000\ 00*ep^6; Fill mncpoch(18,7) = 1/494010316800+695089/672525884878848000*ep+2491409046949/ 8239948547748016619520000*ep^2+746158649625630001/ 11217536354962239905149747200000*ep^3+1680520133126409356069941/137439947\ 629722554255471938633728000000*ep^4+371076347615267005360649932609/ 187105247105199096461229278378411950080000000*ep^5+ 672203138641751347243174296203656069/229245839279220457762613181371911403\ 1248179200000000*ep^6; Fill mncpoch(18,8) = 1/39520825344000+11083/717360943870771200*ep+3509845866349/ 659195883819841329561600000*ep^2+81598335099127831/ 59826860559798612827465318400000*ep^3+3180163710978816320207101/109951958\ 10377804340437755090698240000000*ep^4+17866913657179536531741418541/ 332631550409242838153296494894954577920000000*ep^5+1657296852483437668283\ 659946775174349/183396671423376366210090545097529122499854336000000000* ep^6; Fill mncpoch(18,9) = 1/3201186852864000+1768477/7844341921226883072000*ep+ 43626282040741/480553799304664329250406400000*ep^2+6341322098576939297/ 235514419279703219256599972413440000*ep^3+473413816892251673970873181/ 72139479711888774277612111150071152640000000*ep^4+ 246122147257642086960153029784733/176774043781038423151026042543469555844\ 382720000000*ep^5+2883473637413744217699157744337822684821/10829390050878\ 951048339636597463997154493898686464000000000*ep^6; Fill mncpoch(18,10) = 1/256094948229120000+2074783/627547353698150645760000*ep+ 59514244080691/38444303944373146340032512000000*ep^2+49936180540264833931/ 94205767711881287702639988965376000000*ep^3+855807609806410679522595331/ 5771158376951101942208968892005692211200000000*ep^4+ 508261152987004516562001115242019/141419235024830738520820834034775644675\ 50617600000000*ep^5+6775559655584679353950165584470869480171/ 866351204070316083867170927797119772359511894917120000000000*ep^6; Fill mncpoch(18,11) = 1/19719311013642240000+2424847/48321146234757599723520000 *ep+11533647869413/422887343388104609740357632000000*ep^2+ 15639756978914436191/1450768822762971830620655830066790400000*ep^3+ 1540172095689748578368373331/44437919502523484955009060468443830026240000\ 0000*ep^4+149631422498934380414278193855029/15556115852731381237290291743\ 8253209143056793600000000*ep^5+15942160155576398219385344873862572054971/ 66709042713414338457772161440378222471682415908618240000000000*ep^6; Fill mncpoch(18,12) = 1/1419790392982241280000+566651/ 695824505780509436018688000*ep+15666233612413/ 30447888723943531901305749504000000*ep^2+122986290854820760483/5222767761\ 94669859023436098824044544000000*ep^3+2795886722575639507051899931/ 31995302041816909167606523537279557618892800000000*ep^4+ 44679233920126784544816320489899/1600057630566656355835572865079175865471\ 441305600000000*ep^5+38295171949969044501800041051694943775171/ 4803051075365832368959595623707232017961133945420513280000000000*ep^6; Fill mncpoch(18,13) = 1/92286375543845683200000+16616723/ 1130714821893327833530368000000*ep+4296630026537/ 395822553411265914716974743552000000*ep^2+39337394008338706103/6789598090\ 530708167304669284712579072000000*ep^3+5205742684399278649369003531/ 2079694632718099095894424029923171245228032000000000*ep^4+ 3386116294275986540181282069222449/36401311095391432095259282680551250939\ 47528970240000000000*ep^5+19275537051500212631939807407885805145047/ 62439663979755820796474743108194016233494741290466672640000000000*ep^6; Fill mncpoch(18,14) = 1/5168037030455358259200000+19679783/ 63320030026026358677700608000000*ep+1203785183113/44332125982061782448301\ 17127782400000*ep^2+65148257709241446563/38021749306971965736906147994390\ 4428032000000*ep^3+10194568240871006282100573031/116462899432213549370087\ 745675697589732769792000000000*ep^4+7847055465116321469102850816127429/ 203847342134192019733451983011087005261061622333440000000000*ep^5+ 52925939449671092126750056917072000886883/3496621182866325964602585614058\ 864909075705512266133667840000000000*ep^6; Fill mncpoch(18,15) = 1/232561666370491121664000000+23763863/ 2849401351171186140496527360000000*ep+8791883561309/997472834596390105086\ 776353751040000000*ep^2+115417715850340651571/171097871881373845816077665\ 97475699261440000000*ep^3+21978947864622487488802815031/52408304744496097\ 21653948555406391537974640640000000000*ep^4+ 20670452807251665569569965217814069/9173130396038640888005339235498915236\ 747773005004800000000000*ep^5+171113635511127627373867081882550116977011/ 157347953228984668407116352632648920908406748051976015052800000000000* ep^6; Fill mncpoch(18,16) = 1/7441973323855715893248000000+29889983/ 91180843237477956495888875520000000*ep+2804717413153/63838261414168966725\ 55368664006656000000*ep^2+235691963923794646091/5475131900203963066114485\ 31119222376366080000000*ep^3+58075879215443408921577738031/16770657518238\ 7511092926353773004529215188500480000000000*ep^4+ 10213734180205588474482562633289147/4193431038189092977373869364799504108\ 2275533737164800000000000*ep^5+784305135624330012093778824553194147329483/ 5035134503327509389027723284244765469069015937663232481689600000000000* ep^6; Fill mncpoch(19,0) = 1; Fill mncpoch(19,1) = 1/18+1/324*ep+1/5832*ep^2+1/104976*ep^3+1/1889568*ep^4+1/ 34012224*ep^5+1/612220032*ep^6; Fill mncpoch(19,2) = 1/612+35/187272*ep+919/57305232*ep^2+21455/17535400992* ep^3+469711/5365832703552*ep^4+9874655/1641944807286912*ep^5+201881359/ 502435111029795072*ep^6; Fill mncpoch(19,3) = 1/29376+433/71912448*ep+125065/176041672704*ep^2+30119905/ 430950014779392*ep^3+6532281721/1054965636179951616*ep^4+1323011798353/ 2582555877368521555968*ep^5+255342792121705/6322096787798140769009664* ep^6; Fill mncpoch(19,4) = 1/1762560+2981/21573734400*ep+5559121/264062509056000*ep^2 +8301230861/3232125110845440000*ep^3+10856480458201/ 39561211356748185600000*ep^4+12993299923745141/ 484229227006597791744000000*ep^5+14592263864677675681/ 5926965738560756970946560000000*ep^6; Fill mncpoch(19,5) = 1/123379200+26987/10571129856000*ep+437557369/ 905734406062080000*ep^2+5525173283603/77603323911399014400000*ep^3+ 59880470075790961/6649052792728667553792000000*ep^4+584846868682225266107/ 569690843280992236008898560000000*ep^5+5296028087750682494768809/48811111\ 452315414781242428620800000000*ep^6; Fill mncpoch(19,6) = 1/9623577600+436511/10719125673984000*ep+111347457841/ 11939390940710338560000*ep^2+21679055891892671/ 13298571205400803501670400000*ep^3+3567707614652029688401/ 14812480551423630972300558336000000*ep^4+522830736837015369430864031/ 16498733337397697122187253896970240000000*ep^5+ 70359053570403260874728970376561/1837694914052705096257705088060133212160\ 0000000*ep^6; Fill mncpoch(19,7) = 1/808380518400+529331/900406556614656000*ep+160479961261/ 1002908839019668439040000*ep^2+36574805896138691/ 1117079981253667494140313600000*ep^3+6962581097931622987021/1244248366319\ 585001673246900224000000*ep^4+1169097514347028615086153251/13858936003414\ 06558263729327345500160000000*ep^5+178874684852094456927025715134381/ 1543663727804272280856472273970511898214400000000*ep^6; Fill mncpoch(19,8) = 1/71137485619200+6936481/871593546802987008000*ep+ 27144205309621/10678973317881429538897920000*ep^2+78915368289828852361/ 130841344044279566253666651340800000*ep^3+189838243670759861066750701/ 1603099549153083872835824692223803392000000*ep^4+ 399733753113342469138829668028641/196415604201153803501140047270521728715\ 98080000000*ep^5+762126859139026684033692640366200630181/2406531122417544\ 67740880813276977714544308859699200000000*ep^6; Fill mncpoch(19,9) = 1/6402373705728000+1632341/15688683842453766144000*ep+ 37144122156541/961107598609328658500812800000*ep^2+24885047642990928509/ 2355144192797032192565999724134400000*ep^3+342287031737439448024305781/ 144278959423777548555224222300142305280000000*ep^4+ 163822407857362995880992338849717/353548087562076846302052085086939111688\ 765440000000*ep^5+1765722588362175280360157427240228938221/21658780101757\ 902096679273194927994308987797372928000000000*ep^6; Fill mncpoch(19,10) = 1/576213633515520000+634871/470660515273612984320000*ep+ 50108441924941/86499683874839579265073152000000*ep^2+12842724447592821487/ 70654325783910965776979991724032000000*ep^3+604540602047063899917440581/ 12985106348139979369970180007012807475200000000*ep^4+ 36491320739769019782145968968861/3535480875620768463020520850869391116887\ 654400000000*ep^5+4001224686465313155038158061435416431421/19492902091582\ 11188701134587543519487808901763563520000000000*ep^6; Fill mncpoch(19,11) = 1/50706799749365760000+736973/41418125344077942620160000* ep+67038885805291/7611972180985882975326437376000000*ep^2+ 19687528766084643169/6217580668984164988374239271714816000000*ep^3+ 1056821216013888103206719131/11426893586363181845573758406171270578176000\ 00000*ep^4+14491834801117137497336689574663/62224463410925524949161166975\ 301283657222717440000000*ep^5+8995027630880172313079771602899231919171/ 171537538405922584605699843703829714927183355193589760000000000*ep^6; Fill mncpoch(19,12) = 1/4259371178946723840000+853661/ 3479122528902547180093440000*ep+12778797804013/ 91343666171830595703917248512000000*ep^2+30125455273167325777/52227677619\ 4669859023436098824044544000000*ep^3+1847759019119841608016698731/ 95985906125450727502819570611838672856678400000000*ep^4+ 20618515544753006667442994530613/3733467804655531496949670018518077019433\ 363046400000000*ep^5+20363062671292178341579800591748333959571/ 14409153226097497106878786871121696053883401836261539840000000000*ep^6; Fill mncpoch(19,13) = 1/332230951957844459520000+989797/ 271371557254398680047288320000*ep+17109951516613/712480596140278646490554\ 5383936000000*ep^2+15476805930275572451/135791961810614163346093385694251\ 58144000000*ep^3+3269950574303538456569500531/748690067778515674521992650\ 7723416482820915200000000*ep^4+125449545403314235905692629918727/ 873631466289394370286222784333230022547406952857600000000*ep^5+4726122658\ 9307477581910161281668248682971/11239139516356047743365453759474922922029\ 05343228400107520000000000*ep^6; Fill mncpoch(19,14) = 1/23256166637049112166400000+5765801/ 94980045039039538016550912000000*ep+4633029920081/99747283459639010508677\ 635375104000000*ep^2+972276647483105227/380217493069719657369061479943904\ 42803200000*ep^3+5950278111359178723522658531/524083047444960972165394855\ 540639153797464064000000000*ep^4+1321573779274851026418875128258963/ 305771013201288029600177974516630507891592433500160000000000*ep^5+ 184429809438582369103388536652477688571/125878362583187734725693082106119\ 136726725398441580812042240000000*ep^6; Fill mncpoch(19,15) = 1/1395369998222946729984000000+6786821/ 5698802702342372280993054720000000*ep+6414896199989/598483700757834063052\ 0658122506240000000*ep^2+7917927319201484899/1140652479209158972107184439\ 8317132840960000000*ep^3+11407222563588671298837120031/314449828466976583\ 29923691332438349227847843840000000000*ep^4+ 426490180342842088866751065140089/262089439886818311085866835299969006764\ 2220858572800000000000*ep^5+61460857526770605266414768298646940834171/ 944087719373908010442698115795893525450440488311856090316800000000000* ep^6; Fill mncpoch(19,16) = 1/66977759914701443039232000000+8148181/ 273542529712433869487666626560000000*ep+9267281033573/2872721763637603502\ 64991589880299520000000*ep^2+41416329948615369689/16425395700611889198343\ 45593357667129098240000000*ep^3+24093292924829250726795954031/ 1509359176641487599836337183957040762936696504320000000000*ep^4+ 2557031623473562434471511531976501/29354017267323650841617085553596528757\ 5928736160153600000000000*ep^5+193044191107999031795357544599330752205579/ 45316210529947584501249509558202889221621143438969092335206400000000000* ep^6; Fill mncpoch(19,17) = 1/2277243837099849063333888000000+10190221/93004460102227\ 51562580665303040000000*ep+14618125319789/9767253996367851909009714055930\ 183680000000*ep^2+83207445227846071073/5584634538208042327436775017416068\ 2389340160000000*ep^3+62323702501770178695925461031/513182120058105783944\ 35464254539385939847681146880000000000*ep^4+ 319162535360951652254196420838183/369643180403334862449992929193437769540\ 058408497971200000000000*ep^5+858212753688871384631081484547427071719971/ 1540751158018217873042483324978898233535118876924949139397017600000000000 *ep^6; Fill mncpoch(20,0) = 1; Fill mncpoch(20,1) = 1/19+1/361*ep+1/6859*ep^2+1/130321*ep^3+1/2476099*ep^4+1/ 47045881*ep^5+1/893871739*ep^6; Fill mncpoch(20,2) = 1/684+37/233928*ep+1027/80003376*ep^2+25345/27361154592* ep^3+586531/9357514870464*ep^4+13033657/3200270085698688*ep^5+281651707/ 1094492369308951296*ep^6; Fill mncpoch(20,3) = 1/34884+971/202815576*ep+628885/1179169758864*ep^2+ 339598655/6855692978035296*ep^3+165130395661/39858998974297210944*ep^4+ 74980524443111/231740220036563984428416*ep^5+32441726871224245/ 1347337639292583005466810624*ep^6; Fill mncpoch(20,4) = 1/2232576+10675/103841574912*ep+71280865/4829879332306944* ep^2+381087985915/224647347504260579328*ep^3+1784196875682361/ 10448797427118168065703936*ep^4+7643622142560484675/ 485994465930120233072021471232*ep^5+30724413617353537431505/ 22604574599341752280645862669942784*ep^6; Fill mncpoch(20,5) = 1/167443200+68879/38940590592000*ep+2849921641/ 9056023748075520000*ep^2+91821183361439/2106068882852442931200000*ep^3+ 2538718674137225881/489787379396164128079872000000*ep^4+ 63246613519325064668399/113904952952371929626255032320000000*ep^5+ 1460644458774764824986123721/26489735858603615953881870316339200000000* ep^6; Fill mncpoch(20,6) = 1/14065228800+598433/22897067268096000*ep+209231949649/ 37274593747078840320000*ep^2+55824156998159297/ 60680056652744585733734400000*ep^3+12586696512349442395441/ 98782277826135966007660904448000000*ep^4+2526566903875289523623661473/ 160809645718723261783191339568988160000000*ep^5+ 465632559513010972701751825732369/261785238458423972322092845511147205427\ 200000000*ep^6; Fill mncpoch(20,7) = 1/1279935820800+9407549/27087230578157568000*ep+ 50674936658761/573245977236325485281280000*ep^2+205140415810486182629/ 12131581686413266791988317388800000*ep^3+693440824795419090681592081/ 256740177966296508588177081366478848000000*ep^4+ 2066962792941526519197177519796109/54333821166936143593912480458755372010\ 70080000000*ep^5+5612369498835806831267039256237912043801/114986448400302\ 292943222606744942158764758060236800000000*ep^6; Fill mncpoch(20,8) = 1/122873838796800+11171129/2600374135503126528000*ep+ 70376116340581/55031613814687246587002880000*ep^2+329254327066408022609/ 1164631841895673612030878469324800000*ep^3+1274107170923194951194372301/ 24647057084764464824464999811181969408000000*ep^4+ 4313952717438254671224548622393689/52160468320258697850155981240405157130\ 2727680000000*ep^5+13220370232255564004345228715718974090421/ 11038699046429020122549370247514447241416773782732800000000*ep^6; Fill mncpoch(20,9) = 1/12164510040883200+144045379/2831807433562904788992000*ep +11563936671172141/659223701886138526865707499520000*ep^2+ 682964638539938251189939/153462373174751016183696825024459571200000*ep^3+ 33107756416321668892839436318381/3572489871502561642000421416131600619615\ 0272000000*ep^4+1395424523824507178967790057413570374899/8316490627611523\ 711990816225401006051377683963576320000000*ep^5+5295200568974199167131002\ 0002288914759772858221/19360171434176932904150448056006372252757025767518\ 78288179200000000*ep^6; Fill mncpoch(20,10) = 1/1216451004088320000+33464927/56636148671258095779840000 *ep+15459129684443701/65922370188613852686570749952000000*ep^2+ 208568335200260476871279/3069247463495020323673936500489191424000000*ep^3 +57384334759425043431682350760501/357248987150256164200042141613160061961\ 5027200000000*ep^4+546257828615772235565008402289813568431/16632981255223\ 0474239816324508020121027553679271526400000000*ep^5+116534384861495429218\ 360696197566696018666694901/193601714341769329041504480560063722527570257\ 675187828817920000000000*ep^6; Fill mncpoch(20,11) = 1/120428649404743680000+2575873/ 373798581230303432146944000*ep+20456163600317701/652631464867277141597050\ 4245248000000*ep^2+104797168713396265839349/10128516629533567068123990451\ 6143316992000000*ep^3+98044336735330748463653354832901/353676497278753602\ 558041720197028461341887692800000000*ep^4+3901695014800776788641589261496\ 3791437/609875979358178405545993189862740443767696823995596800000000*ep^5 +252777220486702037010828869195404425757546325701/19166569719835163575108\ 943575446308530229455509843595052974080000000000*ep^6; Fill mncpoch(20,12) = 1/11561150342855393280000+14819303/ 179423318990545647430533120000*ep+26924582630540851/626526206272586055933\ 168407543808000000*ep^2+157029189692522423246587/972337596435222438539903\ 0833549758431232000000*ep^3+166585387478920575522984290444251/ 33952943738760345845572005138914732288821218508800000000*ep^4+22477262491\ 5717378138883377323504506457/17564428205515538079724603868046924780509668\ 5310731878400000000*ep^5+547107566079481220911421539531192588299392600251/ 1839990693104175703210458583242845618902027728944985125085511680000000000 *ep^6; Fill mncpoch(20,13) = 1/1052064681199840788480000+136291/ 130620176225117231329428111360*ep+722918946514099/11635486687919455324473\ 12756867072000000*ep^2+235564594067231841654859/8848272127560524190713118\ 05853028017242112000000*ep^3+284094712260931388092304139835051/ 3089717880227191471947052467641240638282730884300800000000*ep^4+207012112\ 16649520775829064379093487461/7611252222390066501213995009487000738220856\ 36346504806400000000*ep^5+11976844398997963570755101321250803507248947718\ 51/1674391530724799889921517310750989513200845233339936463827815628800000\ 00000*ep^6; Fill mncpoch(20,14) = 1/88373433220786626232320000+19622959/ 1371511850363730928958995169280000*ep+6691889361450493/684166617249663973\ 079019901037838336000000*ep^2+39636503525768697284027/8258387319056489244\ 665576854628261494259712000000*ep^3+491704082578217610786112219715251/ 259536301939084083643552407281864213615749394281267200000000*ep^4+ 368001459911488032779259477943263214661/575410668012689027491778022717217\ 255809496741077957633638400000000*ep^5+2696874473789118126876345385681906\ 474383259909651/140648888580883190753407454103083119108870999600554662961\ 53651281920000000000*ep^6; Fill mncpoch(20,15) = 1/6628007491558996967424000000+113634299/ 514316943886399098359623188480000000*ep+1791861632884649/1026249925874495\ 9596185298515567575040000000*ep^2+36759343878994477827661/371627429357542\ 016009950958458271767241687040000000*ep^3+ 876782662026233073157512154812451/194652226454313062732664305461398160211\ 81204571095040000000000*ep^4+3783897589621264775867769177810666436777/ 215779000504758385309416758518956470928561277904234112614400000000000* ep^5+1279299988357065097769419812185359092380304604391/210973332871324786\ 130111181154624678663306499400831994442304769228800000000000*ep^6; Fill mncpoch(20,16) = 1/424192479459775805915136000000+133033679/32916284408729\ 542295015884062720000000*ep+2455488433612397/6567999525596774141558591049\ 96324802560000000*ep^2+19662996236659528938043/79280518262942296748789537\ 80443131034489323520000000*ep^3+1649218782291627541449949696825951/ 1245774249307603601489051554952948225355597092550082560000000000*ep^4+ 8354443569737343846589672770612297481117/13809856032304536659802672545213\ 214139427921785870983207321600000000000*ep^5+3321394909630494639499669865\ 710145065396621598387/135022933037647863123271155938959794344516159616532\ 47644307505230643200000000000*ep^6; Fill mncpoch(20,17) = 1/21633816452448566101671936000000+158899519/167873050484\ 5206657045810087198720000000*ep+3512363456777501/334967975805435481219488\ 14354812564930560000000*ep^2+304157289802731019494563/3638975788269051420\ 769439785223397144830599495680000000*ep^3+ 3419357635687618766938680368107951/63534486714687783675941629302600359493\ 135451720054210560000000000*ep^4+6996460118839792568226709790805116460079/ 234767552549177123216645433268624640370274670359806714524467200000000000* ep^5+2032407026008299343034169136508042531424864017959/ 1377233916984008203857365790577389902314064828088631259719365533525606400\ 00000000*ep^6; Fill mncpoch(20,18) = 1/778817392288148379660189696000000+197698279/60434298174\ 427439653649163139153920000000*ep+5484764391463397/1205884712899567732390\ 157316773252337500160000000*ep^2+602080169996039164077371/131003128377685\ 851147699832268042297213901581844480000000*ep^3+ 8675349539385611774407351611598951/22872415217287602123338986548936129417\ 52876261921951580160000000000*ep^4+23024688913827073458150756334330874369\ 639/845163189177037643579923559767048705332988813295304172288081920000000\ 0000*ep^5+43929885665398066829245940510472343485868209330587/ 2479021050571214766943258423039301824165316690559536267494857960346091520\ 0000000000*ep^6; Fill mncpoch(21,0) = 1; Fill mncpoch(21,1) = 1/20+1/400*ep+1/8000*ep^2+1/160000*ep^3+1/3200000*ep^4+1/ 64000000*ep^5+1/1280000000*ep^6; Fill mncpoch(21,2) = 1/760+39/288800*ep+1141/109744000*ep^2+29679/41702720000* ep^3+723901/15847033600000*ep^4+16954119/6021872768000000*ep^5+386128261/ 2288311651840000000*ep^6; Fill mncpoch(21,3) = 1/41040+541/140356800*ep+195211/480020256000*ep^2+58726081/ 1641669275520000*ep^3+15907469851/5614508922278400000*ep^4+4023543044521/ 19201620514192128000000*ep^5+969677567613091/65669542158537077760000000* ep^6; Fill mncpoch(21,4) = 1/2790720+12617/162252460800*ep+99566119/9433358070912000* ep^2+629037362933/548455438242823680000*ep^3+3479915570656231/ 31887199179437768755200000*ep^4+17614167008208763517/ 1853921760292511875427328000000*ep^5+83646110364087120543919/ 107787011143406640437344849920000000*ep^6; Fill mncpoch(21,5) = 1/223257600+65003/51920787456000*ep+2537876509/ 12074698330767360000*ep^2+77146426286027/2808091843803257241600000*ep^3+ 2012181692155397581/653049839194885504106496000000*ep^4+ 47283967911884477681243/151873270603162572835006709760000000*ep^5+ 1029886941650541728844759229/35319647811471487938509160421785600000000* ep^6; Fill mncpoch(21,6) = 1/20093184000+80507/4672870871040000*ep+3786057037/ 1086722849769062400000*ep^2+5433818183507/10109130637691726069760000*ep^3 +4118329620082710781/58774485527539695369584640000000*ep^4+ 111134550341646825629867/13668594354284631555150603878400000000*ep^5+ 2752917010147434113410217197/3178768303032433914465824437960704000000000* ep^6; Fill mncpoch(21,7) = 1/1969132032000+679829/3205589417533440000*ep+264567310933/ 5218443124591037644800000*ep^2+15471775567772353/ 1699041586276848400544563200000*ep^3+18883399732921434619381/138295188956\ 59035241072526622720000000*ep^4+4063600108536162615902797349/225133504006\ 21256649646787539658342400000000*ep^5+796393353947420464985775918751573/ 36649933384179356125092998371560608759808000000000*ep^6; Fill mncpoch(21,8) = 1/204789731328000+10465697/4333956892505210880000*ep+ 61749193007917/91719356357812077645004800000*ep^2+54096040178685508069/ 388210613965224537343626156441600000*ep^3+979648908410397655642573141/ 41078428474607441374108333018636615680000000*ep^4+ 3103576326078171977720055003798977/86934113867097829750259968734008595217\ 1212800000000*ep^5+8896412581122772353147560018397791958397/1839783174404\ 8366870915617079190745402361289637888000000000*ep^6; Fill mncpoch(21,9) = 1/22117290983424000+12229277/468067344390562775040000*ep+ 83316501339577/9905690486643704385660518400000*ep^2+83483103265175749201/ 41926746308244250033111624895692800000*ep^3+1715794564692390894522071041/ 4436470275257603668403699966012754493440000000*ep^4+ 6129517304478378711481289050285757/93888842976465656130280766232729282834\ 490982400000000*ep^5+19706306708954751481141731761700747288457/ 1986965828357223622058886644552600503455019280891904000000000*ep^6; Fill mncpoch(21,10) = 1/2432902008176640000+155685007/ 566361486712580957798400000*ep+13376052237829537/ 131844740377227705373141499904000000*ep^2+33546276427873663571287/ 1227698985398008129469574600195676569600000*ep^3+ 42869410876462125767012740349281/7144979743005123284000842832263201239230\ 054400000000*ep^4+1894408519005680278985033026339791282367/16632981255223\ 04742398163245080201210275536792715264000000000*ep^5+75002216130999040005\ 632021996598286884167697697/387203428683538658083008961120127445055140515\ 350375657635840000000000*ep^6; Fill mncpoch(21,11) = 1/267619220899430400000+178964263/ 62299763538383905357824000000*ep+3508441426211573/29005842882990095182091\ 12997888000000*ep^2+249405288261152635886123/6752344419689044712082660301\ 07622113280000000*ep^3+71899258642387961096351961171721/78594777173056356\ 1240092711548952136315305984000000000*ep^4+356816976715204207666505099655\ 8344401943/182962793807453521663797956958822133130309047198679040000000000 *ep^5+31613310718398363686217874079707021030633138421/8518475431037850477\ 826197144642803791213091337708264467988480000000000*ep^6; Fill mncpoch(21,12) = 1/28902875857138483200000+68276701/ 2242791487381820592881664000000*ep+4568061960487877/313263103136293027966\ 584203771904000000*ep^2+122520682680406128102601/243084399108805609634975\ 77083874396078080000000*ep^3+119435764265920301764172676919321/ 84882359346900864613930012847286830722053046272000000000*ep^4+73971957065\ 9117117205428798902799366287/21955535256894422599655754835058655975637085\ 66384148480000000000*ep^5+13210710645113143179406447455713718431899764673/ 183999069310417570321045858324284561890202772894498512508551168000000000* ep^6; Fill mncpoch(21,13) = 1/3005899089142402252800000+77976391/ 233250314687709341659693056000000*ep+5929486236521699/3257936272617447490\ 8524757192278016000000*ep^2+180034861033933286675911/25280777507315783402\ 03748016722937192120320000000*ep^3+198018469620920758028858699460871/ 8827765372077689919848721336117830395093516812288000000000*ep^4+137995882\ 7191566739687075611760671309617/22833756667170199503641985028461002214662\ 5690903951441920000000000*ep^5+138333486542783263039119021658018467993464\ 984507/956795160414171365669438463286279721829054419051392265044466073600\ 00000000*ep^6; Fill mncpoch(21,14) = 1/294578110735955420774400000+89061751/ 22858530839395515482649919488000000*ep+1100941866605621/45611107816644264\ 8719346600691892224000000*ep^2+265465219546700294335831/24775161957169467\ 7339967305638847844827791360000000*ep^3+330443458297860188895697838498071/ 865121006463613612145174690939547378719164647604224000000000*ep^4+ 371569579831022268697049515535951917591/319672593340382793050987790398454\ 0310052759672655320186880000000000*ep^5+588062054430723474927416519522183\ 40414543449167/1875318514411775876712099388041108254784946661340728839487\ 153504256000000000*ep^6; Fill mncpoch(21,15) = 1/26512029966235987869696000000+101994671/205726777554559\ 6393438492753920000000*ep+1440136160440589/410499970349798383847411940622\ 70300160000000*ep^2+131947126603765803454997/7432548587150840320199019169\ 165435344833740800000000*ep^3+560815778698370791596289811665471/ 77860890581725225093065722184559264084724818284380160000000000*ep^4+ 2150849539585028745812789751048513353533/86311600201903354123766703407582\ 5883714245111616936450457600000000000*ep^5+644522266561735863051652284582\ 933977506909725971/843893331485299144520444724618498714653225997603327977\ 769219076915200000000000*ep^6; Fill mncpoch(21,16) = 1/2120962397298879029575680000000+4700567/658325688174590\ 8459003176812544000000*ep+1909103457032669/328399976279838707077929552498\ 1624012800000000*ep^2+201079916992041251032741/59460388697206722561592153\ 3533234827586699264000000000*ep^3+982104956468853833677919602528111/ 6228871246538018007445257774764741126777985462750412800000000000*ep^4+ 24732839655047676871730070400369814083/3945673152087010474229335012918061\ 18269369193882028091637760000000000*ep^5+14908925622888415093420089880528\ 34130671436230531/6751146651882393156163557796947989717225807980826623822\ 1537526153216000000000000*ep^6; Fill mncpoch(21,17) = 1/144225443016323774011146240000000+27382711/223830733979\ 3608876061080116264960000000*ep+2592084677757329/223311983870290320812992\ 095698750432870400000000*ep^2+318411200189355854830121/404330643141005713\ 41882664280259968275895549952000000000*ep^3+ 1815997238747320968392957220400411/42356324476458522450627752868400239662\ 0903011467028070400000000000*ep^4+1872198545452668789019780076649838497053 /939070210196708492866581733074498561481098681439226858097868800000000000 *ep^5+3779020496465907922039085085124472799077917940351/ 4590779723280027346191219301924633007713549426962104199064551778418688000\ 000000000*ep^6; Fill mncpoch(21,18) = 1/7788173922881483796601896960000000+32555879/12086859634\ 8854879307298326278307840000000*ep+3674765594251649/120588471289956773239\ 01573167732523375001600000000*ep^2+1620589892856994073881483/ 6550156418884292557384991613402114860695079092224000000000*ep^3+ 3702303588088847790211455041232811/22872415217287602123338986548936129417\ 528762619219515801600000000000*ep^4+2194423691588781637301433536686607339\ 77/2414751969077250410228353027905853443808539466558011920823091200000000\ 000*ep^5+11288449477143071208076450493848872632073685174991/ 2479021050571214766943258423039301824165316690559536267494857960346091520\ 00000000000*ep^6; Fill mncpoch(21,19) = 1/295950609069496384270872084480000000+40315631/459300666\ 1256485413677336398575697920000000*ep+5685875368931369/458236190901835738\ 308259780373835888250060800000000*ep^2+3164824289660551569998563/ 248905943917603117180629681309280364706413005504512000000000*ep^3+ 9227910200640807772651340119417411/86915177825692888068688148885957291786\ 6092979530341600460800000000000*ep^4+164864004605711110259964848862893050\ 3757/21410800792484953637358063514098567201769049936814372364631408640000\ 0000000*ep^5+47556711908537510787153661623430506914067600903431/ 9420279992170616114384382007549346931828203424126237816480460249315147776\ 000000000000*ep^6; Fill mncpoch(22,0) = 1; Fill mncpoch(22,1) = 1/21+1/441*ep+1/9261*ep^2+1/194481*ep^3+1/4084101*ep^4+1/ 85766121*ep^5+1/1801088541*ep^6; Fill mncpoch(22,2) = 1/840+41/352800*ep+1261/148176000*ep^2+34481/62233920000* ep^3+884101/26138246400000*ep^4+21766121/10978063488000000*ep^5+521088541/ 4610786664960000000*ep^6; Fill mncpoch(22,3) = 1/47880+1199/382082400*ep+958801/3049017552000*ep^2+ 639201599/24331160064960000*ep^3+383681598001/194162657318380800000*ep^4+ 215041341602399/1549418005400678784000000*ep^5+114832432963357201/ 12364355683097416696320000000*ep^6; Fill mncpoch(22,4) = 1/3447360+4927/82529798400*ep+15182119/1975763373696000* ep^2+37450661443/47299775166282240000*ep^3+80887589157271/ 1132356617480796825600000*ep^4+159835539588553387/ 27108617422490276004864000000*ep^5+296294111283063404239/ 648980301094417207556444160000000*ep^6; Fill mncpoch(22,5) = 1/293025600+107699/119255558688000*ep+6965946451/ 48534627274842240000*ep^2+350759857706399/19752622608315294835200000*ep^3 +15153003327495623251/8038922349132158692029696000000*ep^4+ 589706509393829867034599/3271680617649805944482245678080000000*ep^5+ 21269393390276908468002055051/1331508577771118023285384346064998400000000 *ep^6; Fill mncpoch(22,6) = 1/28130457600+532541/45794134536192000*ep+165638527261/ 74549187494157680640000*ep^2+39301522849379981/ 121360113305489171467468800000*ep^3+7877902294149045719101/ 197564555652271932015321808896000000*ep^4+1405396634537476440533360621/ 321619291437446523566382679137976320000000*ep^5+ 230111515907589757527003193872541/523570476916847944644185691022294410854\ 400000000*ep^6; Fill mncpoch(22,7) = 1/2953698048000+641069/4808384126300160000*ep+235212463693/ 7827664686886556467200000*ep^2+12965732221810777/ 2548562379415272600816844800000*ep^3+14913627226992445750381/207442783434\ 88552861608789934080000000*ep^4+3023942770228512592930709789/337700256009\ 31884974470181309487513600000000*ep^5+558293976874949772212587265853133/ 54974900076269034187639497557340913139712000000000*ep^6; Fill mncpoch(22,8) = 1/330814181376000+757349/538539022145617920000*ep+ 323277005413/876698444931294324326400000*ep^2+4096772451939101/ 57087797298902106258297323520000*ep^3+26822944744779412357381/23233591744\ 70717920500184472616960000000*ep^4+877559255021637523120996067/5403204096\ 14910159591522900951800217600000000*ep^5+ 1272592108092361850532153224548453/61571888085421318290156237264221822716\ 47744000000000*ep^6; Fill mncpoch(22,9) = 1/38705259220992000+11473457/819117852683484856320000*ep+ 73311684034237/17334958351626482674905907200000*ep^2+68872156719154043893/ 73371806039427437557945343567462400000*ep^3+1326681931686871052010621541/ 7763822981700806419706474940522320363520000000*ep^4+ 634364758507847592727754138279591/234722107441164140325701915581823207086\ 22745600000000*ep^5+13371424584359851783478810591146276341517/ 3477190199625141338603051627967050881046283741560832000000000*ep^6; Fill mncpoch(22,10) = 1/4644631106519040000+13237037/98294142322018182758400000 *ep+96656257746697/2080195002195177920988708864000000*ep^2+ 20592873065307604589/1760923344946258501390688245619097600000*ep^3+ 2234611408699750684537337041/93165875780409677036477699286267844362240000\ 0000*ep^4+1197352756815662780190090832389131/2816665289293969683908422986\ 981878485034729472000000000*ep^5+28152816208414617744692293322440041884377 /417262823955016960632366195356046105725554048987299840000000000*ep^6; Fill mncpoch(22,11) = 1/562000363888803840000+166770367/ 130829503430606201251430400000*ep+15224761793356657/304561350271395999411\ 95686477824000000*ep^2+201485775218089148104739/1417992328134699389537358\ 663226006437888000000*ep^3+54037122642320109361184487954481/1650490320634\ 183478604194694252799486262142566400000000*ep^4+5088631585428469237741087\ 9627160750623/78412625917480080713056267268066628484418163085148160000000\ 00*ep^5+102642779516603254522781939957201679111950482417/8944399202589743\ 0017175070018749439807737459045936776913879040000000000*ep^6; Fill mncpoch(22,12) = 1/67440043666656460800000+190049623/ 15699540411672744150171648000000*ep+3929795123975429/73094724065135039858\ 8696475467776000000*ep^2+292968481936664897505563/17015907937616392674448\ 3039587120772546560000000*ep^3+88137564096995099037413300460121/ 198058838476102017432503363310335938351457107968000000000*ep^4+6493151992\ 41472523961490128706707332929/6586660577068326779896726450517596792691125\ 699152445440000000000*ep^5+41690360550287193487728315978131280310854085637 /2146655808621538320412201680449986555385699017102482645933096960000000000 *ep^6; Fill mncpoch(22,13) = 1/7890485108998805913600000+888541/ 7559037975990580516749312000000*ep+5046762087872213/855208271562079966348\ 77487629729792000000*ep^2+141169074206544499803161/6636204095670393143034\ 838543897710129315840000000*ep^3+142909414392614203809242209263721/ 23172884101703936039602893507309304787120481632256000000000*ep^4+39246087\ 8183969706913699067000422691483/25687976250566474441597233157018627491495\ 3902266945372160000000000*ep^5+843259477320246077040101782538965760459823\ 76661/2511587296087199834882275966126484269801267850009904695741723443200\ 00000000*ep^6; Fill mncpoch(22,14) = 1/883734332207866262323200000+27223837/ 22858530839395515482649919488000000*ep+258908043889163/383133305659811824\ 924251144581189468160000*ep^2+203952268312326386289911/743254858715084032\ 019901916916543534483374080000000*ep^3+231931734376801714471699616505271/ 2595363019390840836435524072818642136157493942812672000000000*ep^4+ 713841724557872538605699074603281558053/287705334006344513745889011358608\ 62790474837053897881681920000000000*ep^5+17156889504171166632226292529132\ 4247653454281643/28129777716176638150681490820616623821774199920110932592\ 307302563840000000000*ep^6; Fill mncpoch(22,15) = 1/92792104881825957543936000000+10306319/ 800048579378843041892747182080000000*ep+8323539050744483/1005724927357006\ 040426159254525622353920000000*ep^2+296221695163887248358791/780417601650\ 83823362089701276237071120754278400000000*ep^3+ 54242760036912775158242421356353/3893044529086261254653286109227963204236\ 2409142190080000000000*ep^4+1315142246960663939833873282610142850133/ 3020906007066617394331834619265390592999857890659277576601600000000000* ep^5+355262093302186773034430926995975429282348727931/2953626660198547005\ 821556536164745501286290991611647922192266769203200000000000*ep^6; Fill mncpoch(22,16) = 1/8908042068655291924217856000000+105689791/6912419725833\ 20388195333565317120000000*ep+10783918752019979/9654959302627257988091128\ 8434459745976320000000*ep^2+435689253670261475167471/74920089758480470427\ 60611322518758827592410726400000000*ep^3+90466051724909048255960993790553/ 3737322747922810804467154664858844676066791277650247680000000000*ep^4+ 828377485544924889401452112807953851631/966689922261317566186187078164924\ 98975995452501096882451251200000000000*ep^5+76022633586555549905854082761\ 7717396796734125187/28354815937906051255886942747181556812348393519471820\ 0530457609843507200000000000*ep^6; Fill mncpoch(22,17) = 1/757183575835699813558517760000000+24241859/117511135339\ 16446599320670610391040000000*ep+14169913401481403/8206715407233169289877\ 459516929078407987200000000*ep^2+655599281384205714951583/636820762947083\ 998634651962414094500345354911744000000000*ep^3+ 155874038173876016234622114914473/317672433573438918379708146513001797465\ 677258600271052800000000000*ep^4+326948014371359746510775945955165662419/ 1643372867844239862516518032880372482591922692518647001671270400000000000 *ep^5+1719225758046118387555592788188808110007280638451/ 2410159354722014356750390133510432329049613449155104704508889683669811200\ 0000000000*ep^6; Fill mncpoch(22,18) = 1/54517217460170386576213278720000000+5624347/16921603488\ 8396831030217656789630976000000*ep+19079811413200103/59088350932078818887\ 1177085218893645375078400000000*ep^2+1025735793317211529087723/ 45851094932190047901694941293814804024865553645568000000000*ep^3+ 283793856679203461190610776561373/228724152172876021233389865489361294175\ 28762619219515801600000000000*ep^4+138795267772744029848180667679155374467 /236645692969570540202378596734773637493236867722685168240662937600000000\ 00*ep^5+4263678081976446636035200919697570372976891423151/ 1735314735399850336860280896127511276915721683391675387246400572242264064\ 000000000000*ep^6; Fill mncpoch(22,19) = 1/3107481395229712034844156887040000000+11098301/ 16075523314397698947870677395014942720000000*ep+26830617117521783/ 33680360031284926765657093857476937786379468800000000*ep^2+ 1719732242780291164680443/26135124111348327303966116537474438294173365577\ 97376000000000*ep^3+569751621901607388170140710778573/1303727667385393321\ 030322233289359376799139469295512400691200000000000*ep^4+5029349874960654\ 936768060495684299546269/202332067488982811873033700208231460056717521902\ 89581884576681164800000000000*ep^5+12459244709670841970083325422874089675\ 256484133631/989129399177914692010360110792681427841961359533254970730448\ 32617809051648000000000000*ep^6; Fill mncpoch(22,20) = 1/124299255809188481393766275481600000000+2736977/ 128604186515181591582965419160119541760000000*ep+41166444473571983/ 1347214401251397070626283754299077511455178752000000000*ep^2+ 3316939241963736875821523/10454049644539330921586446614989775317669346231\ 1895040000000000*ep^3+1397064597795747817979670470352373/5214910669541573\ 2841212889331574375071965578771820496027648000000000000*ep^4+317404493636\ 7080931766288877468413327553/16186565399118624949842696016658516804537401\ 7522316655076613449318400000000000*ep^5+512511821399971601363189601708574\ 98202363507931831/3956517596711658768041440443170725711367845438133019882\ 921793304712362065920000000000000*ep^6; Fill mncpoch(23,0) = 1; Fill mncpoch(23,1) = 1/22+1/484*ep+1/10648*ep^2+1/234256*ep^3+1/5153632*ep^4+1/ 113379904*ep^5+1/2494357888*ep^6; Fill mncpoch(23,2) = 1/924+43/426888*ep+1387/197222256*ep^2+39775/91116682272* ep^3+1069531/42095907209664*ep^4+27613783/19448309130864768*ep^5+ 693269347/8985118818459522816*ep^6; Fill mncpoch(23,3) = 1/55440+661/256132800*ep+291391/1183333536000*ep^2+ 107086321/5467000936320000*ep^3+35432250151/25257544325798400000*ep^4+ 10946228084881/116689854785188608000000*ep^5+3221848034607511/ 539107129107571368960000000*ep^6; Fill mncpoch(23,4) = 1/4213440+17179/369855763200*ep+184559131/ 32465938893696000*ep^2+1587168260959/2849860116088634880000*ep^3+ 11950283637559051/250160720990260369766400000*ep^4+82314254820268574839/ 21959108088525055258094592000000*ep^5+531866536505869659968371/1927570508\ 010729350555543285760000000*ep^6; Fill mncpoch(23,5) = 1/379209600+66167/99861056064000*ep+2629055389/ 26297410503893760000*ep^2+81316623386963/6925160082095382758400000*ep^3+ 2157635174793551821/1823671656018998095597056000000*ep^4+ 51568566528554926827107/480245693896042958494528727040000000*ep^5+ 1142178833425537561597517869/126467901030583952689949194978713600000000* ep^6; Fill mncpoch(23,6) = 1/38679379200+1388179/173159071214976000*ep+1125360065281/ 775195066833780257280000*ep^2+695860890291247759/ 3470377771300130780185958400000*ep^3+363455854283229426496801/15536117799\ 000999474120894845952000000*ep^4+168932454832480049913623239039/ 69551781440211694425754939628460994560000000*ep^5+ 72056093057733715599405381560250721/3113680241159109093713311986299016112\ 26316800000000*ep^6; Fill mncpoch(23,7) = 1/4332090470400+6671911/77575263904309248000*ep+ 25472930476141/1389149559766134221045760000*ep^2+73044273402884483071/ 24875667864679337432372949811200000*ep^3+174795484267648032213828901/ 445451569532956656921994297023135744000000*ep^4+ 368617065763389910525106433630631/797675470981499881030098251610893454409\ 7280000000*ep^5+707696134081534470005310937858021015261/14284070379922236\ 1495916930033864623953295284633600000000*ep^6; Fill mncpoch(23,8) = 1/519850856448000+7865719/9309031668517109760000*ep+ 34863088744093/166697947171936106525491200000*ep^2+22932821530058531843/ 597016028752304098376950795468800000*ep^3+311682413293428611125969621/ 53454188343954798830639315642776289280000000*ep^4+ 740706024212391333916177974937399/957210565177799857236117901933072145291\ 673600000000*ep^5+1591956911434480943565115533762087440653/17140884455906\ 683379510031604063754874395434156032000000000*ep^6; Fill mncpoch(23,9) = 1/65501207912448000+9144799/1172937990233155829760000*ep+ 46560018249013/21003941343663949422211891200000*ep^2+34843619158448041451/ 75224019622790316395495800229068800000*ep^3+534521295259367215421695021/ 6735227731338304652660553770989812449280000000*ep^4+ 203485931793248964545394234628297/172297901732003974302501222347952986152\ 50124800000000*ep^5+3413880410901243142560175537160622327973/ 2159751441444242105818263982112033114173824703660032000000000*ep^6; Fill mncpoch(23,10) = 1/8515157028618240000+136789507/ 1982265203494033352294400000*ep+10318149200673037/ 461456591320296968805995249664000000*ep^2+22701019694796315586507/ 4296946448893028453143511100684867993600000*ep^3+ 25429209808829812008795312240781/2500742910051793149400294991292120433730\ 5190400000000*ep^4+140604889437866859681372877519720600981/83164906276115\ 2371199081622540100605137768396357632000000000*ep^5+341029490865161193140\ 60279501783300475933221197/1355212000392385303290531363920446057692991803\ 726314801725440000000000*ep^6; Fill mncpoch(23,11) = 1/1124000727777607680000+156188887/ 261659006861212402502860800000*ep+13348116771363097/609122700542791998823\ 91372955648000000*ep^2+165294136380390745268507/2835984656269398779074717\ 326452012875776000000*ep^3+41462228625904935088530158869081/3300980641268\ 366957208389388505598972524285132800000000*ep^4+2555108221179822424896200\ 47999959539521/1097776762844721129982787741752932798781854283192074240000\ 00000*ep^5+68800209813170115801218277069169486118483500057/ 178887984051794860034350140037498879615474918091873553827758080000000000* ep^6; Fill mncpoch(23,12) = 1/148368096066644213760000+177351847/ 34538988905680037130377625600000*ep+17101406815350217/8040419647164854384\ 475661230145536000000*ep^2+237677414055787550940971/374349974627560638837\ 862687091665699602432000000*ep^3+66612016658735283633838817039881/ 435729444647424438351507399282739064373205637529600000000*ep^4+4568975998\ 42003450794132266780290969201/1449065326955031891577279819113871294392047\ 6538135379968000000000*ep^5+136485349220036393244345602845233872105417464\ 777/236132138948369215245342184849498521092426891881273091052640665600000\ 00000*ep^6; Fill mncpoch(23,13) = 1/19287852488663747788800000+200631103/ 4490068557738404826949091328000000*ep+4354389924729917/209050910826286213\ 996367191983783936000000*ep^2+339044371837396019642723/486654967015828830\ 48922149321916540948316160000000*ep^3+106075520295544945207058703310321/ 56644827804165176985695961906756078368516732878848000000000*ep^4+80966319\ 8741030084934288346978720969369/18837849250415414590504637648480326827096\ 61949957599395840000000000*ep^5+10736953894437424504022195763807007043799\ 249241/122788712253151991927577936121739230968061983778262007347373146112\ 000000000*ep^6; Fill mncpoch(23,14) = 1/2430269413571632221388800000+25166327/ 62860959808337667577287278592000000*ep+5526096662355341/26340414764112062\ 963542266189956775936000000*ep^2+160660501310137764364721/204395086146648\ 1088054730271520494719829278720000000*ep^3+ 168409802613662152072292328769921/713724830332481230019769120025126587443\ 3108342734848000000000*ep^4+477319209524941792099885725621010484963/ 79118966851744741280119478123617372673805801898219174625280000000000*ep^5 +105539071142681328215940393247262258156972774669/77356888719485754914374\ 099756695715509879049780305064628845082050560000000000*ep^6; Fill mncpoch(23,15) = 1/291632329628595866566656000000+9466519/2514438392333506\ 703091491143680000000*ep+7013617917156923/3160849771693447555625071942794\ 813112320000000*ep^2+228690420885005598818591/245274103375977730566567632\ 582459366379513446400000000*ep^3+268229981098595750128503780925471/ 856469796398977476023722944030151904931973001128181760000000000*ep^4+ 848997447433832965180449559736007885533/949427602220936895361433737483408\ 4720856696227786300955033600000000000*ep^5+209300222984014716668732943602\ 216813080015142771/928282664633829058972489197080348586118548597363660775\ 5461409846067200000000000*ep^6; Fill mncpoch(23,16) = 1/32662820918402737055465472000000+32094677/8448512998240\ 58252238741024276480000000*ep+8934835579752011/35401517442966612623000805\ 7593019068579840000000*ep^2+327736289827365351477551/27470699578109505823\ 455574849235449034505505996800000000*ep^3+ 61674049314232353556855299260953/1370351674238363961637956710448243047891\ 1568018050908160000000000*ep^4+1532676486739851728005471019951405833613/ 1063358914487449322804805785981417488735949977512065706963763200000000000 *ep^5+423377632784000399338423319246396116843437734339/ 1039676584389888546049187900729990416452774429047300068611677902759526400\ 000000000*ep^6; Fill mncpoch(23,17) = 1/3331607733677079179657478144000000+109216951/2585244977\ 46161825185054753428602880000000*ep+11477324941620467/3610954779182594487\ 5460821874487944995143680000000*ep^2+476171615111347521551191/ 2802011356967169593992468634622015801519561611673600000000*ep^3+ 101263052628912808768125629239153/139775870772313124087071584465720790884\ 8979937841192632320000000000*ep^4+35090165991918157663937510282111511733/ 1339044558984195443531977656421044245074899971681860519880294400000000000 *ep^5+177308919904227732290716978651392575355844054351/ 2120940232155372633940343317489180449563659835256492139967822921629433856\ 0000000000*ep^6; Fill mncpoch(23,18) = 1/299844696030937126169173032960000000+24947291/465344095\ 9430912853330985561714851840000000*ep+14961851183793443/32498593012643350\ 38791473968703915049562931200000000*ep^2+708372124405634595363463/ 252181022127045263459322177115981422136760545050624000000000*ep^3+ 171936092745924018430650493054273/125798283695081811678364426019148711796\ 408194405707336908800000000000*ep^4+3673777549640073039006328254939196327\ 31/6507756556663189855565411410206275031064013862373842126618230784000000\ 00000*ep^5+1964131981141700659938536286698174355074357216891/ 9544231044699176852731544928701312023036469258654214629855203147332452352\ 000000000000*ep^6; Fill mncpoch(23,19) = 1/22788196898351221588857150504960000000+28827167/ 353661512916749376853154902690328739840000000*ep+19994913686401583/ 246989306896089462948152021621497543766782771200000000*ep^2+ 1096261053075339736582003/19165757681655440022908485460814588082393801423\ 847424000000000*ep^3+44093019650466508511673294540739/1365809937260888241\ 079385196779328870932431824976251086438400000000000*ep^4+8517264466139391\ 3998131741621798843583/54954388700711381002552363019519655817873894837823\ 55573588728217600000000000*ep^5+47746883266063901862789041714752139325107\ 87913431/7253615593971374408075974145812997137507716636577203118689954391\ 97266378752000000000000*ep^6; Fill mncpoch(23,20) = 1/1367291813901073295331429030297600000000+755563/ 471548683888999169137539870253771653120000000*ep+27909938711909183/ 14819358413765367776889121297289852626006966272000000000*ep^2+ 1818175062207388758590723/11499454608993264013745091276488752849436280854\ 30845440000000000*ep^3+610978014167135045315681918514373/ 573640173649573061253341782647318125791621366490025456304128000000000000* ep^4+1092070663490121069211038524565146144081/178052219390304874448269656\ 1832436848499114192745483205842747942502400000000000*ep^5+136725957175231\ 23830684023515200227950426857221031/4352169356382824644845584487487798282\ 5046299819463218712139726351835982725120000000000000*ep^6; Fill mncpoch(23,21) = 1/57426256183845078403920019272499200000000+13920029/ 297075670850069476556650118259876141465600000000*ep+42492095049738263/ 622413053378145446629343094486173810292292583424000000000*ep^2+ 3466815659939371687544603/48297709357771708857729383361252761967632379588\ 095508480000000000*ep^3+1475673256158609095246069325536173/ 24092887293282068572640354871187361283248097392581069164773376000000000000 *ep^4+16911211818273884590109069563793700229501/3739096607196402363413662\ 77984811738184813980476551473226977067925504000000000000*ep^5+55009040782\ 244563766882453836423225227557173002911/182791112968078635083514548474487\ 5278651944592417455185909868506777111274455040000000000000*ep^6; Fill mncpoch(24,0) = 1; Fill mncpoch(24,1) = 1/23+1/529*ep+1/12167*ep^2+1/279841*ep^3+1/6436343*ep^4+1/ 148035889*ep^5+1/3404825447*ep^6; Fill mncpoch(24,2) = 1/1012+45/512072*ep+1519/259108432*ep^2+45585/131108866592 *ep^3+1282711/66341086495552*ep^4+34655985/33568589766749312*ep^5+ 910467559/16985706421975151872*ep^6; Fill mncpoch(24,3) = 1/63756+1451/677471256*ep+1404085/7198809566256*ep^2+ 1132629695/76494550451036256*ep^3+822573543661/812831093092711256256*ep^4 +557760756086951/8637143195203149808976256*ep^5+360314213411765845/ 91778283592228669870181696256*ep^6; Fill mncpoch(24,4) = 1/5100480+19823/541977004800*ep+245728099/ 57590476530048000*ep^2+2438183084987/6119564036082900480000*ep^3+ 21179802167145931/650264874474169005004800000*ep^4+168304364522741431403/ 69097145561625198471810048000000*ep^5+1254515302121091070044139/734226268\ 7378293589614535700480000000*ep^6; Fill mncpoch(24,5) = 1/484545600+482897/978268493664000*ep+140020478959/ 1975065392597996160000*ep^2+31602073874109173/ 3987538523731798367270400000*ep^3+6118209368087465596831/ 8050601027103076995616901376000000*ep^4+1066859196143369629874798957/ 16253680437659486269530786864061440000000*ep^5+ 172384235798462354941955365312279/328152055828082432090064868313282036736\ 00000000*ep^6; Fill mncpoch(24,6) = 1/52330924800+1785181/316958991947136000*ep+1860879865321/ 1919763561605252267520000*ep^2+1479423460482810961/ 11627662335201924038960486400000*ep^3+993386159032945773610201/7042665778\ 5097717557656653237248000000*ep^4+593511293315834743421672681041/ 426561589405935557657565970460428431360000000*ep^5+ 325378722984924289566644101756137481/258360676594565860433149872120413213\ 1629875200000000*ep^6; Fill mncpoch(24,7) = 1/6227380051200+36404897/641208040709056128000*ep+ 758292189325309/66022588647166230732280320000*ep^2+ 11861246759501368308773/6798077901288799283606131492300800000*ep^3+ 154810041986473741557640079581/699970481299428429707831918868354634752000\ 000*ep^4+1780357722898055058631611494692623557/72073118579248069727590838\ 888283871220596346880000000*ep^5+1863715764038389383941196923786596583363\ 2429/7421076403243741992686934661520703787067650217065267200000000*ep^6; Fill mncpoch(24,8) = 1/797104646553600+171361073/328298516843036737536000*ep+ 16543763519418349/135214261549396440539710095360000*ep^2+ 1184980833086742211269737/55689854167357843731301429184928153600000*ep^3+ 70134537088727156169022626312181/2293663273121967078466623631747824467155\ 3536000000*ep^4+3628453442699022139656323570440859051153/9446767798419202\ 995334786434765143568626004378255360000000*ep^5+1697395775634476670888625\ 84341948812706927611389/3890781305303855001861847599819366747114124197004\ 714809753600000000*ep^6; Fill mncpoch(24,9) = 1/107609127284736000+198818657/44320299773809959567360000* ep+22002843494763037/18253925309168519472860862873600000*ep^2+ 357825151316610371958469/1503626062518661780745138587993060147200000*ep^3 +119259607836669855585627161706661/30964454187146555559299419028595630306\ 59727360000000*ep^4+6903034142681442979666550555683086818177/ 1275313652786592404370196168693294381764510591064473600000000*ep^5+ 359280217390991372944267188214863846396315315757/525255476216020425251349\ 425975614510860406766595636499316736000000000*ep^6; Fill mncpoch(24,10) = 1/15065277819863040000+228237497/ 6204841968333394339430400000*ep+28717325901006517/25555495432835927262005\ 20802304000000*ep^2+21071649379940947378981/84203059501045059721727760927\ 61136824320000*ep^3+196747543042242598134459836961661/4335023586200517778\ 30191866400338824292361830400000000*ep^4+18130169474048987450526461408120\ 39701631/25506273055731848087403923373865887635290211821289472000000000* ep^5+732638205841943292722599306967031908787826212037/7353576667024285953\ 5188919636586031520456947323389109904343040000000000*ep^6; Fill mncpoch(24,11) = 1/2154334728240414720000+3378951221/ 11534801219131780077001113600000*ep+6244895632007752333/61759965812534585\ 414087986229280768000000*ep^2+1671769581354514379794161841/66135398516257\ 068644587330945971477930835968000000*ep^3+9062013104980971772498765012875\ 910621/1770520303630263732204959715165191033967822912041779200000000*ep^4 +172335475525640556140878182826187623680668309/19346471310864340646915064\ 0534164077648726090334281509371904000000000*ep^5+701426279533928095997606\ 2564219524317198928014517610093/50756863355173442122396554242307476629063\ 214675787646664922913811988480000000000*ep^6; Fill mncpoch(24,12) = 1/310224200866619719680000+3825136961/ 1661011375554976331088160358400000*ep+7951617197552888473/889343507700498\ 0299628670017016430592000000*ep^2+476269844410377345257351369/ 1904699477268203576964115131243978564408075878400000*ep^3+143746334291791\ 98759320935288307862121/2549549237227579774375141989837875088913664993340\ 16204800000000*ep^4+2122599250654777948848246338226992909804157383/ 195012430813512553720903845658437390269915899056955761446879232000000000* ep^5+13643777416977214045473821145088232153248976533589839033/ 7308988323144975665625103810892276634585102913313421119748899588926341120\ 000000000*ep^6; Fill mncpoch(24,13) = 1/44362060723926619914240000+4311885041/ 237524626704361615345606931251200000*ep+10050418962440359753/127176121601\ 1712182846899812433349574656000000*ep^2+3359753648684574171143161693/ 1361860126246765557529342318839444673551774253056000000*ep^3+225514016180\ 30253776428562084294359321/3645855409235439077356453045468161377146540940\ 4764317286400000000*ep^4+3690720884781223578503868031325718274707993623/ 27886777606332295182089249929156546808597973565144673886903730176000000000 *ep^5+26218936548359346623686230402836444727094175730122295913/ 1045185330209731520184389844957595558745669716603819220124092641216466780\ 160000000000*ep^6; Fill mncpoch(24,14) = 1/6210688501349726787993600000+4847307929/332534477386106\ 26148384970375168000000*ep+2529155714562167741/35609314048327941119713194\ 748133788090368000000*ep^2+4713921505577153678569817701/19066041767454717\ 8054107924637522254297248395427840000000*ep^3+351711089496373924234269395\ 99809061761/5104197572929614708299034263655425928005157316667004420096000\ 000000*ep^4+6380923274492294893381092439544480002800134447/ 3904148864886521325492494990081916553203716299120254344166522224640000000\ 000*ep^5+10026876624500983096523705318573508187999329647385891293/ 2926518924587248256516291565881267564487875206490693816347459395406106984\ 4480000000000*ep^6; Fill mncpoch(24,15) = 1/838442947682213116379136000000+67187929/554224128976843\ 76913974950625280000000*ep+3176686904272708877/48072573965242720511612812\ 90998061392199680000000*ep^2+2201259345028485791562745447/857971879535462\ 3012434856608688501443376177794252800000000*ep^3+548145195455063975031851\ 26273835577361/6890666723454979856203696255934825002806962377500455967129\ 60000000000*ep^4+525689833625766746802209008898805349096106467/ 2509809984569906566388032493624089212773817620863020649821335715840000000\ 0000*ep^5+19221444675631136160905686721164566140253589775195370029/ 3950800548192785146296993613939711212058631528762436652069070183798244429\ 004800000000000*ep^6; Fill mncpoch(24,16) = 1/107320697303323278896529408000000+679055651/63846619658\ 132402204899143120322560000000*ep+159789850570310963/24613157870204272901\ 945760209910074328062361600000*ep^2+3092458754043531029766090697/ 1098204005805391745591661645912128184752150757664358400000000*ep^3+ 85860266991335192409590893376166944911/8820053406022374215940731207596576\ 0035929118432005836379258880000000000*ep^4+641623074710368625713801276645\ 6362206433728779/22487897461746362834836771142871839346453405882932665022\ 399168013926400000000000*ep^5+3725727785824656614993010012364847477760328\ 5803365062227/50570247016867649872601518258428303514350483568159189146484\ 0983526175286912614400000000000*ep^6; Fill mncpoch(24,17) = 1/12771162979095470188686999552000000+254681137/253258257\ 9772585287460999343772794880000000*ep+5046682540564893707/732241446638577\ 11883288636624482471125985525760000000*ep^2+4379177487704689382154169657/ 130686276690841617725407735863543253985505940162058649600000000*ep^3+ 2777634541017669792674998339597973839/21420129700340051667284632932734541\ 7230113573334871316921057280000000000*ep^4+113735944396378036552193756210\ 65535245853152219/2676059797947817177345575766001748882227955300068987137\ 665500993657241600000000000*ep^5+7379537454911625319225718633517468988920\ 6194513368593059/60178593950072503348395806727529681182077075446109435084\ 316077039614859142601113600000000000*ep^6; Fill mncpoch(24,18) = 1/1379285601742310780378195951616000000+2589587393/ 2461670267538952899412091362147156623360000000*ep+6433206901253344691/ 7908207623696632883395172755444106881606436782080000000*ep^2+ 6292780942243909734440107217/14114117882610894714344035473262671430434641\ 537502334156800000000*ep^3+31476652307293671943100828624170755073/ 1619361805345707906046718249714731354259658614411627155923193036800000000\ 00*ep^4+6912183347090942199128609899086025134974441633/ 9633815272612141838444072757606295976020639080248353695595803577166069760\ 0000000000*ep^5+151515139120899965281125925642649280791586906765262811243/ 6499288146607830361626747126573205567664324148179818989106136320278404787\ 400920268800000000000*ep^6; Fill mncpoch(24,19) = 1/131032132165519524135928615403520000000+589307197/ 46771735083240105088829735880795975843840000000*ep+8326378269274894307/ 751279724251180123922541411767190153752611494297600000000*ep^2+ 9264869941920980118272572961/13408411988480349978626833699599537858912909\ 46062721744896000000000*ep^3+52736466969783915269026896849753603793/ 1538393715078422510744382337228994786546675683691045798127033384960000000\ 0000*ep^4+2637383844879446779794152115860457321717368957/ 1830424901796306949304373823945196235443921425247187202163202679661553254\ 400000000000*ep^5+3294417141696270385227662320371991804801139164117922760\ 59/6174323739277438843545409770244545289281107940770828039650829504264484\ 54803087425536000000000000*ep^6; Fill mncpoch(24,20) = 1/10482570573241561930874289232281600000000+135708869/ 748347761331841681421275774092735613501440000000*ep+11051189565544657007/ 60102377940094409913803312941375212300208919543808000000000*ep^2+ 14195753136103801407987053141/1072672959078427998290146695967963028713032\ 75685017739591680000000000*ep^3+93454669513361171077828116096344806693/ 1230714972062738008595505869783195829237340546952836638501626707968000000\ 000000*ep^4+1083451980619549276020528230815471715936449229/ 2928679842874091118886998118312313976710274280395499523461124287458485207\ 0400000000000*ep^5+786274392591830331840127275482340168697958717053828040\ 759/493945899142195107483632781619563623142488635261666243172066360341158\ 76384246994042880000000000000*ep^6; Fill mncpoch(24,21) = 1/660401946114218401645080221633740800000000+265842403/ 78576514939843376549233956279737239417651200000000*ep+ 15321332780558252927/3786449810225947824569608715306638374913161931259904\ 000000000*ep^2+23310633408743323668441267781/6757839642194096389227924184\ 598167080892106368156117594275840000000000*ep^3+1826050028049228482869393\ 87908376031893/7753504323995249454151686979634133724195245445802870822560\ 2482601984000000000000*ep^4+379786459237509929285254656299776256026312199\ 87/2767602451516016107348213221805136707991209194973747049670762451648268\ 5206528000000000000*ep^5+220969893238952324170623504272265534598600709136\ 2028412679/31118591645958291771468865242032508257976784021484973319840180\ 70149300212207560624701440000000000000*ep^6; Fill mncpoch(24,22) = 1/29057685629025609672383529751884595200000000+65066767/ 691473331470621713633258815261687706875330560000000*ep+ 23159935948049949527/1666037916499417042810627834734920884961791249754357\ 76000000000*ep^2+43977899727409860241775557741/29734494425654024112602866\ 4122319351559252680198869174148136960000000000*ep^3+434891867950182135397\ 594895481557917693/341154190255790975982674227103901883864590799615326316\ 1926509234487296000000000000*ep^4+231191331784569425230775789388484511892\ 23067823/2435490157334094174466427635188520303032264091576897403710270957\ 45047629817446400000000000*ep^5+87084182859841919051182421235529172392679\ 53052617558145279/1369218032422164837944630070649430363350978496945338826\ 07296795086569209337132667486863360000000000000*ep^6; Fill mncpoch(25,0) = 1; Fill mncpoch(25,1) = 1/24+1/576*ep+1/13824*ep^2+1/331776*ep^3+1/7962624*ep^4+1/ 191102976*ep^5+1/4586471424*ep^6; Fill mncpoch(25,2) = 1/1104+47/609408*ep+1657/336393216*ep^2+51935/185689055232 *ep^3+1526281/102500358488064*ep^4+43067087/56580197885411328*ep^5+ 1181645977/31232269232747053056*ep^6; Fill mncpoch(25,3) = 1/72864+793/442430208*ep+419365/2686436222976*ep^2+ 184870225/16312040745910272*ep^3+73370462221/99046711409167171584*ep^4+ 27186245001433/601411631676463065858048*ep^5+9596761549055605/ 3651771427539483735890067456*ep^6; Fill mncpoch(25,4) = 1/6120576+2525/86716320768*ep+35880685/11057371493769216* ep^2+45344331205/156660839323722252288*ep^3+451493258869381/ 19976136943846471833747456*ep^4+152304619521190175/ 94340636073472270980177985536*ep^5+3903430348682843100445/ 36088689561001788651673365874999296*ep^6; Fill mncpoch(25,5) = 1/612057600+5389/14452720128000*ep+1412388751/ 27643428734423040000*ep^2+10670722356667/1958260491546528153600000*ep^3+ 622344574079193751/1248508558990404489609216000000*ep^4+ 3632200289399662156667/88444346318880254043916861440000000*ep^5+ 176778380023651853674683751/56388577439065294768239634179686400000000* ep^6; Fill mncpoch(25,6) = 1/69774566400+378013/93913775391744000*ep+750878307391/ 1137637666136445788160000*ep^2+126382703939957393/ 1531214793113010573031833600000*ep^3+161681123962533844305151/18548584766\ 445489397901340770304000000*ep^4+757302900958818948038440699/924653820453\ 517441111084763822161920000000*ep^5+21352997643418726723216067267649511/ 302424934651160769414203782637520725055897600000000*ep^6; Fill mncpoch(25,7) = 1/8791595366400+4075097/106498221294237696000*ep+ 9500363545579/1290081113398729523773440000*ep^2+16630553678040304253/ 15627578178511385908362893721600000*ep^3+24288201055212805344901171/ 189306856126342664794981083901722624000000*ep^4+ 31251466545709547095252218337997/2293195104646309557967074657195263246991\ 360000000*ep^5+36597947237983862785387350935221714579/2777893994744772131\ 3772274250386828679284418150400000000*ep^6; Fill mncpoch(25,8) = 1/1195656969830400+81390289/246223887632277553152000*ep+ 3731537725114291/50705348081023665202391285760000*ep^2+ 126908414868665494824229/10441847656379595699619017972174028800000*ep^3+ 3565897691022089799934064086651/21503093185518441360624596547635854379581\ 44000000*ep^4+87568614441064348294096805055352426069/44281724055090014040\ 6318114129616104779343955230720000000*ep^5+194416014735304964093812219651\ 6848028475399611/91190186843059101606137053120766408135487285867298003353\ 600000000*ep^6; Fill mncpoch(25,9) = 1/172174603655577600+188522063/70912479638095935307776000* ep+19778988757340719/29206280494669631156577380597760000*ep^2+ 1524407861361578716621547/12029008500149294245961108703944481177600000* ep^3+96294885153474594909177828163711/49543126699434488894879070445753008\ 49055563776000000*ep^4+5280969003868948128146775187780021885043/ 2040501844458547846992313869909271010823216945703157760000000*ep^5+ 260366233829152647226508111871689890475931683959/840408761945632680402159\ 081560983217376650826553018398906777600000000*ep^6; Fill mncpoch(25,10) = 1/25826190548336640000+215979647/ 10636871945714390296166400000*ep+25709268057133567/4380942074200444673486\ 607089664000000*ep^2+89212889944753617269747/7217405100089576547576665222\ 3666887065600000*ep^3+157534145641995290046376050944911/74314690049151733\ 3423186056686295127358334566400000000*ep^4+960647604070226773219950950218\ 8195040067/306075276668782177048847080486390651623482541855473664000000000 *ep^5+524136856660722582473865648786820439596954702087/126061314291844902\ 060323862234147482606497623982952759836016640000000000*ep^6; Fill mncpoch(25,11) = 1/3977233344443842560000+245398487/ 1638078279640016105609625600000*ep+32928606882428647/67466507942686847971\ 6937491808256000000*ep^2+639808733183181521850631/55574019270689739416340\ 322212223503040512000000*ep^3+251646299402588829457777137385111/ 114444622675693669347170652729689449613183523225600000000*ep^4+2429945465\ 631303441686448837511256275901/673365608671320789507463577070059433571661\ 5920820420608000000000*ep^5+102454009469565228707082642841932796565504632\ 5967/19413442400944114917289874784058712321400634093374725014746562560000\ 000000*ep^6; Fill mncpoch(25,12) = 1/620448401733239439360000+3602044091/ 3322022751109952662176320716800000*ep+7048485986135483503/177868701540099\ 60599257340034032861184000000*ep^2+1986262974914863424498546563/ 19046994772682035769641151312439785644080758784000000*ep^3+11277618643223\ 446207645810330717439671/509909847445515954875028397967575017782732998668\ 032409600000000*ep^4+1565770658662658845236764389805513762229713273/ 390024861627025107441807691316874780539831798113911522893758464000000000* ep^5+9459448685359181425279351744868099966481198347972254663/ 1461797664628995133125020762178455326917020582662684223949779917785268224\ 0000000000*ep^6; Fill mncpoch(25,13) = 1/96789950670385352540160000+4048229831/ 518235549173152615299506031820800000*ep+8854748408970293443/2774751744025\ 553853484145045309126344704000000*ep^2+2776435469188910028074967127/ 2971331184538397580064019604740606560476598370304000000*ep^3+174716482151\ 34951310996060245898284571/7954593620150048896050443008294170277410634779\ 2213055897600000000*ep^4+2679427842646897052459728286648472057378601493/ 60843878413815916760921999845432465764213760505770197571426320384000000000 *ep^5+17828106148595246665668290545308364340016754719207423403/ 2280404356821232407675032388998390309990552108953787389361656671745018429\ 440000000000*ep^6; Fill mncpoch(25,14) = 1/14905652403239344291184640000+4534977911/79808274572665\ 502756123928900403200000*ep+11062140199991954323/427311768579935293436558\ 336977605457084416000000*ep^2+770666113959257996901711419/915170004837826\ 45465971803826010682062679229805363200000*ep^3+26849654497403202016409909\ 793706422571/122500741750310752999176822327730222272123775600008106082304\ 00000000*ep^4+4546430381971807562079678584514157381679017733/ 9369957275727651181181987976196599727688919117888610425999653339136000000\ 000*ep^5+33318869963544354280470641051514051208467378123973341883/ 3511822709504697907819549879057521077385450247788832579616951274487328381\ 33760000000000*ep^6; Fill mncpoch(25,15) = 1/2235847860485901643677696000000+5070400799/119712411858\ 99825413418589335060480000000*ep+2755389767822008367/12819353057398058803\ 096750109328163712532480000000*ep^2+5328629316849199174327860991/ 68637750362836984099478852869508011547009422354022400000000*ep^3+41115004\ 986947528428439103747025232611/183751112625466129498765233491595333408185\ 6634000121591234560000000000*ep^4+769127534057835727288210233599471044645\ 8074957/14054935913591476771772981964294899591533378676832915638999480008\ 70400000000000*ep^5+12429092790066777553973403253052578149646368234951050\ 519/105354681285140937234586496371725632321563507433664977388508538234619\ 85144012800000000000*ep^6; Fill mncpoch(25,16) = 1/321962091909969836689588224000000+1888438373/5746195769\ 23191619844092288082903040000000*ep+3429465186143129183/18459868402653204\ 67645932015743255574604677120000000*ep^2+2456289088675737431634820517/ 3294612017416175236774984937736384554256452272993075200000000*ep^3+ 63034228280641718948032739789921784211/2646016021806712264782219362278972\ 80107787355296017509137776640000000000*ep^4+16109152105529318924475260860\ 9913993354991757/24986552735273736483151967936524265940503784314369627802\ 66574223769600000000000*ep^5+46593711613939502650130113604063517869235845\ 39868392347/3034214821012058992356091095505698210861029014089551348789045\ 90115705172147568640000000000*ep^6; Fill mncpoch(25,17) = 1/43786844499755897789783998464000000+2111531243/ 78148262461554060298796551179274813440000000*ep+4277386803315096521/ 251054210276083583599846754141082758146236088320000000*ep^2+ 3410543586727427828831725787/44806723436859983220139795153214829937887750\ 9127058227200000000*ep^3+97273286346681929140369970169289525261/ 35985817896571286801038183326994030094659080320258381242737623040000000000 *ep^4+2483203528803023776967619644483568133119401483/30583540547975053455\ 37800875430570151117663200078842443046286849893990400000000000*ep^5+ 44237488883884973562362621784456832699095967355376612473/ 2063266078288200114802141944943874783385499729580894917176551212786795170\ 60346675200000000000*ep^6; Fill mncpoch(25,18) = 1/5517142406969243121512783806464000000+2366494523/ 9846681070155811597648365448588626493440000000*ep+5363451373550104313/ 31632830494786531533580691021776427526425747128320000000*ep^2+ 4778026741048267668816352427/56456471530443578857376141893050685721738566\ 150009336627200000000*ep^3+21727606855546270354648808875480592923/ 6477447221382831624186872998858925417038634457646508623692772147200000000\ 00*ep^4+1443261388538848290254542499159594216372341321/ 1284508703014952245125876367680839463469418544033113826079440476955475968\ 00000000000*ep^5+17193253729312885431501577877094055628791492903920117013/ 5199430517286264289301397701258564454131459318543855191284909056222723829\ 920736215040000000000*ep^6; Fill mncpoch(25,19) = 1/628954234394493715852457353936896000000+2663951683/ 1122521641997762522131913661139103420252160000000*ep+6789792077154424817/ 3606142676405664594828198776482512738012535172628480000000*ep^2+ 755299889923235972923854683/715115306052285332193431130645308685808688504\ 566784930611200000000*ep^3+34726334124542805805918168540400809123/ 7384289832376428051573035218699174975424043281717019831009760247808000000\ 0000*ep^4+23318949222747223925750812098865317890780742569/ 1317905929293341003499149153240541289519623426177974785557505929356318343\ 16800000000000*ep^5+17336476261234514465566527106170894834079672084715021\ 9969/29636753948531706449017966897173817388549318115699974590323981620469\ 52583054819642572800000000000*ep^6; Fill mncpoch(25,20) = 1/62895423439449371585245735393689600000000+120836011/ 4490086567991050088527654644556413681008640000000*ep+8730743056675017857/ 360614267640566459482819877648251273801253517262848000000000*ep^2+ 3304708483501015860648566497/21453459181568559965802933919359260574260655\ 1370035479183360000000000*ep^3+8210853659038345394188381065354003349/ 1054898547482346864510433602671310710774863325959574261572822892544000000\ 000000*ep^4+1753396711669188886520296213085132729188103393/ 5271623717173364013996596612962165158078493704711899142230023717425273372\ 67200000000000*ep^5+37051459615838543164568753755706503104309212577090860\ 6609/29636753948531706449017966897173817388549318115699974590323981620469\ 5258305481964257280000000000000*ep^6; Fill mncpoch(25,21) = 1/5283215568913747213160641773069926400000000+693417203/ 1885836358556241037181614950713693746023628800000000*ep+ 11515278867318584837/3029159848180758259655686972245310699930529545007923\ 2000000000*ep^2+1672453185913772463688369319/6006968570839196790424821497\ 420592960792983438360993417134080000000000*ep^3+1006504082933797217415300\ 05824118163343/6202803459196199563321349583707306979356196356642296658048\ 19860815872000000000000*ep^4+17748738939482698081849211941593358157667982\ 729/221408196121281288587857057744410936639296735597899763973660996131861\ 481652224000000000000*ep^5+8694263518785193118790152230673951962289320353\ 10411927589/2489487331676663341717509219362600660638142721718797865587214\ 4561194401697660484997611520000000000000*ep^6; Fill mncpoch(25,22) = 1/348692227548307316068602357022615142400000000+812400067/ 124465199664711908453986586747103787237559500800000000*ep+ 15865054768163919797/1999245499799300451372753401681905061954149499705229\ 312000000000*ep^2+24490426942388948167762116911/3568139331078482893512343\ 969467832218711032162386430089777643520000000000*ep^3+2775897171726536866\ 4367042804956940649/58483575472421310168458438932097465805358422791198797\ 06159730116263936000000000000*ep^4+13622877545263106921254976814201316507\ 780084627/487098031466818834893285527037704060606452818315379480742054191\ 4900952596348928000000000000*ep^5+240116644389109523168155215981626393880\ 8446385083687910549/16430616389065978055335560847793164360211741963344065\ 91287561541038830512045592009842360320000000000000*ep^6; Fill mncpoch(25,23) = 1/16039842467222136539155708423040296550400000000+ 990874363/5725399184576747788883382990366774212927737036800000000*ep+ 23823106964403224957/9196529299076782076314665647736763284989087698644054\ 8352000000000*ep^2+45749488162411761339413143271/164134409229610213101567\ 822595520282060707479469775784129771601920000000000*ep^3+4567626921255752\ 76738233586013090584343/1883171130211966187424361733613538398932541213876\ 601265383433097436987392000000000000*ep^4+4079634418398870395820878199661\ 5246116061933803/22406509447473666405091134243734386787896829642507456114\ 1344928085443819432050688000000000000*ep^5+928180481708356432997612302934\ 7158448400635476938819075709/75580835389703499054543579899848556056974013\ 031382703199227830887786203554097232452748574720000000000000*ep^6; Fill mncpoch(26,0) = 1; Fill mncpoch(26,1) = 1/25+1/625*ep+1/15625*ep^2+1/390625*ep^3+1/9765625*ep^4+1/ 244140625*ep^5+1/6103515625*ep^6; Fill mncpoch(26,2) = 1/1200+49/720000*ep+1801/432000000*ep^2+58849/259200000000 *ep^3+1803001/155520000000000*ep^4+53037649/93312000000000000*ep^5+ 1517044201/55987200000000000000*ep^6; Fill mncpoch(26,3) = 1/82800+1727/1142640000*ep+1988929/15768432000000*ep^2+ 1909373183/217604361600000000*ep^3+1650177512641/3002940190080000000000* ep^4+1331475008462207/41440574623104000000000000*ep^5+1023461992024653889/ 571879929798835200000000000000*ep^6; Fill mncpoch(26,4) = 1/7286400+25897/1106075520000*ep+419349709/ 167902263936000000*ep^2+5434888698673/25487563665484800000000*ep^3+ 61660980983420581/3869012164420592640000000000*ep^4+639896150373448908457/ 587316046559045962752000000000000*ep^5+6228408787629985336604029/89154575\ 867663177145753600000000000000*ep^6; Fill mncpoch(26,5) = 1/765072000+77293/270988502400000*ep+32281213141/ 863857147950720000000*ep^2+43180200105919/11332525992746112000000000*ep^3 +325026383495312428381/975397311711253507507200000000000*ep^4+ 9067023201396454893505133/345485727808125992359050240000000000000*ep^5+ 2109140187427861997700206597221/11013394031067440384421803550720000000000\ 00000*ep^6; Fill mncpoch(26,6) = 1/91808640000+95003/32518620288000000*ep+47423741311/ 103662857754086400000000*ep^2+2005739861477623/ 36717384216497402880000000000*ep^3+644721260016230758351/ 117047677405350420900864000000000000*ep^4+6828345572094633874633781/ 13819429112325039694362009600000000000000*ep^5+ 5374250189636353077533841657991/13216072837280928461306164260864000000000\ 0000000*ep^6; Fill mncpoch(26,7) = 1/12210549120000+2159257/82174553467776000000*ep+ 24003250077871/4977164789346950323200000000*ep^2+7419773629152308119/ 11165107866449035428357120000000000*ep^3+154978982451610392124305271/ 2028751458829975402895459146752000000000000*ep^4+ 105616534512514253417469418489157/136530915676339684664058609658116096000\ 00000000000*ep^5+589520723604852237203849900374421969671/8269431806867677\ 28866963468149470732574720000000000000000*ep^6; Fill mncpoch(26,8) = 1/1758319073280000+22798213/106498221294237696000000*ep+ 292742957624539/6450405566993647618867200000000*ep^2+ 2788055769994822154017/390689454462784647709072343040000000000*ep^3+ 21934826439036018828120530251/2366335701579283309937263548771532800000000\ 0000*ep^4+150802951144335190496077978320185353/14332469404039434737294216\ 60747039529369600000000000000*ep^5+93719745781351076342185936662254531019\ 9859/86809187335774129105538357032458839622763806720000000000000000*ep^6; Fill mncpoch(26,9) = 1/269022818211840000+448137821/277001873586312247296000000 *ep+111745615923383971/285217582955758116763450982400000000*ep^2+ 20465948812355266275007721/293676965335676129051784880467394560000000000* ep^3+3071604319871223567341377454165971/302387247921353081633783388951129\ 202212864000000000000*ep^4+400160170569766573843635807983178779476721/ 311355872262351661223192423997386323672976218521600000000000000*ep^5+ 46858649547701940982213908915234753331677433274971/3205905006201296540840\ 75577377694403601322489377219543040000000000000000*ep^6; Fill mncpoch(26,10) = 1/43043650913894400000+1024983067/ 88640599547619919134720000000*ep+578905394915708359/182539253091685194728\ 608628736000000000*ep^2+238237013197051045137927343/375906515629665445186\ 284646998265036800000000000*ep^3+79808541626223034690723437421277311/ 774111354678663888982485475714890757664931840000000000000*ep^4+2307707734\ 3949009633725030873102963852989247/15941420659832405054627452108666179772\ 05638238830592000000000000000*ep^5+59691447725184405841186320522976084506\ 13680263657119/3282846726350127657820933912347590692877542291222728120729\ 600000000000000000*ep^6; Fill mncpoch(26,11) = 1/7102202400792576000000+1162270987/ 14625698925357286657228800000000*ep+738471161197285399/301189767601280571\ 30220423741440000000000*ep^2+339620182897811067213007423/6202457507889479\ 8455736966754713731072000000000000*ep^3+ 126434290126283088661377423469507471/127728373521979541682110103492956975\ 014713753600000000000000*ep^4+40434978052062952207221121676190827971039567 /263033440887234683401352959792991966238930309407047680000000000000000* ep^5+11520378804531815001707428827288760745835522654787759/ 5416697098477710635404540955373524643247944780517501399203840000000000000\ 00000*ep^6; Fill mncpoch(26,12) = 1/1193170003333152768000000+1309365187/ 2457117419460024158414438400000000*ep+931071185886900799/5059988095701513\ 597877031188561920000000000*ep^2+476575354128896030721273223/104201286132\ 54326140563810414791906820096000000000000*ep^3+ 196535760581589747183498531188114071/214583667516925630025944973868167718\ 02471910604800000000000000*ep^4+99063212180290615424828701889259309647896\ 81/6312802581293632401632471035031807189734327425769144320000000000000000 *ep^5+21720515566094887692103415456296121467482286719439159/ 9100051125442553867479628805027521400656547231269402350662451200000000000\ 0000000*ep^6; Fill mncpoch(26,13) = 1/201645730563302817792000000+19081066231/539828697055367\ 3076036521164800000000*ep+196645028828429677831/1445183200013309298689658\ 87776516997120000000000*ep^2+1451990857814111789529958793731/ 3868920813201038515708358860339331458953904128000000000000*ep^3+860336992\ 8895512082788588856419296424631/10357543776237042833399014333716367548711\ 7640354444083200000000000000*ep^4+887022765427935544872762116426385461428\ 224215419/565884285842781963922265623562429927122523814227773414912819200\ 00000000000000*ep^5+19434725020588004669072540373513680120586174077192163\ 9896431/74231912656941159104004960579374684570004951463339433247449761450\ 033152000000000000000000*ep^6; Fill mncpoch(26,14) = 1/33876482734634873389056000000+21311994931/9069122110530\ 17076774135555686400000000*ep+244190569974252097531/242790777602235962179\ 86269146454855516160000000000*ep^2+1996762608639029054947065833431/ 649978696617774470639004288537007685104255893504000000000000*ep^3+ 13058004939595189941603875005009933794331/1740067354407823196011034408064\ 3497481835763579546605977600000000000000*ep^4+103707990700647881887772503\ 54968884670979415965033/6654799201511115895725843733094175942960880055318\ 6153593747537920000000000000000*ep^5+356302843217265974499074703803033708\ 142207994071333852926131/124709613263661147294728333773349470077608318458\ 41024785571559923605569536000000000000000000*ep^6; Fill mncpoch(26,15) = 1/5589619651214754109194240000000+23745735331/14964051482\ 3747817667732366688256000000000*ep+301981525377014169931/4006047830436893\ 375967734409165051160166400000000000*ep^2+2731707247002693671680605745831/ 107246484941932787655435707608606268042202222428160000000000000*ep^3+ 19706271227598424439197301105110970066731/2871111134772908273418206773306\ 177084502900990625189986304000000000000000*ep^4+1722222027291677112220893\ 8250750772433064263198233/10980418682493341227947642159605390305885452091\ 275715342968343756800000000000000000*ep^5+6497037360085419765227873156367\ 36104553091546063743877918531/2057708618850408930363017507260266256280537\ 254563769089619307387394918973440000000000000000000*ep^6; Fill mncpoch(26,16) = 1/894339144194360657471078400000000+26422849771/ 23942482371799650826837178670120960000000000*ep+372718518044908963171/ 640967652869902940154837505466408185626624000000000000*ep^2+ 3729517373716120025471118035071/17159437590709246024869713217377002886752\ 355588505600000000000000*ep^3+29690616043004725820159198999743970591971/ 4593777815636653237469130837289883335204641585000303978086400000000000000\ 00*ep^4+28577245550234430048121657499471935286592964935553/ 1756866989198934596471622745536862448941672334604114454874935001088000000\ 000000000000*ep^5+1185235633034250342991762004816730376866476499883422117\ 715771/329233379016065428858082801161642601004885960730203054339089181983\ 187035750400000000000000000000*ep^6; Fill mncpoch(26,17) = 1/136833889061737180593074995200000000+9799140457/ 1221066600961782192168696112176168960000000000*ep+460163252768318626771/ 98068050889095149843690138336360452400873472000000000000*ep^2+ 1699435305588127330805044779557/87513131712617154726835537408622714722437\ 0135013785600000000000000*ep^3+44855892031124020386348673013739508935571/ 7028480057924079453327770181053521502863101625050465086472192000000000000\ 0000*ep^4+756162769569362443210669825262266440099425126831/ 4266676973768841162859655239160951661715489955467135104696270716928000000\ 000000000000*ep^5+2177159425042471404365114438944856611086083860825091872\ 139371/503727069894580106152866685777313179537475519917210673138806448434\ 27616469811200000000000000000000*ep^6; Fill mncpoch(26,18) = 1/19704080024890154005402799308800000000+10914604807/ 175833590538496635672292240153368330240000000000*ep+569736925777242800821/ 14121799328029701577491379920435905145725779968000000000000*ep^2+ 2334956535171237716415021010907/12601890966616870280664317386841670920030\ 9299441985126400000000000000*ep^3+682969389951713517486759646932489859246\ 21/1012101128341067441279198906071707096412286634007266972451995648000000\ 0000000000*ep^4+2973630599840234034427407343344938034399714387389/ 1433603463186330630720844160358079758336404625036957395177946960887808000\ 000000000000000*ep^5+4057886475058709867886387068306376380984302373786424\ 191718421/725366980648195352860128027519330978533964748680783369319881285\ 7453576771652812800000000000000000000*ep^6; Fill mncpoch(26,19) = 1/2620642643310390482718572308070400000000+12189421207/ 23385867541620052544414867940397987921920000000000*ep+ 709590392327965354021/187819931062795030980635352941797538438152873574400\ 0000000000*ep^2+3239554004593362128352797755307/1676051498560043747328354\ 2124499422323641136825784021811200000000000000*ep^3+215235649303761208367\ 2314872905835543629/27471316340686116263292541736232049759762065780197246\ 395125596160000000000000000*ep^4+1532323029678598073919071355723812198554\ 8527498567/57200778181134592165761681998287382357622544538974600067600083\ 7394235392000000000000000000*ep^5+774987017360612098426682705432511124072\ 3711459629995742391621/96473808426209981930397027660071020145017311574544\ 1881195442110041325710629824102400000000000000000000*ep^6; Fill mncpoch(26,20) = 1/314477117197246857926228676968448000000000+13676707007/ 2806304104994406305329784152847758550630400000000000*ep+ 892660941428409759421/225383917275354037176762423530157046125783448289280\ 000000000000*ep^2+1522398648998155893373689092369/67042059942401749893134\ 1684979976892945645473031360872448000000000000000*ep^3+237999998941264017\ 47538639935879871037603/2307590572617633766116573505843492179820013525536\ 5686971905500774400000000000000000*ep^4+813670927728936429417815447996614\ 08656703790433101/2059228014520845317967420551938345764874411603403085602\ 43360301461924741120000000000000000000*ep^5+15373885838715783407894487906\ 128927488619806665621594680137021/115768570111451978316476433192085224174\ 020773889453025743453053204959085275578892288000000000000000000000*ep^6; Fill mncpoch(26,21) = 1/33020097305710920082254011081687040000000000+ 15461449967/294661931024412662059627336049014647816192000000000000*ep+ 1141013367248369100301/23665311313912173903560054470666489843207262070374\ 400000000000000*ep^2+27175356055378144046768769169/8690637399940967578739\ 61443492562639003614502077690019840000000000000000*ep^3+38953105974334350\ 937583048967184738055443/242297010124851545442240218113566678881101420181\ 3397132050077581312000000000000000000*ep^4+150888374430720816463802290859\ 179640920599774364381/216218941524688758386579157953526305311813218357323\ 98825552831653502097817600000000000000000000*ep^5+32339594571413381457175\ 551613024900065647013740909894944125901/121556998617024577232300254851689\ 48538272181258392567703062570586520703953935783690240000000000000000000000 *ep^6; Fill mncpoch(26,22) = 1/2905768562902560967238352975188459520000000000+ 17692378667/25930249930148314261247205572313289007824896000000000000*ep+ 1496247285303671486401/20825473956242713035132847934186511062022390621929\ 47200000000000000*ep^2+3313877510845979312582820505589/619468633867792169\ 0125597169214986490817764170809774461419520000000000000000*ep^3+674690574\ 13653368974336864053957492857743/2132213689098693599891713919399386774153\ 69249759578947620406827155456000000000000000000*ep^4+30140703097678788916\ 0339964345151760316983650288481/19027266854172610738018965899910314867439\ 56321544451096648649185508184607948800000000000000000000*ep^5+ 74701903106051405008809495290543173446287848881048034109322001/ 1069701587829816279644242242694867471367951950738545957869506211613821947\ 946348964741120000000000000000000000*ep^6; Fill mncpoch(26,23) = 1/200498030840276706739446355288003706880000000000+ 20666950267/1789187245180233684026057184489616941539917824000000000000*ep +2049525195209147041201/1436957702980747199424166507458869263279544952913\ 13356800000000000000*ep^2+16038091971691522786728986008367/ 1282300072106329789855998614027502203599277183357623313513840640000000000\ 000000*ep^3+128805925424315435942824305210467859314143/ 1471227445478098583925282604385576874166047823341094738580807107372646400\ 0000000000000000*ep^4+76061053183963837150831596268215719705069877380809/ 1458757125486566823248120718993124139837033179850745840763964375556274866\ 0940800000000000000000000*ep^5+202985113700301870879618321648614135688471\ 968146519720361956801/738094095602573232954527147459458555243886846009596\ 71092995928601353714408298078567137280000000000000000000000*ep^6; Fill mncpoch(26,24) = 1/9623905480333281923493425053824177930240000000000+ 25128807667/85880987768651216833250744855501613193916055552000000000000* ep+3058615603188773213401/68973969743075865572359992358025724637418157739\ 83041126400000000000000*ep^2+29685198634534814145864017025767/ 6155040346110382991308793347332010577276530480116591904866435072000000000\ 0000000*ep^3+299100226678847079441271790044939333118743/ 7061891738294873202841356501050768995997029552037254745187874115388702720\ 00000000000000000*ep^4+673030679468121933076970256079066791124185809891827 /210061026070065622547729383535009876136532777898507401070010870080103580\ 7175475200000000000000000000*ep^5+770545861128944906096755593408540894485\ 023792591438763761749001/354285165889235151818173030780540106517065686084\ 6064212463804572864978291598307771222589440000000000000000000000*ep^6; Fill mncpoch(27,0) = 1; Fill mncpoch(27,1) = 1/26+1/676*ep+1/17576*ep^2+1/456976*ep^3+1/11881376*ep^4+1/ 308915776*ep^5+1/8031810176*ep^6; Fill mncpoch(27,2) = 1/1300+51/845000*ep+1951/549250000*ep^2+66351/357012500000 *ep^3+2115751/232058125000000*ep^4+64775151/150837781250000000*ep^5+ 1928294551/98044557812500000000*ep^6; Fill mncpoch(27,3) = 1/93600+937/730080000*ep+585469/5694624000000*ep^2+ 304931953/44418067200000000*ep^3+142975097461/346460924160000000000*ep^4+ 62585037048457/2702395208448000000000000*ep^5+26097993717321709/ 21078682625894400000000000000*ep^6; Fill mncpoch(27,4) = 1/8611200+29351/1544849280000*ep+538650901/ 277145960832000000*ep^2+7911584099951/49719985373260800000000*ep^3+ 101720650228201501/8919765375962987520000000000*ep^4+ 1196239836891548580551/1600205908447759961088000000000000*ep^5+ 13194110428814212819112101/287076939975528137019187200000000000000*ep^6; Fill mncpoch(27,5) = 1/947232000+412561/1869267628800000*ep+102183480721/ 3688812738673920000000*ep^2+19696176657708481/ 7279503058499113728000000000*ep^3+3256039086187548921841/ 14365371335642151030835200000000000*ep^4+484722328002243928735456801/ 28348623793756220844250183680000000000000*ep^5+ 66853764287181816083609527809361/5594317419459852621404331247411200000000\ 0000000*ep^6; Fill mncpoch(27,6) = 1/119351232000+1181909/549564682867200000*ep+7339369775929/ 22774729848572782080000000*ep^2+3861208677400035061/ 104868521060738232365568000000000*ep^3+15437459049917534150717641/ 4345898328686477382754449715200000000000*ep^4+ 2033498747752163074955431856023/66703744814232512522103797195366400000000\ 00000*ep^5+19903997801065009316771725011270876889/82928897110336057333005\ 3690327617138688000000000000000*ep^6; Fill mncpoch(27,7) = 1/16709172480000+470713/25646351867136000000*ep+ 10265420633659/3188462178800189491200000000*ep^2+6224616469887346631/ 14681592948503352531179520000000000*ep^3+28335300098677008484413811/ 608425766016106833585622960128000000000000*ep^4+ 12624132384974896888232887274599/2801557282197765525928359482205388800000\ 000000000*ep^5+46062083791999943911972443746349226819/1161004559544704802\ 66207516645866399416320000000000000000*ep^6; Fill mncpoch(27,8) = 1/2539794216960000+31435241/222199992576866304000000*ep+ 5008537245128299/174957296675123997761126400000000*ep^2+ 65756954965875076117429/15306558997135243241726769807360000000000*ep^3+ 6417744917682501802110114423931/12052179446453728916276219407599845376000\ 000000000*ep^4+20269916607421601669350932274726663967/3514712813678919877\ 29941372600150237449420800000000000000*ep^5+46870724789748628035500492380\ 79512625734783939/8302313317017234641577607667128963648634763470438400000\ 00000000000*ep^6; Fill mncpoch(27,9) = 1/411446663147520000+326660869/323967589177071071232000000 *ep+59366190261429991/255087738552330788735722291200000000*ep^2+ 7923210169174796262818449/200852667160408661817938673412177920000000000* ep^3+866427867009614181252770655859711/1581486986963658308393765510665251\ 71023872000000000000*ep^4+82231068306539502711337312623557654166529/ 124524166160955923900791848663997628226905092915200000000000000*ep^5+ 7013967019853447028541911896771083660725052108831/98048659811310137670103\ 231027259634897646829633183416320000000000000000*ep^6; Fill mncpoch(27,10) = 1/69945932735078400000+6340621373/ 936266332721735395860480000000*ep+22149349290327069199/125324605950760116\ 50586036166656000000000*ep^2+56366832391078817943792373337/16775415613904\ 4918436960559420585120563200000000000*ep^3+116747410389691406825194325895\ 810006631/2245485368849258994781046716676632297544418263040000000000000* ep^4+208681704478062050570517817296140495539085910953/3005710652877538719\ 1141124017648005671632693366920511488000000000000000*ep^5+333613290676623\ 000127023452200462166970359557838689201639/402331569564014322829974715927\ 381454103648908943375598183553433600000000000000000*ep^6; Fill mncpoch(27,11) = 1/12310484161373798400000+14354439271/ 329565749118050859342888960000000*ep+112615195067869010071/88228522589335\ 12202012569461325824000000000*ep^2+639362012178386110356326189971/ 236197851843775245159240467664183849752985600000000000*ep^3+2937736863228\ 945829159580707158927156871/632328679867951332930342755416139654988508182\ 8720640000000000000*ep^4+115932256542170580590196242631518553988554362237\ 71/1692816239700629806605068104673935679426353290424963207004160000000000\ 00000*ep^5+40748995481480705148204381164740948686770416568648868500671/ 4531862799569057332356835200206024699023501310338182737939545876070400000\ 000000000000*ep^6; Fill mncpoch(27,12) = 1/2215887149047283712000000+16139182231/ 59321834841249154681720012800000000*ep+141419486934803353831/158811340660\ 8032196362262503038648320000000000*ep^2+891759445892088375090592469731/ 42515613331879544128663284179553092955537408000000000000*ep^3+45292982562\ 98351476300354979740342500631/1138191623762312399274616959749051378979314\ 729169715200000000000000*ep^4+1967685883088581651595228965874437430484540\ 9031531/30470692314611336518891225884130842229674359227649337726074880000\ 000000000000*ep^5+7586713075481799673890195782906577316694815422599423877\ 2431/81573530392243031982423033603708444582423023586087289282911825769267\ 2000000000000000000*ep^6; Fill mncpoch(27,13) = 1/403291461126605635584000000+18051406831/107965739411073\ 46152073042329600000000*ep+175937831141649596431/289036640002661859737931\ 775553033994240000000000*ep^2+1228192094671796817966022872331/ 7737841626402077031416717720678662917907808256000000000000*ep^3+687787739\ 3255290277816705880374340043231/20715087552474085666798028667432735097423\ 5280708888166400000000000000*ep^4+468984359686463666647631841916583493489\ 6684387733/79223800017989474949117187298740189797153333991888278087794688\ 0000000000000000*ep^5+138643370827357284464788037618999920461290022638607\ 104595031/148463825313882318208009921158749369140009902926678866494899522\ 900066304000000000000000000*ep^6; Fill mncpoch(27,14) = 1/73399045925042225676288000000+20110725631/1964976457281\ 536999677293703987200000000*ep+217352226515209759231/52604668480484458472\ 303583150652186951680000000000*ep^2+1675789620956426761093894715131/ 1408287176005178019717842625163516651059221102592000000000000*ep^3+ 10328862464535733887760471832464252806031/3770145934550283591357241217472\ 7577877310821089017646284800000000000000*ep^4+772847511912646096174235121\ 0803561525098454628133/14418731603274084440739328088370714543081906786523\ 6666119786332160000000000000000*ep^5+250051129584402808916662769851273681\ 950433458905236175197831/270204162071265819138578056508923851834818023326\ 55553702071713167812067328000000000000000000*ep^6; Fill mncpoch(27,15) = 1/13211828266507600621731840000000+22341654331/3536957623\ 10676659941912866717696000000000*ep+267194864367716958931/946884032648720\ 2525014644967117393651302400000000000*ep^2+ 2271882312366973878249783934831/25349169168093204354921167252943299719065\ 9798466560000000000000*ep^3+15397269918217580844898220581477660355731/ 6786262682190510464443034191450964017915947796023176331264000000000000000 *ep^4+12635648170869068669092878192824875938877382825233/ 2595371688589335199333079055906728617754743221574259990156153978880000000\ 0000000000*ep^5+447375740616862973569713504333113730592300452785131862407\ 531/486367491728278474449440501716062933302672441987799966637290837020617\ 2119040000000000000000000*ep^6; Fill mncpoch(27,16) = 1/2325281774905337709424803840000000+24775394731/ 62250454166679092149776664542314496000000000*ep+327491743450498791331/ 1666515897461747644402577514212661282629222400000000000*ep^2+ 3068912199068888186863208407231/44614537735844039664661254365180207505556\ 124530114560000000000000*ep^3+22866205521144376408349960155775397188131/ 1194382232065529841741974017695369667153206812100079034302464000000000000\ 000*ep^4+20585706481085086254494048959896429862134642138433/ 4567854171917229950826219138395842367248348069970697582674831002828800000\ 000000000000*ep^5+7980775992957732453550414439260591787910050144680593559\ 59931/8560067854417701150310152830202707626127034978985279412816318731562\ 86292951040000000000000000000*ep^6; Fill mncpoch(27,17) = 1/395297901733907410602216652800000000+27452509171/ 10582577208335445665462032972193464320000000000*ep+400985252166415320571/ 283307702568497099548438177416152418046967808000000000000*ep^2+ 4142395607870639924601061552471/75844714150934867429924132420806352759445\ 41170119475200000000000000*ep^3+33955872619167444202539973277224328969371/ 2030449794511400730961355830082128434160451580570134358314188800000000000\ 00000*ep^4+33571957468452769919138912836706626176879416683753/ 7765352092259290916404572535272932024322191718950185890547212704808960000\ 00000000000000*ep^5+14272094041207985290147123553733998756636461782680238\ 43813171/1455211535251009195552725981134460296441595946427497500178774184\ 36568669801676800000000000000000000*ep^6; Fill mncpoch(27,18) = 1/64038260080893000517559097753600000000+10142360257/ 571459169250114065934949780498447073280000000000*ep+491492782498738024171/ 45895847816096530126846984741416691723608784896000000000000*ep^2+ 1868125360098787695713410565357/40956145641504828412159031507235430490100\ 5223186451660800000000000000*ep^3+506264905433363254248356316977769571529\ 71/3289328667108469184157396444733048063339931560523617660468985856000000\ 0000000000*ep^4+2040189541042572445984372458059330704337567772539/ 4659211255355574549842743521163759214593315031370111534328327622885376000\ 000000000000000*ep^5+2574191789059827632491797894953274882780315575120010\ 240076771/235744268710663489679541608943782568023538543321254595028961417\ 86724124507871641600000000000000000000*ep^6; Fill mncpoch(27,19) = 1/9733815532295736078668982858547200000000+11257824607/ 86861793726017338022112366635763955138560000000000*ep+ 604512100567689368221/697616886804667257928074168069533714198853530419200\ 0000000000*ep^2+2542437057425659947837958986707/6225334137508733918648172\ 7890997854344952793924340652441600000000000000*ep^3+761504716404313634481\ 60557135680998712021/4999779574004873159919242595994233056276695971995898\ 843912858501120000000000000000*ep^4+1016547987791758422120626854374895720\ 9948671981967/21246003324421419947282910456506742018545516543047708596537\ 17396035731456000000000000000000*ep^5+47173063355026575280617600342410881\ 57963852062082608170225821/3583312884402085043129032455945495033957785858\ 483069844440213551582066925196489523200000000000000000000*ep^6; Fill mncpoch(27,20) = 1/1362734174521403051013657600196608000000000+12532641007/ 12160651121642427323095731329006953719398400000000000*ep+ 748303447187014401421/976663641526534161099303835297347199878394942586880\ 000000000000*ep^2+3496386564076199773805633091107/87154677925122274861074\ 41904739699608293391149407691341824000000000000000*ep^3+16609390004863896\ 620010565775430582643603/999955914800974631983848519198846611255339194399\ 17976878257170022400000000000000000*ep^4+57411513784388142047458714505604\ 99493940719492789/9914801551396662642065358213036479608654574386755597345\ 0506811815000801280000000000000000000*ep^5+886713053501266015234237806172\ 4488165951028079779033268979021/50166380381629190603806454383236930475409\ 0020187629778221629897221489369527508533248000000000000000000000*ep^6; Fill mncpoch(27,21) = 1/171704505989696784427720857624772608000000000+ 14019926807/1532242041326945842710062147454876168644198400000000000*ep+ 935968189700828366821/123059618832343304298512283247465747184677762765946\ 880000000000000*ep^2+543159862429994228001744170323/122016549095171184805\ 504186666355794516107476091707678785536000000000000000*ep^3+2595718286090\ 5153285797062184014657555803/12599444526492280362996491341905467301817273\ 849429665086660403422822400000000000000000*ep^4+9027611188297693747150215\ 5323046482620074984932501/11243384959283815436102116213583367876214287354\ 5808473892874724598210908651520000000000000000000*ep^5+173259124298267203\ 84560120859450259285420440241374363103484421/6320963928085278016079613252\ 2878532399015342543641352055925367049907660560466075189248000000000000000\ 000000*ep^6; Fill mncpoch(27,22) = 1/18887495658866646287049294338724986880000000000+ 15804669767/168546624545964042698106836220036378550861824000000000000*ep+ 1189833647616831179701/13536558071557763472836351157221232190314553904254\ 156800000000000000*ep^2+2337328662675069425831850729289/ 4026546120140649098581638159989741219031546711026353399922688000000000000\ 0000*ep^3+42047373382293683711817807725082376269643/138593889791415083992\ 9614047609601403199900123437263159532644376510464000000000000000000*ep^4+ 165319865513516978128635656463020869087391390895781/ 1236772345521219697971232783494170466383571609003893212821621970580319995\ 1667200000000000000000000*ep^5+359142807956006817125601779829236240609390\ 55050323116810945301/6953060320893805817687574577516638563891687679800548\ 726151790375489842661651268270817280000000000000000000000*ep^6; Fill mncpoch(27,23) = 1/1737649600615731458408535079162698792960000000000+ 18035598467/15506289458228691928225828932243346826679287808000000000000* ep+1551958855792187905801/12453633425833142395009443064643533615089389591\ 91382425600000000000000*ep^2+1163810615625684612482211064063/ 1234807476843132390231702369063520640503007658048081709309624320000000000\ 000000*ep^3+10298740254713070509646021003263411098849/ 1821519694401455389621778462572618987062725876517545866814332609128038400\ 0000000000000000*ep^4+326150151970109872984286202141902831449636788359881/ 1137830557879522122133534160814636829072885880283581755795892212933894395\ 553382400000000000000000000*ep^5+8175419807158790015358209843738309151635\ 1265941179837254481401/63968154952223013522725686113153074787803526654165\ 0482805964714545065524871916680915189760000000000000000000000*ep^6; Fill mncpoch(27,24) = 1/125110771244332665005414525699714313093120000000000+ 21010170067/1116452840992465818832259683121520971520908722176000000000000 *ep+2114425152524402580601/8966616066599862524406799006543344202864360506\ 1779534643200000000000000*ep^2+16763804549655917735562345108167/ 8001552449943497888701431351531613750459489624151569476326365593600000000\ 00000000*ep^3+136203500681879428426559369321897074308343/ 9180459259783335163693763451365999694796138417648431168744236350005313536\ 000000000000000000*ep^4+2437657389730030184687207959469097089367745064062\ 27/2730793338910853093120481985955128389774926112680596213910141311041346\ 5493281177600000000000000000000*ep^5+218797841825786301843883915980513837\ 102226842347216226854236201/460570715656005697363624940014702138472185391\ 90998834762029459447244717790778001025893662720000000000000000000000*ep^6 ; Fill mncpoch(27,25) = 1/6255538562216633250270726284985715654656000000000000+ 25472027467/55822642049623290941612984156076048576045436108800000000000000 *ep+3137298140744137432801/4483308033299931262203399503271672101432180253\ 088976732160000000000000000*ep^2+30761981474941388846722489685567/ 4000776224971748944350715675765806875229744812075784738163182796800000000\ 0000000000*ep^3+312674953845261050359164491771859521352943/ 4590229629891667581846881725682999847398069208824215584372118175002656768\ 00000000000000000000*ep^4+70880275784271517596099104442341321463980341851\ 5627/13653966694554265465602409929775641948874630563402981069550706555206\ 73274664058880000000000000000000000*ep^5+81652486273754145645116156652754\ 3149266923538445123975170708401/23028535782800284868181247000735106923609\ 26959549941738101472972362235889538900051294683136000000000000000000000000 *ep^6; *--#] poch.h : *--#] Tables : #endif