#ifndef `SUMMER6HFILE' #define SUMMER6HFILE "1" *--#[ nndecl.h : #ifndef `NNDECLHFILE' #define NNDECLHFILE "1" * * Include file for declarations for harmonic summation program SUMMER * * Parameters: * MAXWEIGHT: the maximum number of nested sums/ maximum weight * sometimes the maximum number of indices of the R in S(R(),n) * sometimes the maximum value of the absolute value of the indices * File by J. Vermaseren * #define MAXWEIGHT "10" * * First some automatic declarations. This way we do not have to worry how * many j1, j2, etc and S1, S2 etc. have been declared. * When a ifac8 or something like it will be encountered it will be * automatically declared as a CommutingFunction if it did not exist yet. * AutoDeclare Symbols i,j,k,l,m,n,x,y; AutoDeclare CF sum,sign,bino,fac,ifac,invfac,num,den,S,H,X,Y,Z ,theta,delta,Gamma,InvGamma; * * Now the fixed declarations. * S k,n,N,a,ep,[1-x],[1+x],[1-xxx],[1+xxx],one,[1-one],[1+one],Mel; CF f,f1,f2,f3,f4,R,RR,T,TT,su,A,div,addarg,ln,SSZZ; CF Conj,Conjp,rep,pow,ipow,epow,acc,acc1,G,GG,InvG,Num,Den,Even,Odd; S z1,...,z`MAXWEIGHT',ln2; S li4half,li5half,li6half,li7half,li8half,li9half,li10half; S s6,s7a,s7b,s8a,s8b,s8c,s8d,s9a,s9b,s9c,s9d,s9e,s9f; S s10a,s10b,s10c,s10d,s10e,s10f,s10g,s10h,s10i,s10j,s10k,s10l; * * Some sets are needed for generating the sums in the mellin programs * (and other programs as well) * Set ii:i1,...,i`MAXWEIGHT'; Set jset:j1,...,j`MAXWEIGHT'; Set sumset:sum1,...,sum`MAXWEIGHT'; Set j2mset:j2m1,...,j2m`MAXWEIGHT'; Set sum2mset:sum2m1,...,sum2m`MAXWEIGHT'; Set denset:den1,...,den`MAXWEIGHT'; Set Sset:S1,...,S`MAXWEIGHT'; Set signset:sign1,...,sign`MAXWEIGHT'; Set zz:z1,...,z`MAXWEIGHT'; Set pos1:x1x1x,2,...,{2*`MAXWEIGHT'}; * * The powsum tables are to be used in more complete versions of the * summation program summit.prc * The program that derives these tables is below in this file * (in the fold programs, and then in the subfold sumprog) * * Sum table: powsum(k,n) = sum_(j,1,n,j^k) * CTable powsum(0:20,n?); Fill powsum(0) = n; Fill powsum(1) = n*(n+1)/2; Fill powsum(2) = n*(n+1)*(2*n+1)/6; Fill powsum(3) = n^2*(n+1)^2/4; Fill powsum(4) = n*(n+1)*(2*n+1)*(3*n^2+3*n-1)/30; Fill powsum(5) =-1/12*n^2+5/12*n^4+1/2*n^5+1/6*n^6; Fill powsum(6) =1/42*n-1/6*n^3+1/2*n^5+1/2*n^6+1/7*n^7; Fill powsum(7) =1/12*n^2-7/24*n^4+7/12*n^6+1/2*n^7+1/8*n^8; Fill powsum(8) =-1/30*n+2/9*n^3-7/15*n^5+2/3*n^7+1/2*n^8+1/9*n^9; Fill powsum(9) =-3/20*n^2+1/2*n^4-7/10*n^6+3/4*n^8+1/2*n^9+1/10*n^10; Fill powsum(10)=5/66*n-1/2*n^3+n^5-n^7+5/6*n^9+1/2*n^10+1/11*n^11; Fill powsum(11)= 5/12*n^2-11/8*n^4+11/6*n^6-11/8*n^8+11/12*n^10+1/2*n^11+1/12*n^12 ; Fill powsum(12)= -691/2730*n+5/3*n^3-33/10*n^5+22/7*n^7-11/6*n^9+n^11+1/2*n^12+1/ 13*n^13; Fill powsum(13)= -691/420*n^2+65/12*n^4-143/20*n^6+143/28*n^8-143/60*n^10+13/12* n^12+1/2*n^13+1/14*n^14; Fill powsum(14)= 7/6*n-691/90*n^3+91/6*n^5-143/10*n^7+143/18*n^9-91/30*n^11+7/6* n^13+1/2*n^14+1/15*n^15; Fill powsum(15)= 35/4*n^2-691/24*n^4+455/12*n^6-429/16*n^8+143/12*n^10-91/24*n^12+ 5/4*n^14+1/2*n^15+1/16*n^16; Fill powsum(16)= -3617/510*n+140/3*n^3-1382/15*n^5+260/3*n^7-143/3*n^9+52/3*n^11- 14/3*n^13+4/3*n^15+1/2*n^16+1/17*n^17; Fill powsum(17)= -3617/60*n^2+595/3*n^4-11747/45*n^6+1105/6*n^8-2431/30*n^10+221/9 *n^12-17/3*n^14+17/12*n^16+1/2*n^17+1/18*n^18; Fill powsum(18)= 43867/798*n-3617/10*n^3+714*n^5-23494/35*n^7+1105/3*n^9-663/5* n^11+34*n^13-34/5*n^15+3/2*n^17+1/2*n^18+1/19*n^19; Fill powsum(19)= 43867/84*n^2-68723/40*n^4+2261*n^6-223193/140*n^8+4199/6*n^10- 4199/20*n^12+323/7*n^14-323/40*n^16+19/12*n^18+1/2*n^19+1/20*n^20 ; Fill powsum(20)= -174611/330*n+219335/63*n^3-68723/10*n^5+6460*n^7-223193/63*n^9+ 41990/33*n^11-323*n^13+1292/21*n^15-19/2*n^17+5/3*n^19+1/2*n^20+1/ 21*n^21; * * Sum table: mpowsum(k,n) = sum_(j,1,n,(-1)^j*j^k) * CTable mpowsum(0:20,n?); Fill mpowsum(0) = (sign_(n)-1)/2; Fill mpowsum(1) = ((2*n+1)*sign_(n)-1)/4; Fill mpowsum(2) = n*(n+1)*sign_(n)/2; Fill mpowsum(3) = ((4*n^3+6*n^2-1)*sign_(n)+1)/8; Fill mpowsum(4) = n*(n+1)*(n^2+n-1)*sign_(n)/2; Fill mpowsum(5) = ((2*n^5+5*n^4-5*n^2+1)*sign_(n)-1)/4; Fill mpowsum(6) = n*(n+1)*(n^4+2*n^3-2*n^2-3*n+3)*sign_(n)/2; Fill mpowsum(7) = ((8*n^7+28*n^6-70*n^4+84*n^2-17)*sign_(n)+17)/16; Fill mpowsum(8) = n*(n+1)*(n^6+3*n^5-3*n^4-11*n^3+11*n^2+17*n-17)*sign_(n)/2; Fill mpowsum(9) = ((2*n^9+9*n^8-42*n^6+126*n^4-153*n^2+31)*sign_(n)-31)/4; Fill mpowsum(10)= n*(n+1)*(n^8+4*n^7-4*n^6-26*n^5+26*n^4+100*n^3-100*n^2-155*n+155)*sign_(n)/2; Fill mpowsum(11)= +sign_(n)*(-691/8+1705/4*n^2-2805/8*n^4+231/2*n^6-165/8*n^8+11/4* n^10+1/2*n^11) +691/8; Fill mpowsum(12)= +sign_(n)*(-2073/2*n+1705*n^3-1683/2*n^5+198*n^7-55/2*n^9+3*n^11+ 1/2*n^12); Fill mpowsum(13)= +sign_(n)*(5461/4-26949/4*n^2+22165/4*n^4-7293/4*n^6+1287/4*n^8- 143/4*n^10+13/4*n^12+1/2*n^13) -5461/4; Fill mpowsum(14)= +sign_(n)*(38227/2*n-62881/2*n^3+31031/2*n^5-7293/2*n^7+1001/2* n^9-91/2*n^11+7/2*n^13+1/2*n^14); Fill mpowsum(15)= +sign_(n)*(-929569/32+573405/4*n^2-943215/8*n^4+155155/4*n^6- 109395/16*n^8+3003/4*n^10-455/8*n^12+15/4*n^14+1/2*n^15) +929569/32; Fill mpowsum(16)= +sign_(n)*(-929569/2*n+764540*n^3-377286*n^5+88660*n^7-12155*n^9+ 1092*n^11-70*n^13+4*n^15+1/2*n^16); Fill mpowsum(17)= +sign_(n)*(3202291/4-15802673/4*n^2+3249295*n^4-1068977*n^6+ 376805/2*n^8-41327/2*n^10+1547*n^12-85*n^14+17/4*n^16+1/2*n^17 ) -3202291/4; Fill mpowsum(18)= +sign_(n)*(28820619/2*n-47408019/2*n^3+11697462*n^5-2748798*n^7+ 376805*n^9-33813*n^11+2142*n^13-102*n^15+9/2*n^17+1/2*n^18); Fill mpowsum(19)= +sign_(n)*(-221930581/8+547591761/4*n^2-900752361/8*n^4+37041963* n^6-26113581/4*n^8+1431859/2*n^10-214149/4*n^12+2907*n^14-969/ 8*n^16+19/4*n^18+1/2*n^19) +221930581/8; Fill mpowsum(20)= +sign_(n)*(-1109652905/2*n+912652935*n^3-900752361/2*n^5+ 105834180*n^7-14507545*n^9+1301690*n^11-82365*n^13+3876*n^15- 285/2*n^17+5*n^19+1/2*n^20); * * The next two tables are for speed purposes only. * * powsum1(k,n) = sum_(j,1,n-1,j^k) * CTable powsum1(0:20,n?); Fill powsum1(0) = -1+n; Fill powsum1(1) = -1/2*n+1/2*n^2; Fill powsum1(2) = 1/6*n-1/2*n^2+1/3*n^3; Fill powsum1(3) = 1/4*n^2-1/2*n^3+1/4*n^4; Fill powsum1(4) = -1/30*n+1/3*n^3-1/2*n^4+1/5*n^5; Fill powsum1(5) =-1/12*n^2+5/12*n^4-1/2*n^5+1/6*n^6; Fill powsum1(6) =1/42*n-1/6*n^3+1/2*n^5-1/2*n^6+1/7*n^7; Fill powsum1(7) =1/12*n^2-7/24*n^4+7/12*n^6-1/2*n^7+1/8*n^8; Fill powsum1(8) =-1/30*n+2/9*n^3-7/15*n^5+2/3*n^7-1/2*n^8+1/9*n^9; Fill powsum1(9) =-3/20*n^2+1/2*n^4-7/10*n^6+3/4*n^8-1/2*n^9+1/10*n^10; Fill powsum1(10)=5/66*n-1/2*n^3+n^5-n^7+5/6*n^9-1/2*n^10+1/11*n^11; Fill powsum1(11)= +5/12*n^2-11/8*n^4+11/6*n^6-11/8*n^8+11/12*n^10-1/2*n^11+1/12* n^12; Fill powsum1(12)= -691/2730*n+5/3*n^3-33/10*n^5+22/7*n^7-11/6*n^9+n^11-1/2*n^12+1/ 13*n^13; Fill powsum1(13)= -691/420*n^2+65/12*n^4-143/20*n^6+143/28*n^8-143/60*n^10+13/12* n^12-1/2*n^13+1/14*n^14; Fill powsum1(14)= +7/6*n-691/90*n^3+91/6*n^5-143/10*n^7+143/18*n^9-91/30*n^11+7/6* n^13-1/2*n^14+1/15*n^15; Fill powsum1(15)= +35/4*n^2-691/24*n^4+455/12*n^6-429/16*n^8+143/12*n^10-91/24*n^12 +5/4*n^14-1/2*n^15+1/16*n^16; Fill powsum1(16)= -3617/510*n+140/3*n^3-1382/15*n^5+260/3*n^7-143/3*n^9+52/3*n^11- 14/3*n^13+4/3*n^15-1/2*n^16+1/17*n^17; Fill powsum1(17)= -3617/60*n^2+595/3*n^4-11747/45*n^6+1105/6*n^8-2431/30*n^10+221/9 *n^12-17/3*n^14+17/12*n^16-1/2*n^17+1/18*n^18; Fill powsum1(18)= +43867/798*n-3617/10*n^3+714*n^5-23494/35*n^7+1105/3*n^9-663/5* n^11+34*n^13-34/5*n^15+3/2*n^17-1/2*n^18+1/19*n^19; Fill powsum1(19)= +43867/84*n^2-68723/40*n^4+2261*n^6-223193/140*n^8+4199/6*n^10- 4199/20*n^12+323/7*n^14-323/40*n^16+19/12*n^18-1/2*n^19+1/20* n^20; Fill powsum1(20)= -174611/330*n+219335/63*n^3-68723/10*n^5+6460*n^7-223193/63*n^9+ 41990/33*n^11-323*n^13+1292/21*n^15-19/2*n^17+5/3*n^19-1/2* n^20+1/21*n^21; * * mpowsum1(k,n) = sum_(j,1,n-1,(-1)^j*j^k) * CTable mpowsum1(0:20,n?); Fill mpowsum1(0) = -1/2-1/2*sign_(n); Fill mpowsum1(1) = -1/4+1/4*sign_(n)-1/2*sign_(n)*n; Fill mpowsum1(2) = 1/2*sign_(n)*n-1/2*sign_(n)*n^2; Fill mpowsum1(3) = 1/8-1/8*sign_(n)+3/4*sign_(n)*n^2-1/2*sign_(n)*n^3; Fill mpowsum1(4) = -1/2*sign_(n)*n+sign_(n)*n^3-1/2*sign_(n)*n^4; Fill mpowsum1(5) = -1/4+1/4*sign_(n)-5/4*sign_(n)*n^2+5/4*sign_(n)*n^4 -1/2*sign_(n)*n^5; Fill mpowsum1(6) = 3/2*sign_(n)*n-5/2*sign_(n)*n^3+3/2*sign_(n)*n^5 -1/2*sign_(n)*n^6; Fill mpowsum1(7) = 17/16-17/16*sign_(n)+21/4*sign_(n)*n^2-35/8*sign_(n)*n^4 +7/4*sign_(n)*n^6-1/2*sign_(n)*n^7; Fill mpowsum1(8) = -17/2*sign_(n)*n+14*sign_(n)*n^3-7*sign_(n)*n^5 +2*sign_(n)*n^7-1/2*sign_(n)*n^8; Fill mpowsum1(9) = -31/4+31/4*sign_(n)-153/4*sign_(n)*n^2+63/2*sign_(n)*n^4 -21/2*sign_(n)*n^6+9/4*sign_(n)*n^8-1/2*sign_(n)*n^9; Fill mpowsum1(10) = 155/2*sign_(n)*n-255/2*sign_(n)*n^3+63*sign_(n)*n^5 -15*sign_(n)*n^7+5/2*sign_(n)*n^9-1/2*sign_(n)*n^10; Fill mpowsum1(11)= +sign_(n)*(-691/8+1705/4*n^2-2805/8*n^4+231/2*n^6-165/8*n^8+11/4* n^10-1/2*n^11) +691/8; Fill mpowsum1(12)= +sign_(n)*(-2073/2*n+1705*n^3-1683/2*n^5+198*n^7-55/2*n^9+3*n^11- 1/2*n^12); Fill mpowsum1(13)= +sign_(n)*(5461/4-26949/4*n^2+22165/4*n^4-7293/4*n^6+1287/4*n^8- 143/4*n^10+13/4*n^12-1/2*n^13) -5461/4; Fill mpowsum1(14)= +sign_(n)*(38227/2*n-62881/2*n^3+31031/2*n^5-7293/2*n^7+1001/2* n^9-91/2*n^11+7/2*n^13-1/2*n^14); Fill mpowsum1(15)= +sign_(n)*(-929569/32+573405/4*n^2-943215/8*n^4+155155/4*n^6- 109395/16*n^8+3003/4*n^10-455/8*n^12+15/4*n^14-1/2*n^15) +929569/32; Fill mpowsum1(16)= +sign_(n)*(-929569/2*n+764540*n^3-377286*n^5+88660*n^7-12155*n^9+ 1092*n^11-70*n^13+4*n^15-1/2*n^16); Fill mpowsum1(17)= +sign_(n)*(3202291/4-15802673/4*n^2+3249295*n^4-1068977*n^6+ 376805/2*n^8-41327/2*n^10+1547*n^12-85*n^14+17/4*n^16-1/2*n^17 ) -3202291/4; Fill mpowsum1(18)= +sign_(n)*(28820619/2*n-47408019/2*n^3+11697462*n^5-2748798*n^7+ 376805*n^9-33813*n^11+2142*n^13-102*n^15+9/2*n^17-1/2*n^18); Fill mpowsum1(19)= +sign_(n)*(-221930581/8+547591761/4*n^2-900752361/8*n^4+37041963* n^6-26113581/4*n^8+1431859/2*n^10-214149/4*n^12+2907*n^14-969/ 8*n^16+19/4*n^18-1/2*n^19) +221930581/8; Fill mpowsum1(20)= +sign_(n)*(-1109652905/2*n+912652935*n^3-900752361/2*n^5+ 105834180*n^7-14507545*n^9+1301690*n^11-82365*n^13+3876*n^15- 285/2*n^17+5*n^19-1/2*n^20); #endif *--#] nndecl.h : *--#[ Procedures : *--#[ adjustsm : * #procedure adjustsm(i) * * Adjusts the sum boundaries * repeat; id sum`i'(j`i',x1?,x2?)*invfac`i'(x3?,-j`i') = f1(x1,x2,x3,x3-x2); if ( match(f1(?a,x4?pos0_)) == 0 ); id f1(x1?,x2?,x3?,x4?) = sum`i'(j`i',x1,x2)*f3(x3,-j`i'); endif; endrepeat; id f3(?a) = invfac`i'(?a); id f1(x1?,x2?,x3?,0) = sum`i'(j`i',x1,x2)*invfac`i'(x3,-j`i'); id f1(x1?,x2?,x3?,n?) = sum`i'(j`i',x1,x3)*invfac`i'(x3,-j`i') -sum_(jjj,x2+1,x3,su(jjj))*invfac`i'(x3,-j`i'); id sum_(jjj,x1?,x2?,su(jjj)) = f1(x1,x2,x2-x1)*su(jjj); repeat id f1(x1?,x2?,x3?pos_) = f1(x1,x2-1,x3-1)+replace_(jjj,x2); id f1(x1?,x2?,0) = replace_(jjj,x2); id f1(x1?,x2?,x3?neg_) = 0; id f1(x1?,x2?,x3?)*su(jjj) = sum_(jjj,x1,x2,su(jjj)); if ( count(su,1) ); id su(n?) = replace_(j`i',n); id S`i'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id den`i'(x1?,x2?) = den(x1+x2); id fac`i'(x1?,x2?) = fac(x1+x2); id invfac`i'(x1?,x2?) = invfac(x1+x2); id sign`i'(x?) = sign_(x); id fac(x?int_) = fac_(x); id invfac(x?int_) = invfac_(x); id den(x?pos_) = 1/x; id den(x?neg_) = 1/x; #call subesses(S) endif; if ( match(den`i'(x1?pos_,j`i')) ); id,once,den`i'(x1?pos_,j`i') = den`i'(x1,j`i')*X(x1); #call movej(`i',X) id X(x1?) = 1; endif; if ( match(den`i'(0,j`i')) ); id sum`i'(j`i',n1?pos_,n2?) = sum`i'(j`i',1,n2) - sum_(jjj,1,n1-1,su(jjj)); id sum_(jjj,x1?,x2?,su(jjj)) = f1(x1,x2,x2-x1)*su(jjj); repeat id f1(x1?,x2?,x3?pos_) = f1(x1,x2-1,x3-1)+replace_(jjj,x2); id f1(x1?,x2?,0) = replace_(jjj,x2); id f1(x1?,x2?,x3?neg_) = 0; id f1(x1?,x2?,x3?)*su(jjj) = sum_(jjj,x1,x2,su(jjj)); if ( count(su,1) ); id su(n?) = replace_(j`i',n); id S`i'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id den`i'(x1?,x2?) = den(x1+x2); id fac`i'(x1?,x2?) = fac(x1+x2); id invfac`i'(x1?,x2?) = invfac(x1+x2); id sign`i'(x?) = sign_(x); id fac(x?int_) = fac_(x); id invfac(x?int_) = invfac_(x); id den(x?pos_) = 1/x; id den(x?neg_) = 1/x; #call subesses(S) endif; elseif ( match(invfac`i'(n?int_,j`i')) || match(S`i'(R(?a),n?int_,j`i')) || match(fac`i'(n?int_,j`i')) ); if ( match(invfac`i'(n?int_,j`i')) ); id,once,invfac`i'(x1?int_,j`i') = invfac`i'(x1,j`i')*X(x1); elseif ( match(fac`i'(n?int_,j`i')) ); id,once,fac`i'(x1?int_,j`i') = fac`i'(x1,j`i')*X(x1); else; id,once,S`i'(R(?a),x1?int_,j`i') = S`i'(R(?a),x1,j`i')*X(x1); endif; #call movej(`i',X) id X(x1?) = 1; if ( match(den`i'(0,j`i')) ); id sum`i'(j`i',n1?pos_,n2?) = sum`i'(j`i',1,n2) - sum_(jjj,1,n1-1,su(jjj)); else; id sum`i'(j`i',n1?pos_,n2?) = sum`i'(j`i',0,n2) - sum_(jjj,0,n1-1,su(jjj)); endif; id sum_(jjj,x1?,x2?,su(jjj)) = f1(x1,x2,x2-x1)*su(jjj); repeat id f1(x1?,x2?,x3?pos_) = f1(x1,x2-1,x3-1)+replace_(jjj,x2); id f1(x1?,x2?,0) = replace_(jjj,x2); id f1(x1?,x2?,x3?neg_) = 0; id f1(x1?,x2?,x3?)*su(jjj) = sum_(jjj,x1,x2,su(jjj)); if ( count(su,1) ); id su(n?) = replace_(j`i',n); id S`i'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id den`i'(x1?,x2?) = den(x1+x2); id fac`i'(x1?,x2?) = fac(x1+x2); id invfac`i'(x1?,x2?) = invfac(x1+x2); id sign`i'(x?) = sign_(x); id fac(x?int_) = fac_(x); id invfac(x?int_) = invfac_(x); id den(x?pos_) = 1/x; id den(x?neg_) = 1/x; #call subesses(S) endif; endif; if ( count(sum`i',1) ); if ( match(invfac`i'(x1?,-j`i')) == 0 ); if ( match(S`i'(R(?a),x1?,-j`i')) ); repeat; if ( count(X,1) == 0 ); id sum`i'(j`i',x1?,x2?)*S`i'(R(?a),x3?,-j`i') = sum`i'(j`i',x1,x2)*f1(R(?a),x3,-j`i')*X(x3-x2); if ( match(X(x?pos0_)) == 0 ) id X(x?) = 1; endif; endrepeat; id f1(?a) = S`i'(?a); elseif ( match(fac`i'(x1?,-j`i')) ); repeat; if ( count(X,1) == 0 ); id sum`i'(j`i',x1?,x2?)*fac`i'(x3?,-j`i') = sum`i'(j`i',x1,x2)*f1(x3,-j`i')*X(x3-x2); if ( match(X(x?pos0_)) == 0 ) id X(x?) = 1; endif; endrepeat; id f1(?a) = fac`i'(?a); endif; id X(0) = 1; if ( count(X,1) ); id sum`i'(j`i',x1?,x2?)*X(x3?) = sum`i'(j`i',x1,x2+x3)-sum_(jjj,1,x3,su(x2+jjj)); id sum_(jjj,x1?,x2?,su(jjj)) = f1(x1,x2,x2-x1)*su(jjj); repeat id f1(x1?,x2?,x3?pos_) = f1(x1,x2-1,x3-1)+replace_(jjj,x2); id f1(x1?,x2?,0) = replace_(jjj,x2); id f1(x1?,x2?,x3?neg_) = 0; id f1(x1?,x2?,x3?)*su(jjj) = sum_(jjj,x1,x2,su(jjj)); if ( match(sum`i'(j`i',0,n?)*den`i'(0,j`i')) ) print "--4-> %t"; if ( count(su,1) ); id su(n?) = replace_(j`i',n); id S`i'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id den`i'(x1?,x2?) = den(x1+x2); id fac`i'(x1?,x2?) = fac(x1+x2); id invfac`i'(x1?,x2?) = invfac(x1+x2); id sign`i'(x?) = sign_(x); id fac(x?int_) = fac_(x); id invfac(x?int_) = invfac_(x); id den(x?pos_) = 1/x; id den(x?neg_) = 1/x; #call subesses(S) endif; endif; endif; endif; id invfac`i'(0,j`i')*invfac`i'(x1?,-j`i') = bino`i'(x1,0,j`i')*invfac(x1); .sort:boundary adjustment; id fac(x?) = fac_(x); id invfac(x?) = invfac_(x); #call simfacs id fac_(x?) = fac(x); id invfac_(x?) = invfac(x); repeat id num(n1?)*num(n2?) = num(n1*n2); id num(x?) = x; repeat id j`i'*den`i'(x?,j`i') = 1-x*den`i'(x,j`i'); repeat id j`i'*den`i'(x?,-j`i') = -1+x*den`i'(x,-j`i'); * #endprocedure * *--#] adjustsm : *--#[ basis : * #procedure basis(S) * * Routine expresses products of harmonic sums into sums of * terms, each with a single higher harmonic sum. See appendix A. * * J.Vermaseren,29-oct-1997 * repeat; id,once,`S'(R(?a),n?)*`S'(R(?b),n?) = SS(R(?a),R,R(?b),n); repeat id SS(R(x1?,?a),R(?b),R(x2?,?c),n?) = +SS(R(x1,?a),R(?b,x2),R(?c),n) +SS(R(?a),R(?b,x1),R(x2,?c),n) -SS(R(?a),R(?b,x1*sig_(x2)+x2*sig_(x1)),R(?c),n); id,SS(R(?a),R(?b),R(?c),n?) = `S'(R(?b,?a,?c),n); endrepeat; #endprocedure * *--#] basis : *--#[ basis2 : * #procedure basis2(S) * * Routine expresses products of harmonic sums into sums of * terms, each with a single higher harmonic function. See appendix A. * This routine is different from basis in that it allows the S function * to have two arguments outside the R. * * J.Vermaseren,29-oct-1997 * repeat; id,once,`S'(R(?a),n1?,n2?)*`S'(R(?b),n1?,n2?) = SS(R(?a),R,R(?b),n1,n2); repeat id SS(R(x1?,?a),R(?b),R(x2?,?c),n1?,n2?) = +SS(R(x1,?a),R(?b,x2),R(?c),n1,n2) +SS(R(?a),R(?b,x1),R(x2,?c),n1,n2) -SS(R(?a),R(?b,x1*sig_(x2)+x2*sig_(x1)),R(?c),n1,n2); id,SS(R(?a),R(?b),R(?c),n1?,n2?) = `S'(R(?b,?a,?c),n1,n2); endrepeat; #endprocedure * *--#] basis2 : *--#[ basisn : * #procedure basisn(S,n) * * Routine expresses products of harmonic sums into sums of * terms, each with a single higher harmonic function. See appendix A. * * J.Vermaseren,29-oct-1997 * *repeat; id,once,`S'(R(?a),`n')*`S'(R(?b),`n') = SS(R(?a),R,R(?b),`n'); repeat id SS(R(x1?,?a),R(?b),R(x2?,?c),`n') = +SS(R(x1,?a),R(?b,x2),R(?c),`n') +SS(R(?a),R(?b,x1),R(x2,?c),`n') -SS(R(?a),R(?b,x1*sig_(x2)+x2*sig_(x1)),R(?c),`n'); id,SS(R(?a),R(?b),R(?c),`n') = `S'(R(?b,?a,?c),`n'); *endrepeat; #endprocedure * *--#] basisn : *--#[ conjug : * #procedure conjug(n,par) * * Find the conjugate of a harmonic function (first case) or * an harmonic function with one or more powers of 1/n (second case). * Routine to be used from summit. * The algorithm is from appendix B in the paper. * * J.Vermaseren,27-oct-1997 * Argument Conj; id R(?a)/`n'^j?pos_ = SS(j,?a); EndArgument; if ( match(Conj(SS(?a))) ); Multiply R(0); repeat; repeat; id Conj(SS(1,?a))*R(?b,m?) = Conj(SS(?a))*R(?b,m+1); endrepeat; id Conj(SS(m?,?a))*R(?b,j?) = Conj(SS(m-1,?a))*R(?b,j+1); repeat; id Conj(SS(m?pos_,?a))*R(?b) = Conj(SS(m-1,?a))*R(?b,1); endrepeat; id Conj(SS(0,?a)) = Conj(SS(?a)); endrepeat; id Conj(SS) = 1; id R(?a,0) = R(?a); id R = 1; else if ( match(Conj(R(?a))) ); Multiply SS(0); repeat; repeat; id Conj(R(1,?a))*SS(?b,m?) = Conj(R(?a))*SS(?b,m+1); endrepeat; id Conj(R(m?,?a))*SS(?b,j?) = Conj(R(m-1,?a))*SS(?b,j+1); repeat; id Conj(R(m?pos_,?a))*SS(?b) = Conj(R(m-1,?a))*SS(?b,1); endrepeat; id Conj(R(0,?a)) = Conj(R(?a)); endrepeat; id Conj(R) = 1; id SS(?a,0) = SS(?a); id SS = 1; id SS(m?) = 1/`n'^m; id SS(m?,?a) = R(?a)/`n'^m; endif; #if `par' == 0 id R(?a) = S(R(?a),`n'); #endif #endprocedure * *--#] conjug : *--#[ densplit : * #procedure densplit(i) * * Procedure splits the fractions. * It does this for one summation parameter only, or for N. * If the argument is N it does this for N, and if the argument is * a number m it does this for jm * This routine is optimized for higher powers of the denominators. * In that case one uses the sum formula rather than repeated splitting * of pairs (which may involve more pattern matching, but the evaluation * of the sums requires more time afterwards). * #if `i' == N * * Go to the notation with one argument in den. * Then separate the N. * id den(x1?,x2?) = den(x1+x2); SplitArg,(N),den; * * Make simple substitutions. * We assume that N/2 and 2*N can occur too. * Make that N has always a positive sign inside den. * id den(N) = den(0,N); id den(-N) = -den(0,N); id den(2*N) = den(0,N)/2; id den(-2*N) = -den(0,N)/2; id den(N/2) = 2*den(0,N); id den(-N/2) = -2*den(0,N); id den(x?,N/2) = 2*den(2*x,N); id den(x?,-N/2) = -2*den(-2*x,N); id den(x?,-N) = -den(-x,N); id den(x?,-2*N) = -den(-x/2,N)/2; id den(x1?,2*N) = den(x1/2,N)/2; * * Simple partial fractioning with the numerator * id N*den(0,N) = 1; repeat id N*den(x?,N) = 1-x*den(x,N); * * Notation with power in the first argument * Collect the powers * id den(x1?,N) = den(1,x1,N); repeat id den(x1?,y?,N)*den(x2?,y?,N) = den(x1+x2,y,N); * * Split the fractions. If x is numerical, the delta_ and deltap_ should * act immediately. den(x2-x1) is our function and hence a zero there * is only a problem if something goes wrong with deltap_. * repeat; id den(n1?,x1?,N)*den(n2?,x2?,N) = +sum_(jjj,1,n1,binom_(n1+n2-1-jjj,n2-1)*den(jjj,x1,N) *den(x1-x2)^(n1+n2-jjj))*sign_(n2)*deltap_(x1-x2) +sum_(jjj,1,n2,binom_(n1+n2-1-jjj,n1-1)*den(jjj,x2,N) *den(x2-x1)^(n1+n2-jjj))*sign_(n1)*deltap_(x1-x2) +delta_(x1-x2)*den(n1+n2,x1,N); endrepeat; * * Back to regular notation. * id den(n1?,x1?,x2?) = den(x1+x2)^n1; id den(x1?,x2?) = den(x1+x2); * #else * * We do j`i' * First put the den functions to one argument notation. * id f?{den,den0,...,den`i'}(x1?,x2?) = den(x1+x2); id f?{den0,...,den`i'}(x1?) = den(x1); * * Single out the j`i' * SplitArg,(j`i'),den; id den(x?,j`i') = den`i'(1,x,j`i'); id den(x?,-j`i') = den`i'(1,x,-j`i'); id den(j`i') = den`i'(1,0,j`i'); id den(-j`i') = -den`i'(1,0,j`i'); * * Now the first parameter is the power. * We recognize only cases with j and -j. * Multiples we don't use. (not needed for two loop structure functions) * Now do some simplifications with the numerators. * id j`i'*den`i'(1,0,j`i') = 1; repeat id j`i'*den`i'(1,x?,j`i') = 1-x*den`i'(1,x,j`i'); * * Collect the powers * repeat id,den`i'(n1?,x1?,x2?)*den`i'(n2?,x1?,x2?) = den`i'(n1+n2,x1,x2); * * The cases den(x+j) and den(x-j) are considered separately, because * There is ordering according to the 'biggest' objects, meaning that * the sign of N is more important than the sign of j1 than the sign * of j2 etc. * Hence we need three formula's * The function deltap_(x) = 1-delta_(x) * It will be replaced later by two theta functions. * repeat; id den`i'(n1?,x1?,j`i')*den`i'(n2?,x2?,j`i') = +sum_(jjj,1,n1,binom_(n1+n2-1-jjj,n2-1)*den`i'(jjj,x1,j`i') *den(x1-x2)^(n1+n2-jjj))*sign_(n2)*deltap_(x1-x2) +sum_(jjj,1,n2,binom_(n1+n2-1-jjj,n1-1)*den`i'(jjj,x2,j`i') *den(x2-x1)^(n1+n2-jjj))*sign_(n1)*deltap_(x2-x1) +delta_(x1-x2)*den`i'(n1+n2,x1,j`i'); endrepeat; repeat; id den`i'(n1?,x1?,-j`i')*den`i'(n2?,x2?,-j`i') = +sum_(jjj,1,n1,binom_(n1+n2-1-jjj,n2-1)*den`i'(jjj,x1,-j`i') *den(x1-x2)^(n1+n2-jjj))*sign_(n2)*deltap_(x1-x2) +sum_(jjj,1,n2,binom_(n1+n2-1-jjj,n1-1)*den`i'(jjj,x2,-j`i') *den(x2-x1)^(n1+n2-jjj))*sign_(n1)*deltap_(x2-x1) +delta_(x1-x2)*den`i'(n1+n2,x1,-j`i'); endrepeat; repeat; id den`i'(n1?,x1?,j`i')*den`i'(n2?,x2?,-j`i') = +sum_(jjj,1,n1,binom_(n1+n2-1-jjj,n2-1)*den`i'(jjj,x1,j`i') *den(x1+x2)^(n1+n2-jjj))*deltap_(x1+x2) +sum_(jjj,1,n2,binom_(n1+n2-1-jjj,n1-1)*den`i'(jjj,x2,-j`i') *den(x2+x1)^(n1+n2-jjj))*deltap_(x1+x2) +delta_(x1+x2)*den`i'(n1+n2,x1,j`i')*sign_(n2); endrepeat; * * Cleanup. Go to the 'own' functions. * id den`i'(n1?,x1?,x2?) = den`i'(x1,x2)^n1; id delta_(x?) = delta(x); id deltap_(x?) = deltap(x); #endif * * Simple substitutions: * id den(x?pos_) = 1/x; id den(x?neg_) = 1/x; id sign(x?int_) = sign_(x); #endprocedure * *--#] densplit : *--#[ dosign : * #procedure dosign * * Deals with all signs. * assumes that N, j1,...,jm are all integers. * id sign_(x?) = sign(x); splitarg sign; * * Each term in the original gets its own function. * Flip signs if possible. * repeat id sign(n1?,n2?,?a) = sign(n1)*sign(n2,?a); id sign(-N) = sign(N); #do ii = 0,`MAXWEIGHT' id sign(-j`ii') = sign(j`ii'); #enddo * * Eliminate squares and sign of integers. * id sign(x?{N,j0,...,j`MAXWEIGHT'})*sign(x?{N,j0,...,j`MAXWEIGHT'}) = 1; id sign(x?int_) = sign_(x); #ifdef 'WITHHALVES' * * If there are halfs, we add all arguments and try again * repeat id sign(n1?)*sign(n2?) = sign(n1+n2); splitarg sign; repeat id sign(n1?,n2?,?a) = sign(n1)*sign(n2,?a); id sign(5*N/2) = sign(N/2); id sign(3*N/2) = sign(N)*sign(N/2); id sign(-3*N/2) = sign(N/2); id sign(-N/2) = sign(N/2)*sign(N); id sign(3*N) = sign(N); id sign(N)*sign(N) = 1; id sign(2*N) = 1; id sign(-2*N) = 1; #endif * * Some fixed simplifications. * The function Even(x) = 1/2+sign(x)/2 * and Odd(x) = 1/2-sign(x)/2 * id sign(2*N) = 1; id sign(3*N) = sign(N); id sign(4*N) = 1; id Even(N)*sign(N) = Even(N); id Odd(N)*sign(N) = -Odd(N); id Even(x?even_) = 1; id Even(x?odd_) = 0; id Odd(x?even_) = 0; id Odd(x?odd_) = 1; #endprocedure * *--#] dosign : *--#[ extract1 : * #procedure extract1(S,S1,x) * * Procedure extracts leading indices 1 from the S-sums with argument x. * The extracted indices 1 are left in S1. * * J. Vermaseren, 12-jan-1999 * repeat; if ( match(`S'(R(1,?a),`x')) ); id `S'(R(1,?a),`x') = `S'(R(1),R(?a),`x'); repeat id `S'(R(?b),R(1,?a),`x') = `S'(R(?b,1),R(?a),`x'); id `S'(R(?a),R,`x') = `S1'(R(?a),`x'); id `S'(R(?b),R(?a),`x') = -`S'(R(?b),`x')*`S'(R(?a),`x')*SR(?b,?a) +`S1'(R(?b),`x')*`S'(R(?a),`x'); #call basis(`S') id SR(?a)*`S'(R(?a),`x') = 0; id SR(?a) = 1; endif; endrepeat; #endprocedure * *--#] extract1 : *--#[ extractn : * #procedure extractn(S,S1,x) * * Procedure extracts leading indices 1 from the S-sums with argument x. * The extracted indices 1 are left as powers of S1(R(1),x) * * J. Vermaseren, 12-jan-1999 * repeat; if ( match(`S'(R(1,?a),`x')) ); id `S'(R(1,?a),`x') = `S'(R(1),R(?a),`x'); repeat id `S'(R(?b),R(1,?a),`x') = `S'(R(?b,1),R(?a),`x'); id `S'(R(1),R,`x') = `S1'(R(1),`x'); id `S'(R(1,?a),R(?b),`x') = `S'(R(1),R(?a,?b),`x')/(nargs_(?a)+1); id `S'(R(1),R(?a),`x') = -`S'(R(1),`x')*`S'(R(?a),`x')*SR(1,?a) +`S1'(R(1),`x')*`S'(R(?a),`x'); #call basis(`S') id SR(?a)*`S'(R(?a),`x') = 0; id SR(?a) = 1; endif; endrepeat; #endprocedure * *--#] extractn : *--#[ flipj : * #procedure flipj(i) * * Reverses the direction of summation * id sum`i'(j`i',x1?,x2?) = sum`i'(0,x2-x1)*replace_(j`i',x2-j`i'); id sum`i'(x1?,x2?) = sum`i'(j`i',x1,x2); * * The special functions have to be redone * id f?{den`i',fac`i',invfac`i'}(x1?,x2?) = f(x1+x2); id bino`i'(x1?,x2?,x3?) = bino`i'(x1,x2+x3); id S`i'(x1?,x2?,x3?) = S`i'(x1,x2+x3); SplitArg,(j`i'),den`i',fac`i',invfac`i',S`i',bino`i'; id f?{den`i',fac`i',invfac`i'}(x2?) = f(0,x2); id S`i'(x1?,x2?) = S`i'(x1,0,x2); id bino`i'(x1?,x2?) = bino`i'(x1,0,x2); id bino`i'(x1?,x2?,-j`i') = bino`i'(x1,x1-x2,j`i'); * * Truncated version of dosign. It is only needed for the j`i' related * objects. * SplitArg,sign`i'; repeat id sign`i'(x1?,x2?,?a) = sign(x1)*sign`i'(x2,?a); id sign`i'(-j`i') = sign`i'(j`i'); id sign(x?int_) = sign_(x); id sign(j`i') = sign`i'(j`i'); id sign(-j`i') = sign`i'(j`i'); id sign(x?{N,j1,...,j`MAXWEIGHT'})*sign(x?{N,j1,...,j`MAXWEIGHT'}) = 1; repeat id sign(n1?number_)*sign(n2?number_) = sign(n1+n2); id sign(x?int_) = sign_(x); * #endprocedure * *--#] flipj : *--#[ makei : * #procedure makei(mi) * * Routine singles out the j`mi' summation parameter and all * functions that contain this parameter (and that are recognized * by the system of course). * First all functions are converted into the generic functions * #if `mi' == 0 * * The zero case is for special applications. In that case we only * do this one and nothing more. * Collapse everything into the base notation * repeat id f?{theta,theta0,delta,delta0,deltap,deltap0,den,den0,fac,fac0,invfac,invfac0}(x1?,x2?,?a) = f(x1+x2,?a); repeat id f?{S,S0}(x1?,x2?,x3?,?a) = f(x1,x2+x3,?a); id theta0(x?) = theta(x); id delta0(x?) = delta(x); id deltap0(x?) = deltap(x); id den0(x?) = den(x); id fac0(x?) = fac(x); id invfac0(x?) = invfac(x); id S0(?a) = S(?a); #else * * In this case the `mi' objects and all lower objects are first * converted back to the base notation. This goes best with sets, * because otherwise there would be many id statement. * repeat id f?{theta,theta0,...,theta`mi'\ ,delta,delta0,...,delta`mi',deltap,deltap0,...,deltap`mi'\ ,den,den0,...,den`mi',fac,fac0,...,fac`mi'\ ,invfac,invfac0,...,invfac`mi'}(x1?,x2?,?a) = f(x1+x2,?a); repeat id f?{S,S0,...,S`mi'}(x1?,x2?,x3?,?a) = f(x1,x2+x3,?a); id f?{theta0,...,theta`mi'}(x?) = theta(x); id f?{delta0,...,delta`mi'}(x?) = delta(x); id f?{deltap0,...,deltap`mi'}(x?) = deltap(x); id f?{den0,...,den`mi'}(x?) = den(x); id f?{fac0,...,fac`mi'}(x?) = fac(x); id f?{invfac0,...,invfac`mi'}(x?) = invfac(x); id f?{S0,...,S`mi'}(?a) = S(?a); #endif * * Put the built-in equivalents also into the base functions. * They are sometimes used to convert numerical arguments immediately. * This is especially useful with delta_, theta_ and sign_ functions. * id fac_(x?) = fac(x); id invfac_(x?) = invfac(x); id delta_(x?) = delta(x); id deltap_(x?) = deltap(x); id theta_(x?) = theta(x); id sign_(x?) = sign(x); * * Now the splitarg singles out the j`mi' * We make sure that the 0 is not forgotten (the argument is already `split') * SplitArg,(j`mi'),delta,deltap,theta,den,fac,invfac,S; id f?{delta,deltap,theta,den,fac,invfac}(j`mi') = f(0,j`mi'); id f?{delta,deltap,theta,den,fac,invfac}(-j`mi') = f(0,-j`mi'); id S(x1?,j`mi') = S(x1,0,j`mi'); id S(x1?,-j`mi') = S(x1,0,-j`mi'); * * Create the `mi' functions * Those will be the exclusive object of study. * id f?{delta,deltap,theta,den,fac,invfac}[n](x1?,j`mi') = {delta`mi',deltap`mi',theta`mi',den`mi',fac`mi',invfac`mi'}[n](x1,j`mi'); id f?{delta,deltap,theta,den,fac,invfac}[n](x1?,-j`mi') = {delta`mi',deltap`mi',theta`mi',den`mi',fac`mi',invfac`mi'}[n](x1,-j`mi'); id S(x1?,x2?,j`mi') = S`mi'(x1,x2,j`mi'); id S(x1?,x2?,-j`mi') = S`mi'(x1,x2,-j`mi'); id sum(j`mi',?a) = sum`mi'(j`mi',?a); id sign(j`mi') = sign`mi'(j`mi'); * * Now we have to fix the proper sign on den`mi' * #call normden(`mi') * #endprocedure * *--#] makei : *--#[ movej : * #procedure movej(i,X) * * Makes a translation of j`i'+x -> j`i' with x the argument of X * id sum`i'(j`i',x1?,x2?)*`X'(x3?) = sum`i'(x1+x3,x2+x3)*replace_(j`i',j`i'-x3); id sum`i'(x1?,x2?) = sum`i'(j`i',x1,x2); * * We have to redo some of the special functions * id f?{den`i',fac`i',invfac`i',sign`i'}(x1?,x2?) = f(x1+x2); id S`i'(x1?,x2?,x3?) = S`i'(x1,x2+x3); SplitArg,(j`i'),den`i',fac`i',invfac`i',S`i'; id f?{den`i',fac`i',invfac`i'}(x2?) = f(0,x2); id S`i'(x1?,x2?) = S`i'(x1,0,x2); * * Now a truncated version of dosign. We do not need the whole thing * SplitArg,sign`i'; repeat id sign`i'(x1?,x2?,?a) = sign(x1)*sign`i'(x2,?a); id sign`i'(-j`i') = sign`i'(j`i'); id sign(-j`i') = sign`i'(j`i'); id sign(j`i') = sign`i'(j`i'); id sign(x?int_) = sign_(x); id sign(x?{N,j1,...,j`MAXWEIGHT'})*sign(x?{N,j1,...,j`MAXWEIGHT'}) = 1; repeat id sign(n1?number_)*sign(n2?number_) = sign(n1+n2); id sign(x?int_) = sign_(x); * #endprocedure * *--#] movej : *--#[ normden : * #procedure normden(ndi) * * Fix a proper sign on the den function. * Hierarchy: Most important is N, then j1, then j2 etc * We use f1 as a auxiliary for functions that have the proper sign already * SplitArg,(N),den`ndi'; id den`ndi'(N,x1?) = f1(N,x1); id den`ndi'(-N,x1?) = -f1(N,-x1); id den`ndi'(x2?,N,x1?) = f1(x2+N,x1); id den`ndi'(x2?,-N,x1?) = -f1(-x2+N,-x1); #do ndii = 1,`ndi'-1 if ( count(den`ndi',1) ); SplitArg,(j`ndii'),den`ndi'; id den`ndi'(j`ndii',x1?) = f1(j`ndii',x1); id den`ndi'(-j`ndii',x1?) = -f1(j`ndii',-x1); id den`ndi'(x2?,j`ndii',x1?) = f1(x2+j`ndii',x1); id den`ndi'(x2?,-j`ndii',x1?) = -f1(-x2+j`ndii',-x1); #enddo id den`ndi'(x1?,-j`ndi') = -den`ndi'(-x1,j`ndi'); #do ii = 1,`ndi'-1 endif; #enddo id f1(?a) = den`ndi'(?a); #endprocedure * *--#] normden : *--#[ simfacs : * #procedure simfacs * * Procedure tries to simplify combinations of fac*invfac * It looks for combinations where the difference of the arguments * is a constant integer. Those can be worked out. * * The function f1 is the factorial under consideration (we do one by one) * The function f2 is to put away the fac functions that are not having * a simplification. * The function f3 puts away the invfac functions that do not match with * the current fac (f1) * f4 registers the matches. Those are pairs that need to be worked out. * * The function num stands for composite numerators (num(x)=x) * The function den for denominators (den(x) = 1/x) * The calling routine should decide when these are processed further * to avoid a buildup of terms at the wrong moment. * * J.Vermaseren 6-jun-1998 * id fac_(x?)*invfac_(x?) = 1; repeat; id,once,fac_(x?) = f1(x); repeat; id f1(x1?)*invfac_(x2?) = f1(x1,x2,x1-x2); id f1(x1?,x2?,x3?int_) = f4(x1,x3); id f1(x1?,x2?,x3?) = f1(x1)*f3(x2); endrepeat; id f3(x?) = invfac_(x); id f1(x?) = f2(x); endrepeat; repeat id f4(x1?,x2?pos_) = f4(x1-1,x2-1)*num(x1); repeat id f4(x1?,x2?neg_) = f4(x1+1,x2+1)*den(x1+1); id f4(x1?,0) = 1; id num(x?)*den(x?) = 1; id f2(x?) = fac_(x); #endprocedure * *--#] simfacs : *--#[ subesses : * #procedure subesses(S) * * Procedure evaluates the harmonic functions with a numerical last argument * into their numerical value. The symbolic ones are untouched of course. * * J.Vermaseren,29-oct-1997 * * All operations are done in the arguments to ensure continuous sorting * If this would not be done, there would be many terms. * id `S'(R(?a),n?pos_) = acc1(`S'(?a,n)); id `S'(R(?a),n?neg0_) = 0; repeat; argument acc1; id `S'(m?pos_,?a,n?) = sum_(jjj,1,n,`S'(?a,jjj)/jjj^m); id `S'(n?) = 1; endargument; argument acc1; id `S'(m?neg_,?a,n?) = sum_(jjj,1,n,`S'(?a,jjj)*sign_(jjj)*jjj^m); id `S'(n?) = 1; endargument; endrepeat; id acc1(x?) = x; #endprocedure * *--#] subesses : *--#[ sum2bin : * #procedure sum2bin(i) * * Procedure deals with summation formulae with two binomial coefficients * and a sign_ function. The central identity is * sum_(jjj,0,n,sign_(jjj)*binom_(n,jjj)* * binom_(n+jjj,m+jjj)*f(m+jjj)) = * sum_(jjj,0,n,sign_(jjj)*binom_(n,jjj)* * binom_(n+jjj,m+jjj)*fC(m+jjj))*sign_(m+n+1) * with the condition that 0 <= m <= n. fC is the conjugate function of f. * When m = 0, the sum runs from 1. * * * Routine still under construction * #endprocedure * *--#] sum2bin : *--#[ suminfm : * #procedure suminfm(i) * * Procedure does sums of the type * sum(j,1,inf)*S(R(?a),n1+j)/j^n2 * The central relation is: * F(n1)=sum(j,1,inf)*S(R(a1,?a),n1+j)/j^n2 * =F(n1-1)+sum(j,1,inf)*S(R(?a),n1+j)/(n1+j)^a1/j^n2 * * Bug repaired 14-jan-1999 * SplitArg,(j`i'),S`i'; id den`i'(j`i') = 1/j`i'; id den`i'(0,j`i') = 1/j`i'; id sum`i'(j`i',1,inf)*sign`i'(j`i')*S`i'(R(?a),n1?,j`i')/j`i'^n2?pos_ = SS(R(?a),R,-n2,n1); id sum`i'(j`i',1,inf)*S`i'(R(?a),n1?,j`i')/j`i'^n2?pos_ = SS(R(?a),R,n2,n1); if ( count(S`i',1,fac`i',1,bino`i',1,den`i',1,j`i',1) ); id SS(R(?a),R,n2?pos_,n1?) = sum`i'(j`i',1,inf)*S`i'(R(?a),n1+j`i')*den`i'(0,j`i')^n2; id SS(R(?a),R,n2?neg_,n1?) = sum`i'(j`i',1,inf)*S`i'(R(?a),n1+j`i') *sign`i'(j`i')*den`i'(0,j`i')^(-n2); endif; repeat; id SS(R(n?,?a),R(?b),n2?,n1?) = S(R(n2,n,?a),inf)*S(R(?b),n1) + sum_(jjj,1,abs_(n2),binom_(abs_(n2)+abs_(n)-1-jjj,abs_(n)-1)* SS(R(?a),R(?b,(abs_(n2)+abs_(n)-jjj)*sig_(n)),jjj*sig_(n2*n),n1)*sign_(jjj)) *sign_(n2) + sum_(jjj,1,abs_(n),binom_(abs_(n2)+abs_(n)-1-jjj,abs_(n2)-1)* S(R(sig_(n*n2)*jjj,?a),inf)* S(R(?b,(abs_(n2)+abs_(n)-jjj)*sig_(n2)),n1))*sign_(n2) - sum_(jjj,1,abs_(n),binom_(abs_(n2)+abs_(n)-1-jjj,abs_(n2)-1)* S(R(?b,(abs_(n2)+abs_(n)-jjj)*sig_(n2),jjj*sig_(n*n2),?a),n1)) *sign_(n2) ; endrepeat; id SS(R,R(?b),n2?,n1?) = S(R(n2),inf)*S(R(?b),n1); id S(R,?a) = 1; #endprocedure * *--#] suminfm : *--#[ summer : * #procedure summer(n) * * The summation routine that runs the show. * Routine works its way successively through all sums, starting at * the highest sum which is indicated by `n'. * Notice that for a large number of complicated nested sums this * is not going to be fast. * #do i = `n',1,-1 * * Introduce the proper variables for sum`i' * #call makei(`i') #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif .sort:introduction of `i'; * * Synchronize the sum * #call synch(`i') #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif .sort:Presum `i'; * * Now some cleaning up * #do ii = `i'-1,1,-1 #call densplit(`ii') #enddo #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif #call densplit(N) #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif .sort:densplit-`i'; #do ii = `i'-1,1,-1 #call theta(`ii') #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif #enddo #call theta(N) #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif id sign(x?number_) = sign_(x); .sort:theta cleanup; * * Final regularization of the sum * Introduction of the rather dangerous binomials. * #call sumreg(`i') SplitArg,((inf)),sum`i'; id sum`i'(x1?,x2?,x3?,inf) = sum`i'(x1,x2,inf); if ( match(sum`i'(j`i',x1?!number_,inf)*den`i'(0,j`i')*S`i'(R(?a),x2?!{0,0},j`i')) ); Print +f "<1> %t"; id den`i'(x1?,x2?) = den`i'(x1+x2); id sum`i'(j`i',x1?,inf)*S`i'(R(?a),x2?!{0,0},j`i') = sum`i'(j`i'+x2,x1+x2,inf)*S`i'(R(?a),0,j`i'+x2)*replace_(j`i',j`i'-x2); SplitArg,((j`i')),den`i',sign`i'; id den`i'(j`i') = den`i'(0,j`i'); id sign`i'(x?,j`i') = sign`i'(j`i')*sign(x); Print +f "<2> %t"; endif; *B sum`i',j`i',S`i',bino`i',sign`i',fac`i',invfac`i',den`i'; *Print +f +s; .sort:check sums; * * Now do the sums * #call summit(`i') if ( count(sum`i',1) ); Print +f "<1> %t"; if ( match(den`i'(0,j`i')) ); id S`i'(R(?a),x1?,x2?) = S`i'(R(?a),x1+x2); #call suminfm(`i') else; #call summinf(`i') endif; Print +f "<2> %t"; endif; .sort * * And a little bit of cleaning up * id S(R,?a) = 1; id S`i'(R,?a) = 1; #call subesses(S) .sort:summit `i'; * * Now some major cleaning up * #do ii = `i'-1,1,-1 #call densplit(`ii') #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif #enddo #call densplit(N) #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif .sort:densplit-`i'; #do ii = `i'-1,1,-1 #call theta(`ii') #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif #enddo #call theta(N) #ifdef `EXTRASUMMER' ;`EXTRASUMMER' #endif id sign(x?number_) = sign_(x); *Print +f +s; .sort:do theta (`i'); * * End of sum`i' * #enddo #endprocedure * *--#] summer : *--#[ summinf : * #procedure summinf(i) * * Sums of the type sum(j,1,inf)*S(R(?a),j)*den(x+j)^n0 [*sign(j)] * Routine by J.Vermaseren, 8-jul-1998 * id den`i'(x?,j`i') = den`i'(1,x,j`i'); repeat id den`i'(n1?,x?,j`i')*den`i'(n2?,x?,j`i') = den`i'(n1+n2,x,j`i'); id sum`i'(j`i',1,inf)*S`i'(R(?a),0,j`i')*den`i'(n?,n1?,j`i')*sign`i'(j`i') = SS(R(?a),-n,n1)*RR(n1,1,0); id sum`i'(j`i',1,inf)*S`i'(R(?a),0,j`i')*den`i'(n?,n1?,j`i') = SS(R(?a),n,n1)*RR(n1,1,0); id sum`i'(j`i',0,inf)*S`i'(R(?a),0,j`i')*den`i'(n?,n1?,j`i')*sign`i'(j`i') = SS(R(?a),-n,n1)*RR(n1,1,0); id sum`i'(j`i',0,inf)*S`i'(R(?a),0,j`i')*den`i'(n?,n1?,j`i') = SS(R(?a),n,n1)*RR(n1,1,0); repeat; id SS(R(n1?,?a),n0?,x?)*RR(x?,?b,ns?,np?) = +S(R(n0),inf)*S(R(n1,?a),inf)*RR(x,?b,ns*sig_(n0),np) -sum`i'(j`i',1,inf)*sign1(j`i')^theta_(-n1)*den`i'(abs_(n1),0,j`i') *S`i'(R(?a),j`i')*S`i'(R(n0),j`i')*RR(x,?b,ns*sig_(n0),np) +sum_(k,1,abs_(n1),binom_(abs_(n0)+abs_(n1)-1-k,abs_(n0)-1) *sign(n1-k)*S(R(sig_(n0)*sig_(n1)*k,?a),inf) *RR(x,?b,ns,np+abs_(n0)+abs_(n1)-k)) -sum_(k,1,abs_(n1),binom_(abs_(n0)+abs_(n1)-1-k,abs_(n0)-1) *sign(n1+k)*S(R(sig_(n0)*sig_(n1)*k,?a),inf) *RR(x,?b,ns*sig_(n0),np)*S(RR(n0+sig_(n0)*(abs_(n1)-k)),x)) +sum_(k,1,abs_(n0),binom_(abs_(n0)+abs_(n1)-1-k,abs_(n1)-1) *sign(n1)*SS(R(?a),sig_(n0)*sig_(n1)*k,x) *RR(x,?b,ns,np+abs_(n0)+abs_(n1)-k)) -sum_(k,1,abs_(n0),binom_(abs_(n0)+abs_(n1)-1-k,abs_(n1)-1) *sign(n1)*SS(R(?a),k*sig_(n0)*sig_(n1),x) *RR(x,?b,ns*sig_(n0),np,sig_(n0),abs_(n0)+abs_(n1)-k)) ; endrepeat; id SS(R,n0?,x?)*RR(x?,?b,ns?,np?) = RR(x,?b,ns*sig_(n0),np) *(S(R(n0),inf)-S(RR(n0),x)); id S`i'(R,?a) = 1; id S(R,?a) = 1; if ( count(S`i',1) > 1 ); #call basis(S`i') endif; if ( count(S`i',1) == 1 ); id sum`i'(j`i',1,inf)*sign1(j`i')*S`i'(R(?a),j`i')*den`i'(n?,0,j`i') = S(R(-n,?a),inf); id sum`i'(j`i',1,inf)*S`i'(R(?a),j`i')*den`i'(n?,0,j`i') = S(R(n,?a),inf); endif; #call basis(S); if ( match(RR(x?,?b)*S(RR(?a),x?)) == 0 ); id RR(x?,?b) = RR(x,?b)*S(RR,x); endif; repeat id RR(x?,n1?,n2?,?b,ns?,np?)*S(RR(?a),x?) = RR(x,n1,n2,?b)*S(RR(ns*np,?a),x); id RR(x?,ns?,np?)*S(RR(?a),x?) = S(R(?a),x)*den(x)^np*sign(x)^theta_(-ns); id sign(x?)*sign(x?) = 1; id sign(x?number_) = sign_(x); id den(x?number_) = 1/x; id S(R,?a) = 1; * #endprocedure * *--#] summinf : *--#[ summit : * #procedure summit(i) * * Do the actual sums. Of course much is delegated. * Note: in some cases we have sums to infinity. We use the symbol inf * for infinity. One should be a bit careful with j+inf -> inf because * if j is a summation parameter that can also go to infinity we may want * to obtain 2*inf in due time. This regularizes properly for * S(R(1),n*inf) => S(R(1),inf) + ln_(n) * For more details, see the paper. * *B sum`i',j`i',fac`i',bino`i',invfac`i',den`i',S`i',sign`i'; *Print +f +s; *.end if ( count(sum`i',1) ); * No need if no sum * * First set up a mechanism by which we can go through the thing again * in case we obtain a suitable simplification. * We should be careful not to put a direct repeat for the occurrence of * sum`i', because in the case that it cannot do the sum it would hang in * the loop. Hence we will only send it through the loop in the case something * very useful happened. * Multiply x; repeat; if ( count(x,1) ); id x = 1; * * Double binomials. * if ( ( count(bino`i',1) == 2 ) && ( count(sign`i',1) == 1 ) && ( count(fac`i',1,invfac`i',1) == 0 ) ); if ( count(sign`i',1) == 1 ); #call sum2bin(`i') else; endif; * * Conjugations * elseif ( ( count(bino`i',1) == 1 ) && ( count(sign`i',1) == 1 ) && ( count(fac`i',1,invfac`i',1) == 0 ) ); * conjugation id den`i'(0,j`i') = 1/j`i'; *new if ( ( count(j`i',1) > 0 ) && ( count(den`i',1) == 0 ) && ( count(S`i',1) == 1 ) ); id sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')* S`i'(R(?a),n?,-j`i')*j`i'^n1? = sum`i'(j`i',0,n)*sign(n)*sign`i'(j`i')*bino`i'(n,0,j`i') *S`i'(R(?a),0,j`i')*(n-j`i')^n1; id sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')* S`i'(R(?a),n?,-j`i')*j`i'^n1? = sum`i'(j`i',0,n)*sign(n)*sign`i'(j`i')*bino`i'(n,0,j`i') *S`i'(R(?a),0,j`i')*(n-j`i')^n1; endif; repeat; if ( ( count(j`i',1) > 0 ) && ( count(sum`i',1,S`i',1) == 2 ) ); if ( count(j`i',1) >= 0 ); id sum`i'(j`i',1,n?) = sum`i'(j`i',0,n)-replace_(j`i',0); id S`i'(R(?a),0,0) = 0; id bino`i'(n?,0,0) = 1; id sign`i'(0) = 1; endif; id sum`i'(j`i',0,n?)*S`i'(R(n1?pos_,?a),0,j`i')*bino`i'(n?,0,j`i') *sign`i'(j`i')*j`i'^x?pos_ = +n*sum`i'(j`i',0,n)*S`i'(R(n1,?a),0,j`i')*bino`i'(n,0,j`i') *sign`i'(j`i')*j`i'^x/j`i' -n*sum`i'(j`i',0,n-1)*S`i'(R(n1,?a),0,j`i')*bino`i'(n-1,0,j`i') *sign`i'(j`i')*j`i'^x/j`i'*theta(n-1); endif; endrepeat; *endnew if ( count(den`i',1) == 0 ); if ( ( count(S`i',1) == 1 ) && ( match(S`i'(R(n1?pos_),0,j`i')) #do ia = 2,`MAXWEIGHT' || match(S`i'(R(,...,),0,j`i')) #enddo ) ); if ( count(j`i',1) == 0 ); id sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i') *S`i'(R(?a),0,j`i') = -Conj(R(?a))*rep(j`i',n); id sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i') *S`i'(R(?a),0,j`i') = -Conj(R(?a))*rep(j`i',n); else; id sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i') *S`i'(R(?a),0,j`i')/j`i'^nn?pos_ = -Conj(R(?a)/j`i'^nn)*rep(j`i',n); endif; #call conjug(j`i',0) id 1/j`i' = den(j`i'); id rep(j`i',n?) = replace_(j`i',n); elseif ( count(S`i',1) == 0 ); if ( count(j`i',1) == 0 ); id sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i') = delta(n); id sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i') = -theta(n-1); else if ( count(j`i',1) < 0 ); id sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i') /j`i'^nn? = -y^nn*S`i'(n); repeat id y^nn?pos_*S`i'(?a) = y^nn/y*S`i'(1,?a); id S`i'(?a,n?) = S(R(?a),n); else if ( count(j`i',1) > 0 ); id,only,sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')*j`i'^3 = sum`i'(j`i',0,n-1)*sign`i'(j`i')*bino`i'(n-1,0,j`i')*(j`i'+1)^2; id,only,sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')*j`i'^3 = sum`i'(j`i',0,n-1)*sign`i'(j`i')*bino`i'(n-1,0,j`i')*(j`i'+1)^2; id,only,sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')*j`i'^2 = sum`i'(j`i',0,n-1)*sign`i'(j`i')*bino`i'(n-1,0,j`i')*(j`i'+1); id,only,sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')*j`i'^2 = sum`i'(j`i',0,n-1)*sign`i'(j`i')*bino`i'(n-1,0,j`i')*(j`i'+1); id,only,sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')*j`i' = -n*delta(n-1); id,only,sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')*j`i' = -n*delta(n-1); id sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i') = delta(n); endif; elseif ( ( ( count(S`i',1) == 1 ) && ( match(S`i'(R(n1?pos_),n?,-j`i')) #do ia = 2,`MAXWEIGHT' || match(S`i'(R(,...,),n?,-j`i')) #enddo ) ) || ( ( count(S`i',1) == 2 ) && ( match(S`i'(R(n1?pos_),0,j`i')) #do ia = 2,`MAXWEIGHT' || match(S`i'(R(,...,),0,j`i')) #enddo ) && ( match(S`i'(R(n1?pos_),n?,-j`i')) #do ia = 2,`MAXWEIGHT' || match(S`i'(R(,...,),n?,-j`i')) #enddo ) ) ); #call sumnmic(`i') else; id 1/j`i' = den`i'(0,j`i'); endif; else; id 1/j`i' = den`i'(0,j`i'); endif; * * A number of special sums * elseif ( ( count(bino`i',1) == 0 ) && ( count(fac`i',1,invfac`i',1) == 2 ) ); #call sumspec(`i') * * no binomials or factorials * elseif ( count(bino`i',1,fac`i',1,invfac`i',1) == 0 ); * * Forms involving S(R(...),n-j) * if ( match(S`i'(R(?a),x1?,-j`i')) ); repeat id j`i'*den`i'(x?,j`i') = 1-den`i'(x,j`i')*x; id den`i'(x1?,j`i') = den`i'(1,x1,j`i'); repeat id den`i'(n1?,x1?,j`i')*den`i'(n2?,x1?,j`i') = den`i'(n1+n2,x1,j`i'); * if ( ( count(den`i',1) == 0 ) && ( count(j`i',1) == 0 ) ); if ( count(den`i',1) == 0 ); if ( count(S`i',1) == 2 ); #call sumnmi0(`i') endif; id S`i'(R,0,0) = 0; id S`i'(R,?a) = 1; if ( count(S`i',1) == 1 ); id sum`i'(j`i',n1?,n?)*S`i'(R(?a),n?,-j`i')*sign`i'(j`i')*j`i'^x? = sum`i'(j`i',0,n-n1)*S`i'(R(?a),0,j`i')*sign`i'(j`i')*sign(n) *(n-j`i')^x; id sum`i'(j`i',n1?,n?)*S`i'(R(?a),n?,-j`i')*j`i'^x? = sum`i'(j`i',0,n-n1)*S`i'(R(?a),0,j`i')*(n-j`i')^x; Multiply x; elseif ( ( count(S`i',1) == 0 ) && ( count(sum`i',1) == 1 ) ); Multiply x; endif; elseif ( count(den`i',1) == 1 ); #call sumnmii(`i') endif; elseif ( match(S`i'(R(?a),x1?,j`i')) == 1 ); * * Forms involving a single S(R(...),a+j) * id den`i'(x1?,j`i') = den`i'(1,x1,j`i'); repeat id den`i'(n1?,x1?,j`i')*den`i'(n2?,x1?,j`i') = den`i'(n1+n2,x1,j`i'); if ( count(den`i',1) == 1 ); if ( count(sign`i',1) ); id sum`i'(j`i',x1?,x2?)*den`i'(n?,x3?,j`i') *S`i'(R(?a),x3?,j`i')*sign`i'(j`i') = S(R(-n,?a),x2+x3)-S(R(-n,?a),x1+x3-1); else; id sum`i'(j`i',x1?,x2?)*den`i'(n?,x3?,j`i') *S`i'(R(?a),x3?,j`i') = S(R(n,?a),x2+x3)-S(R(n,?a),x1+x3-1); endif; elseif ( ( count(den`i',1) == 0 ) && ( count(j`i',1) == 0 ) ); id sum`i'(j`i',x1?{0,1},x2?)*S`i'(R(n1?,?a),0,j`i')*sign`i'(j`i') = sign(x2)*S(R(n1,?a),x2)/2+S(R(-n1,?a),x2)/2; repeat; id sum`i'(j`i',x1?{0,1},x2?)*S`i'(R(n1?pos_,?a),0,j`i') = (x2+1)*S(R(n1,?a),x2) -sum`i'(j`i',1,x2)*S`i'(R(?a),0,j`i')*delta_(n1-1) -S(R(n1-1,?a),x2)*theta_(n1-2); id sum`i'(j`i',x1?{0,1},x2?)*S`i'(R(n1?neg_,?a),0,j`i') = (x2+1)*S(R(n1,?a),x2) -sum`i'(j`i',1,x2)*S`i'(R(?a),0,j`i')*sign`i'(j`i')*delta_(n1+1) -S(R(n1+1,?a),x2)*theta_(-n1-2); id sum`i'(j`i',x1?{0,1},x2?)*S`i'(R(n1?,?a),0,j`i')*sign`i'(j`i') = sign(x2)*S(R(n1,?a),x2)/2+S(R(-n1,?a),x2)/2; endrepeat; if ( match(S`i'(R,n?,j`i')) ); id S`i'(R,?a) = 1; id sum`i'(j`i',x1?,x2?)*sign`i'(j`i') = sign(x1)/2+sign(x2)/2; id sum`i'(j`i',x1?,x2?) = x2+1-x1; endif; elseif ( ( count(den`i',1) == 0 ) && ( count(j`i',1) > 0 ) ); #call sumposp(`i') endif; elseif ( count(S`i',1) == 0 ); * * Forms involving no S at all. -> only powers of j, den, sign * id den`i'(x1?,j`i') = den`i'(1,x1,j`i'); repeat id den`i'(n1?,x1?,j`i')*den`i'(n2?,x1?,j`i') = den`i'(n1+n2,x1,j`i'); if ( count(den`i',1) == 1 ); if ( count(sign`i',1) ); id sum`i'(j`i',x1?,x2?)*den`i'(n?,x3?,j`i')*sign`i'(j`i') = S(R(-n),x2+x3)-S(R(-n),x1+x3-1); else; id sum`i'(j`i',x1?,x2?)*den`i'(n?,x3?,j`i') = S(R(n),x2+x3)-S(R(n),x1+x3-1); endif; elseif ( count(den`i',1) == 0 ); if ( count(j`i',1) > 0 ); id sum`i'(j`i',x1?,x2?)*sign`i'(j`i')*j`i'^n? = mpowsum(n,x2)-mpowsum(n,x1-1)*theta_(x1-1); id sum`i'(j`i',x1?,x2?)*j`i'^n? = powsum(n,x2)-powsum(n,x1-1)*theta_(x1-1); else; id sum`i'(j`i',x1?,x2?)*sign`i'(j`i') = sign(x1)/2+sign(x2)/2; id sum`i'(j`i',x1?,x2?) = x2+1-x1; endif; endif; endif; endif; endif; endrepeat; endif; id den`i'(n?,x1?,x2?) = den`i'(x1,x2)^n; id den(N)*N = 1; id sign(x?number_) = sign_(x); * #endprocedure * *--#] summit : *--#[ sumnmi0 : * #procedure sumnmi0(i) * * Procedure for sums sum(j,0,n)*S(R(?a),j)*S(R(?b),n-j) [*sign(j)] * This is the special case of sumnmii with k=0. * * First rotate to the S with the smallest depth * if ( count(den`i',1) == 0 ); id sum`i'(j`i',0,n?)*S`i'(R(?a),0,j`i')*S`i'(R(?b),n?,-j`i') = S`i'(R(?a),n,j`i'-n)*S`i'(R(?b),0,n-j`i')*replace_(j`i',n-j`i')*theta_(nargs_(?a)-nargs_(?b)-1)*sum`i'(n-j`i',0,n) +S`i'(R(?a),0,j`i')*S`i'(R(?b),n,-j`i')*theta_(nargs_(?b)-nargs_(?a))*sum`i'(j`i',0,n); id sum`i'(j`i',1,n?)*S`i'(R(?a),0,j`i')*S`i'(R(?b),n?,-j`i') = S`i'(R(?a),n,j`i'-n)*S`i'(R(?b),0,n-j`i')*replace_(j`i',n-j`i')*theta_(nargs_(?a)-nargs_(?b)-1)*sum`i'(n-j`i',0,n) +S`i'(R(?a),0,j`i')*S`i'(R(?b),n,-j`i')*theta_(nargs_(?b)-nargs_(?a))*sum`i'(j`i',0,n); SplitArg,sign`i'; repeat id sign`i'(x1?,x2?,?a) = sign`i'(x1)*sign`i'(x2,?a); id sign`i'(-j`i') = sign`i'(j`i'); id sign`i'(x?number_) = sign_(x); id sign`i'(x?!{j`i'}) = sign(x); endif; repeat; if ( ( count(den`i',1) == 0 ) && ( match(S`i'(R(?a),0,j`i')*S`i'(R(?b),n?,-j`i')) ) ); if ( count(sign`i',1) ); id sum`i'(j`i',0,n?)*sign`i'(j`i')* S`i'(R(?a),0,j`i')*S`i'(R(n2?,?b),n?,-j`i')*j`i'^x?pos0_ = sum`i'(j`i',1,n)*S`i'(R(?b),0,j`i')*den`i'(abs_(n2),0,j`i') *(theta_(n2)+theta_(-n2)*sign`i'(j`i'))*theta(n-1) *sum(j,1,n,-j`i')*S`i'(R(?a),0,j) *sign`i'(j)*j^x; id sum`i'(j`i',1,n?)*sign`i'(j`i')* S`i'(R(n1?,?a),0,j`i')*S`i'(R(n2?,?b),n?,-j`i')*j`i'^x?pos0_ = sum`i'(j`i',1,n)*S`i'(R(?b),0,j`i')*den`i'(abs_(n2),0,j`i') *(theta_(n2)+theta_(-n2)*sign`i'(j`i')) *sum(j,1,n,-j`i')*S`i'(R(?a),0,j) *sign`i'(j)*j^x; else; id sum`i'(j`i',0,n?)*S`i'(R(?a),0,j`i') *S`i'(R(n2?,?b),n?,-j`i')*j`i'^x?pos0_ = sum`i'(j`i',1,n)*S`i'(R(?b),0,j`i')*den`i'(abs_(n2),0,j`i') *(theta_(n2)+theta_(-n2)*sign`i'(j`i'))*theta(n-1) *sum(j,1,n,-j`i')*S`i'(R(?a),0,j)*j^x; id sum`i'(j`i',1,n?)*S`i'(R(?a),0,j`i') *S`i'(R(n2?,?b),n?,-j`i')*j`i'^x?pos0_ = sum`i'(j`i',1,n)*S`i'(R(?b),0,j`i')*den`i'(abs_(n2),0,j`i') *(theta_(n2)+theta_(-n2)*sign`i'(j`i')) *sum(j,1,n,-j`i')*S`i'(R(?a),0,j)*j^x; endif; repeat; if ( count(j,1) == 0 ); id sum(j,1,x2?,-j`i')*S`i'(R(n1?,?a),0,j)*sign`i'(j) = sign(x2)*sign`i'(j`i')*S`i'(R(n1,?a),x2,-j`i')/2 +S`i'(R(-n1,?a),x2,-j`i')/2; id sum(j,1,x2?,-j`i')*S`i'(R(n1?pos_,?a),0,j) = (x2-j`i'+1)*S`i'(R(n1,?a),x2,-j`i') -sum(j,1,x2,-j`i')*S`i'(R(?a),0,j)*delta_(n1-1) -S`i'(R(n1-1,?a),x2,-j`i')*theta_(n1-2); id sum(j,1,x2?,-j`i')*S`i'(R(n1?neg_,?a),0,j) = (x2-j`i'+1)*S`i'(R(n1,?a),x2,-j`i') -sum(j,1,x2,-j`i')*S`i'(R(?a),0,j)*sign`i'(j)*delta_(n1+1) -S`i'(R(n1+1,?a),x2,-j`i')*theta_(-n1-2); elseif ( count(j,1) > 0 ); id sum(j,x1?,x2?,x3?) = sum(j,x1,x2+x3); id S1(R(?a),j) = S1(R(?a),0,j); #call sumposq(`i') repeat id j`i'*den`i'(n?pos_,0,j`i') = den`i'(n-1,0,j`i'); id den`i'(0,0,j`i') = 1; if ( count(den`i',1) == 0 ); id sum`i'(j`i',0,n?)*S`i'(R(?a),0,j`i')*S`i'(R(?b),n?,-j`i') = S`i'(R(?a),n,j`i'-n)*S`i'(R(?b),0,n-j`i')*replace_(j`i',n-j`i')*theta_(nargs_(?a)-nargs_(?b)-1)*sum`i'(n-j`i',0,n) +S`i'(R(?a),0,j`i')*S`i'(R(?b),n,-j`i')*theta_(nargs_(?b)-nargs_(?a))*sum`i'(j`i',0,n); id sum`i'(j`i',1,n?)*S`i'(R(?a),0,j`i')*S`i'(R(?b),n?,-j`i') = S`i'(R(?a),n,j`i'-n)*S`i'(R(?b),0,n-j`i')*replace_(j`i',n-j`i')*theta_(nargs_(?a)-nargs_(?b)-1)*sum`i'(n-j`i',0,n) +S`i'(R(?a),0,j`i')*S`i'(R(?b),n,-j`i')*theta_(nargs_(?b)-nargs_(?a))*sum`i'(j`i',0,n); SplitArg,sign`i'; repeat id sign`i'(x1?,x2?,?a) = sign`i'(x1)*sign`i'(x2,?a); id sign`i'(-j`i') = sign`i'(j`i'); id sign`i'(x?number_) = sign_(x); id sign`i'(x?!{j`i'}) = sign(x); endif; id theta(x?)*theta(x?) = theta(x); endif; endrepeat; if ( match(S`i'(R,0,j)) ); id S`i'(R,?a) = 1; id sum(j,1,x2?,-j`i')*sign`i'(j) = -1/2+sign(x2)*sign`i'(j`i')/2; id sum(j,1,x2?,-j`i') = x2-j`i'; endif; id S`i'(R,?a) = 1; id sign`i'(j`i')*sign`i'(j`i') = 1; id j`i'*den`i'(n?,0,j`i') = den`i'(n-1,0,j`i'); id den`i'(0,0,j`i') = 1; endif; endrepeat; if ( match(S`i'(R(?a),x1?,-j`i')) ); id den`i'(x1?,j`i') = den`i'(1,x1,j`i'); repeat id den`i'(n1?,x1?,j`i')*den`i'(n2?,x1?,j`i') = den`i'(n1+n2,x1,j`i'); if ( count(den`i',1) == 1 ); #call sumnmii(`i') endif; endif; id sign(x?)*sign(x?) = 1; #endprocedure * *--#] sumnmi0 : *--#[ sumnmic : * #procedure sumnmic(i) * * Sums of the type * sum`i'(j`i',1,n-1)*sign`i'(j`i')*bino`i'(n,j`i')* * S`i'(R(?a),n-j`i')*S`i'(R(?b),j`i')/j`i'^k * with ?a, ?b all positive and k >= 0. * These are described in the second part of appendix C of the paper. * * J.Vermaseren,31-oct-1997 * id S`i'(R,x1?,x2?) = TT(R,x1,x2); #do ii = 1,`MAXWEIGHT' id S`i'(R(,...,),x1?,x2?) = TT(R(n1,...,n`ii'),x1,x2); #enddo if ( count(TT,1) == 2 ); id sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')* TT(R(?a),n?,-j`i')*TT(R(?b),0,j`i')/j`i'^k?pos0_ = -SS(R(?a),R(?b),k,n); if ( count(j`i',1) == 0 ) id sum`i'(j`i',0,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')* TT(R(?a),n?,-j`i')*TT(R(?b),0,j`i') = -SS(R(?a),R(?b),0,n); else if ( ( count(TT,1) == 1 ) && ( count(S`i',1) == 0 ) ); id sum`i'(j`i',1,n?)*sign`i'(j`i')*bino`i'(n?,0,j`i')* TT(R(?a),n?,-j`i')/j`i'^k?pos0_ = -SS(R(?a),R,k,n); endif; id TT(?a) = S`i'(?a); id SS(?a) = acc1(SS(?a)); * * At this point we have in SS a sum we can do. * repeat; argument,acc1; id SS(R(n1?,?a),R(?b),k?{2,...,`MAXWEIGHT'},n?) = +SS(R(n1,?a),R(?b),k-1,1,n) +sum_(jjj,1,k,SS(R(?a),R(?b),jjj,k+n1-jjj,n)*binom_(k+n1-1-jjj,n1-1)) +sum_(jjj,1,n1,SS(R(?b),R(?a),jjj,-(k+n1-jjj),n)*binom_(k+n1-1-jjj,k-1)) -sum_(jjj,1,k-1,SS(R(?a),R(?b),jjj,k+n1-jjj,n)*binom_(k+n1-2-jjj,n1-1)) -sum_(jjj,1,n1,SS(R(?b),R(?a),jjj,-(k+n1-jjj),n)*binom_(k+n1-2-jjj,k-2)); id SS(R(n1?,?a),R(?b),1,n?) = +SS(R(n1,?a),R(?b),0,1,n) +SS(R(?a),R(?b),1,n1,n) +sum_(jjj,1,n1,SS(R(?b),R(?a),jjj,-(n1+1-jjj),n)) -SS(R(?b),R(?a),n1,-1,n); id SS(R(n1?,?a),R(?b),k?{2,...,`MAXWEIGHT'},n2?,?c,n?) = +SS(R(n1,?a),R(?b),k-1,1,n2,?c,n) +sum_(jjj,1,k,SS(R(?a),R(?b),jjj,k+n1-jjj,n2,?c,n)*binom_(k+n1-1-jjj,n1-1)) +sum_(jjj,1,n1,SS(R(?b),R(?a),jjj,-(k+n1-jjj),n2,?c,n)*binom_(k+n1-1-jjj,k-1)) -sum_(jjj,1,k-1,SS(R(?a),R(?b),jjj,k+n1-jjj,n2,?c,n)*binom_(k+n1-2-jjj,n1-1)) -sum_(jjj,1,n1,SS(R(?b),R(?a),jjj,-(k+n1-jjj),n2,?c,n)*binom_(k+n1-2-jjj,k-2)); id SS(R(n1?,?a),R(?b),1,n2?,?c,n?) = +SS(R(n1,?a),R(?b),0,1,n2,?c,n) +SS(R(?a),R(?b),1,n1,n2,?c,n) +sum_(jjj,1,n1,SS(R(?b),R(?a),jjj,-(1+n1-jjj),n2,?c,n)) -SS(R(?b),R(?a),n1,-1,n2,?c,n); id SS(R(n1?,?a),R(n2?,?b),0,n3?,?c,n?) = +SS(R(n1,?a),R(?b),n2-1,sig_(n3)+n3,?c,n) +SS(R(n2,?b),R(?a),n1-1,-n3-sig_(n3),?c,n); id SS(R(n1?,?a),R(n2?,?b),0,n?) = +SS(R(n1,?a),R(?b),n2-1,n)*den(n) +SS(R(n2,?b),R(?a),n1-1,n)*sign(n)*den(n); endargument; endrepeat; id acc1(x?) = x; id SS(R(n1?,?a),R,0,k?,?c,n?) = SS(R,R(n1,?a),0,-k,?c,n); id SS(R(n1?,?a),R,0,n?) = SS(R,R(n1,?a),0,n)*sign(n); id SS(R,R(?b),n1?,n2?,?a,n?) = Conj(R(?b)/nn^n1)*TT(n2,?a,n) +TT(R(?b),-n2-sig_(n2)*n1,?a,n); id SS(R,R(?b),n1?pos0_,n?) = Conj(R(?b)/nn^n1)*TT(n) +S(R(?b),n)*sign(n)*den(n)^n1; #call conjug(nn,1) id R(?b)*TT(n2?,?a,n?)/nn^n1? = TT(R(?b),sig_(n2)*n1+n2,?a,n); id R(?b)*TT(n?)/nn^n1? = S(R(?b),n)*den(n)^n1; id TT(n2?int_,?a,n?)/nn^n1? = TT(R,sig_(n2)*n1+n2,?a,n); id TT(n?)/nn^n1? = den(n)^n1; id TT(R(?a),?b,n?) = S(R(reverse_(?b),?a),n); id sign(x?{N,j1,...,j`MAXWEIGHT'})*sign(x?{N,j1,...,j`MAXWEIGHT'}) = 1; repeat id sign(n1?number_)*sign(n2?number_) = sign(n1+n2); id sign(x?int_) = sign_(x); * #endprocedure * *--#] sumnmic : *--#[ sumnmii : * #procedure sumnmii(i) * * Sums objects of the type * sum`i'(j`i',1,n-1)*S`i'(R(?a),n-j`i')*S`i'(R(?b),j`i')/j`i'^k * for any (integer) values of ?a, ?b and k (k>0) * * Does not do the case k=0. * * J.Vermaseren,30-oct-1997 * if ( count(j`i',1) < 0 ); id 1/j`i'^n? = den`i'(n,0,j`i'); repeat id den`i'(n1?,0,j`i')*den`i'(n2?,0,j`i') = den`i'(n1+n2,0,j`i'); endif; if ( match(S`i'(R(?a),n?)) ); SplitArg,(j`i'),S`i'; id S`i'(R(?a),j`i') = S`i'(R(?a),0,j`i'); if ( match(sum`i'(j`i',n1?,n2?)*S`i'(R(?a),n2?,-j`i')) == 0 ); id sum`i'(j`i',n1?,n2?) = sum`i'(j`i',n1,n2+1); if ( match(sum`i'(j`i',n1?,n2?)*S`i'(R(?a),n2?,-j`i')) == 0 ); id sum`i'(j`i',n1?,n2?) = sum`i'(j`i',n1,n2-1); endif; endif; endif; if ( count(den`i',1) == 1 ); if ( count(S`i',1) == 2 ); id sum`i'(j`i',1,n?)*S`i'(R(?a),n?,-j`i')*S`i'(R(?b),0,j`i') *sign`i'(j`i')*den`i'(k?,0,j`i') = SS(R(?a),R(?b),-k,n); id sum`i'(j`i',1,n?)*S`i'(R(?a),n?,-j`i')*S`i'(R(?b),0,j`i') *den`i'(k?,0,j`i') = SS(R(?a),R(?b),k,n); id sum`i'(j`i',1,n?)*S`i'(R(?a),x1?,-j`i')*S`i'(R(?b),0,j`i') *sign`i'(j`i')*den`i'(k?,0,j`i') = SS(R(?a),R(?b),-k,n+1,x1); id sum`i'(j`i',1,n?)*S`i'(R(?a),x1?,-j`i')*S`i'(R(?b),0,j`i') *den`i'(k?,0,j`i') = SS(R(?a),R(?b),k,n+1,x1); elseif ( count(S`i',1) == 1 ); id sum`i'(j`i',1,n?)*S`i'(R(?a),n?,-j`i') *sign`i'(j`i')*den`i'(k?,0,j`i') = SS(R(?a),R,-k,n); id sum`i'(j`i',1,n?)*S`i'(R(?a),n?,-j`i') *den`i'(k?,0,j`i') = SS(R(?a),R,k,n); id sum`i'(j`i',1,n?)*S`i'(R(?a),x1?,-j`i') *sign`i'(j`i')*den`i'(k?,0,j`i') = SS(R(?a),R,-k,n+1,x1); id sum`i'(j`i',1,n?)*S`i'(R(?a),x1?,-j`i') *den`i'(k?,0,j`i') = SS(R(?a),R,k,n+1,x1); endif; id SS(?a,n?,n?) = SS(?a,n); id SS(R(?a),R(?b),k?pos_,n?,x1?) = sum`i'(j`i',1,n-1)* S`i'(R(?a),x1,-j`i')*S`i'(R(?b),0,j`i')*den`i'(0,j`i')^k; id SS(R(?a),R(?b),k?neg_,n?,x1?) = sum`i'(j`i',1,n-1)*sign`i'(j`i')* S`i'(R(?a),x1,-j`i')*S`i'(R(?b),0,j`i')*den`i'(0,j`i')^(abs_(k)); endif; * * The sums that this routine can handle are now in the function SS. * Notation in the sequel: we add pairs of k,n if there are new denominators * and summations boundaries. * Eventually we hit on sums we can do and then we work backwards in a * combination of sums and synchronizations. * repeat id SS(R(n1?,?a),R(?b),k?,?c) = +sum_(jjj,1,abs_(k), SS(R(?a),R(?b),sig_(n1*k)*jjj,sig_(n1)*(abs_(k)+abs_(n1)-jjj),?c)* binom_(abs_(k)+abs_(n1)-1-jjj,abs_(n1)-1)) +sum_(jjj,1,abs_(n1), SS(R(?b),R(?a),sig_(n1*k)*jjj,sig_(k)*(abs_(k)+abs_(n1)-jjj),?c)* binom_(abs_(k)+abs_(n1)-1-jjj,abs_(k)-1)); id SS(R,R(?a),k?,m?,?c,n?) = SS(R,R(k,?a),m,?c,n) -SS(R,R(?a),sig_(k)*m+sig_(m)*k,?c,n); id SS(R,R(?a),?c,n?) = S(R(reverse_(?c),?a),n); #endprocedure * *--#] sumnmii : *--#[ sumposp : * #procedure sumposp(j) * * Sums positive (or zero) powers of j`j' possibly in combination * with one S`j' function and possibly a sign`j' * * J.Vermaseren 7-jun-1998 * repeat; if ( count(S`j',1) == 1 ); if ( count(j`j',1) < 0 ); id sum`j'(j`j',1,x2?)*sign`j'(j`j')*S`j'(R(?a),0,j`j')/j`j'^m? = S(R(-m,?a),x2); id sum`j'(j`j',x1?,x2?)*sign`j'(j`j')*S`j'(R(?a),0,j`j')/j`j'^m? = S(R(-m,?a),x2)-S(R(-m,?a),x1-1); id sum`j'(j`j',1,x2?)*S`j'(R(?a),0,j`j')/j`j'^m? = S(R(m,?a),x2); id sum`j'(j`j',x1?,x2?)*S`j'(R(?a),0,j`j')/j`j'^m? = S(R(m,?a),x2)-S(R(m,?a),x1-1); else; if ( count(sign`j',1) ); id sum`j'(j`j',x?{0,1},n?)*sign`j'(j`j')* j`j'^m?pos0_*S`j'(R(n1?pos_,?a),0,j`j') = S(R(n1,?a),n)*mpowsum(m,n) -sum`j'(j`j',1,n)*S`j'(R(?a),0,j`j')* mpowsum1(m,j`j')/j`j'^n1; id sign_(j`j') = sign`j'(j`j'); id sum`j'(j`j',x?{0,1},n?)*sign`j'(j`j')* j`j'^m?pos0_*S`j'(R(n1?neg_,?a),0,j`j') = S(R(n1,?a),n)*mpowsum(m,n) -sum`j'(j`j',1,n)*S`j'(R(?a),0,j`j') *mpowsum1(m,j`j')*sign`j'(j`j')*j`j'^n1; id sign_(j`j') = sign`j'(j`j'); id sign`j'(j`j')*sign`j'(j`j') = 1; else; id sum`j'(j`j',x?{0,1},n?)*j`j'^m?pos0_*S`j'(R(n1?pos_,?a),0,j`j') = S(R(n1,?a),n)*powsum(m,n) -sum`j'(j`j',1,n)*S`j'(R(?a),0,j`j')* powsum1(m,j`j')/j`j'^n1; id sum`j'(j`j',x?{0,1},n?)*j`j'^m?pos0_*S`j'(R(n1?neg_,?a),0,j`j') = S(R(n1,?a),n)*powsum(m,n) -sum`j'(j`j',1,n)*S`j'(R(?a),0,j`j') *powsum1(m,j`j')*sign`j'(j`j')*j`j'^n1; endif; endif; elseif ( count(S`j',1) == 0 ); if ( count(j`j',1) >= 0 ); id sum`j'(j`j',x?{0,1},x2?)*sign`j'(j`j')*j`j'^m? = mpowsum(m,x2); id sum`j'(j`j',x1?,x2?)*sign`j'(j`j')*j`j'^m? = mpowsum(m,x2)-mpowsum(m,x1-1); id sum`j'(j`j',x?{0,1},x2?)*j`j'^m? = powsum(m,x2); id sum`j'(j`j',x1?,x2?)*j`j'^m? = powsum(m,x2)-powsum(m,x1-1); else; id sum`j'(j`j',1,x2?)*sign`j'(j`j')/j`j'^m? = S(R(-m),x2); id sum`j'(j`j',x1?,x2?)*sign`j'(j`j')/j`j'^m? = S(R(-m),x2)-S(R(-m),x1-1); id sum`j'(j`j',1,x2?)/j`j'^m? = S(R(m),x2); id sum`j'(j`j',x1?,x2?)/j`j'^m? = S(R(m),x2)-S(R(m),x1-1); endif; endif; id S`j'(R,?a) = 1; id S(R,?a) = 1; endrepeat; #endprocedure * *--#] sumposp : *--#[ sumposq : * #procedure sumposq(j) * * Sums positive (or zero) powers of j`j' possibly in combination * with one S`j' function and possibly a sign`j' * * J.Vermaseren 7-jun-1998 * repeat; if ( match(S`j'(R(?a),0,j)) == 1 ); if ( count(j,1) < 0 ); id sum(j,1,x2?)*sign`j'(j)*S`j'(R(?a),0,j)/j^m? = S`j'(R(-m,?a),x2); id sum(j,x1?,x2?)*sign`j'(j)*S`j'(R(?a),0,j)/j^m? = S`j'(R(-m,?a),x2)-S`j'(R(-m,?a),x1-1); id sum(j,1,x2?)*S`j'(R(?a),0,j)/j^m? = S`j'(R(m,?a),x2); id sum(j,x1?,x2?)*S`j'(R(?a),0,j)/j^m? = S`j'(R(m,?a),x2)-S`j'(R(m,?a),x1-1); else; if ( count(sign`j',1) ); id sum(j,x?{0,1},n?)*sign`j'(j)* j^m?pos0_*S`j'(R(n1?pos_,?a),0,j) = S`j'(R(n1,?a),n)*mpowsum(m,n) -sum(j,1,n)*S`j'(R(?a),0,j)* mpowsum1(m,j)/j^n1; id sign_(j) = sign`j'(j); id sum(j,x?{0,1},n?)*sign`j'(j)* j^m?pos0_*S`j'(R(n1?neg_,?a),0,j) = S`j'(R(n1,?a),n)*mpowsum(m,n) -sum(j,1,n)*S`j'(R(?a),0,j) *mpowsum1(m,j)*sign`j'(j)*j^n1; id sign_(j) = sign`j'(j); id sign`j'(j)*sign`j'(j) = 1; else; id sum(j,x?{0,1},n?)*j^m?pos0_*S`j'(R(n1?pos_,?a),0,j) = S`j'(R(n1,?a),n)*powsum(m,n) -sum(j,1,n)*S`j'(R(?a),0,j)* powsum1(m,j)/j^n1; id sum(j,x?{0,1},n?)*j^m?pos0_*S`j'(R(n1?neg_,?a),0,j) = S`j'(R(n1,?a),n)*powsum(m,n) -sum(j,1,n)*S`j'(R(?a),0,j) *powsum1(m,j)*sign`j'(j)*j^n1; endif; endif; elseif ( match(S`j'(R(?a),0,j)) == 0 ); if ( count(j,1) >= 0 ); id sum(j,x?{0,1},x2?)*sign`j'(j)*j^m? = mpowsum(m,x2); id sum(j,x1?,x2?)*sign`j'(j)*j^m? = mpowsum(m,x2)-mpowsum(m,x1-1); id sum(j,x?{0,1},x2?)*j^m? = powsum(m,x2); id sum(j,x1?,x2?)*j^m? = powsum(m,x2)-powsum(m,x1-1); else; id sum(j,1,x2?)*sign`j'(j)/j^m? = S`j'(R(-m),x2); id sum(j,x1?,x2?)*sign`j'(j)/j^m? = S`j'(R(-m),x2)-S`j'(R(-m),x1-1); id sum(j,1,x2?)/j^m? = S`j'(R(m),x2); id sum(j,x1?,x2?)/j^m? = S`j'(R(m),x2)-S`j'(R(m),x1-1); endif; endif; id S`j'(R,?a) = 1; id sign_(x?) = sign(x); SplitArg,sign; repeat id sign(x1?,x2?,?a) = sign(x1)*sign(x2,?a); id sign(j`i') = sign`i'(j`i'); id sign(-j`i') = sign`i'(j`i'); id sign(x?)*sign(x?) = 1; id sign(x?number_) = sign_(x); endrepeat; id S`j'(R(?a),x1?,x2?) = S`j'(R(?a),x1+x2); SplitArg,((j`j')),S`j'; id S`j'(R(?a),j`j') = S`j'(R(?a),0,j`j'); id S`j'(R(?a),j) = S`j'(R(?a),0,j); #endprocedure * *--#] sumposq : *--#[ sumreg : * #procedure sumreg(j) * * Final regularization of a sum. * if ( count(bino`j',1) == 0 ); id sum`j'(j`j',x1?,x2?)*den`j'(x3?,-j`j') = X(x3-x2)*sum`j'(j`j',x1,x2)*den`j'(x3,-j`j'); if ( count(X,1) ); #call flipj(`j') id X(x1?) = 1; #call synchds(`j') endif; #call dosign *elseif ( ( count(S`j',1,den`j',1) == 1 ) * && match(sum`j'(j`j',n1?,n?)*S`j'(R(?a),n?,-j`j')) ); * #call flipj(`j') * #call synchds(`j') endif; .sort:sumreg-flip direction; if ( match(den`j'(x1?!{0,0},j`j')) ); id,once,den`j'(x1?,j`j') = den`j'(x1,j`j')*X(x1); #call movej(`j',X) endif; id X(x1?) = 1; #call dosign .sort:sumreg den`j' shift; id sum`j'(j`j',x1?,x2?)*den`j'(x3?,-j`j') = X(x3-x2)*sum`j'(j`j',x1,x2)*den`j'(x3,-j`j'); if ( count(X,1) ); #call flipj(`j') endif; id X(x1?) = 1; #call dosign .sort:sumreg-flip direction; if ( count(bino`j',1) == 0 ); if ( match(den`j'(x1?!{0,0},j`j')) ); id,once,den`j'(x1?,j`j') = den`j'(x1,j`j')*X(x1); #call movej(`j',X) id X(x1?) = 1; endif; #call dosign endif; .sort:sumreg den`j' shift; id sum`j'(j`j',n1?,n2?) = sum`j'(j`j',n1,n2)*theta_(n2-n1); id theta_(x?) = theta(x); #do ni = `j'-1,1,-1 #call theta(`ni') #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #enddo #call theta(N) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif repeat; id sum`j'(j`j',0,n?pos_) = sum`j'(j`j',0,n-1)+replace_(j`j',n); endrepeat; id sum`j'(j`j',0,0) = replace_(j`j',0); id sum`j'(j`j',0,n?neg_) = 0; if ( match(den`j'(0,j`j')) ); id sum`j'(j`j',n1?pos_,n2?) = sum`j'(j`j',1,n2) - sum_(jjj,1,n1-1,su(jjj)); endif id sum_(jjj,x1?,x2?,su(jjj)) = f1(x1,x2,x2-x1)*su(jjj); repeat id f1(x1?,x2?,x3?pos_) = f1(x1,x2-1,x3-1)+replace_(jjj,x2); id f1(x1?,x2?,0) = replace_(jjj,x2); id f1(x1?,x2?,x3?neg_) = 0; id f1(x1?,x2?,x3?)*su(jjj) = sum_(jjj,x1,x2,su(jjj)); * * In case some sum has now been eliminated we replace the relevant * objects by their new values. * if ( count(su,1) ); id su(n?) = replace_(j`j',n); id S`j'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id bino`j'(n1?,n2?,n3?) = fac(n1)*invfac(n2+n3)*invfac(n1-n2-n3); id den`j'(x1?,x2?) = den(x1+x2); id fac`j'(x1?,x2?) = fac(x1+x2); id invfac`j'(x1?,x2?) = invfac(x1+x2); id sign`j'(x?) = sign_(x); id fac(x?int_) = fac_(x); id invfac(x?int_) = invfac_(x); * * The next replacement looks dumb, but it protects again divisions * by zero which might be cancelled out in the sort or survive when * there are errors in what we are trying to do. It would be better * if they survive as some kind of indicator of problems. * id den(x?pos_) = 1/x; id den(x?neg_) = 1/x; #call subesses(S) endif; * * The final introduction of binomial coefficients. * After this we should not change anything. * if ( count(fac`j',1,invfac`j',1) >= 2 ); id invfac`j'(n1?,j`j')*invfac`j'(n2?,-j`j') = bino`j'(n1+n2,n1,j`j')*invfac(n1+n2); id fac`j'(n1?,j`j')*invfac`j'(n2?,j`j') = bino`j'(n1,j`j',n2,j`j')*fac(n1-n2); endif; #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #endprocedure * *--#] sumreg : *--#[ sumspec : * #procedure sumspec(i) * * Some special sums. * This deals with a number of sums that can only be handled * for specific cases. If the program comes here and the sum * cannot be done in this routine, we are out of luck! * if ( ( count(S`i',1,den`i',1) == 0 ) && ( count(j`i',1) == 0 ) ); id sum`i'(j`i',0,n1?)*fac`i'(0,j`i')*fac`i'(n2?,-j`i')*sign`i'(j`i') = fac(n2+1)*den(n2+2)+sign(n1)*fac(n1+1)*fac(n2-n1)*den(n2+2); id sum`i'(j`i',n3?,n1?)*fac`i'(0,j`i')*fac`i'(n2?,-j`i')*sign`i'(j`i') = +sign(n1)*fac(n1+1)*fac(n2-n1)*den(n2+2) +sign(n3)*fac(n3)*fac(n2-n3+1)*den(n2+2); id sum`i'(j`i',0,n?)*fac`i'(m?,j`i')*invfac`i'(0,j`i') = fac(n+m+1)*invfac(n)*den(m+1); id sum`i'(j`i',0,n?)*fac`i'(m?,j`i')*invfac`i'(n1?,j`i') = fac(n+m+1)*invfac(n+n1)*den(m+1-n1)*theta(m-n1) -fac(m)*invfac(n1-1)*den(m+1-n1)*theta(m-n1)*theta(n1-1); elseif ( ( count(S`i',1,den`i',1) == 1 ) && ( count(j`i',1) == 0 ) ); id sum`i'(j`i',n3?,n1?)*fac`i'(0,j`i')*fac`i'(n2?,-j`i') *sign`i'(j`i')*S`i'(R(1),0,j`i') = +sign(n1)*fac(n1+1)*fac(n2-n1)* (S(R(1),n1+1)-den(n2+2))*den(n2+2) +sign(n3)*fac(n3)*fac(n2-n3+1)* (S(R(1),n3)-den(n2+2))*den(n2+2); id sum`i'(j`i',n3?pos_,n1?)*fac`i'(0,j`i')*fac`i'(n2?,-j`i') *sign`i'(j`i')*den`i'(0,j`i') = +sign(n1)*fac(n1)*fac(n2-n1)*den(n2+1) +sign(n3)*fac(n3-1)*fac(n2-n3+1)*den(n2+1); id sum`i'(j`i',0,n?)*den(n1?,-j`i') = X(n,n1,n1-n); id X(n?,n1?,1)*fac`i'(m?,j`i')*invfac`i'(0,j`i') = fac(n1+m)*invfac(n1)*(S(R(1),n1+m)-S(R(1),m)); id X(n?,n1?,n2?) = sum`i'(j`i',0,n)*den`i'(n1,-j`i'); id sum`i'(j`i',0,n?)*S`i'(R(1),n1?,-j`i') = X(n,n1,n1-n); id X(n?,n1?,n2?{0,1})*fac`i'(m?,j`i')*invfac`i'(0,j`i') = fac(n+m+2)*invfac(n1)*den(m+1)*(S(R(1),n+m+2)-S(R(1),m+1)); id X(n?,n1?,n2?) = sum`i'(j`i',0,n)*S`i'(R(1),n1,-j`i'); id sum`i'(j`i',0,n?)*fac`i'(m?,j`i')*invfac`i'(0,j`i')*S`i'(R(1),m?,j`i') = +fac(n+m+1)*invfac(n)*den(m+1)*(S(R(1),n+m+1)-den(m+1)); id sum`i'(j`i',0,n?)*fac`i'(m?,j`i')*invfac`i'(0,j`i')*S`i'(R(2),m?,j`i') = +fac(n+m+1)*invfac(n)*den(m+1)*S(R(2),n+m) -sign(m)*fac(m)*den(m+1)*S(R(1),n+m) -sign(m)*fac(m)*den(m+1)*A(1,m,n); elseif ( ( count(S`i',1,den`i',1) == 2 ) && ( count(j`i',1) == 0 ) ); id sum`i'(j`i',n3?pos_,n1?)*fac`i'(0,j`i')*fac`i'(n1?,-j`i') *sign`i'(j`i')*den`i'(0,j`i')*den`i'(0,j`i') = fac(n1)*(S(R(2),n1)+2*S(R(-2),n1)) -sum_(j,1,n3-1,fac_(j)*fac(n1-j)*sign_(j)/j^2); id sum`i'(j`i',n3?pos_,n2?)*fac`i'(0,j`i')*fac`i'(n1?,-j`i') *sign`i'(j`i')*den`i'(0,j`i')*den`i'(0,j`i') = X(n1,n2,n3,n1-n2); id X(n1?,n2?,n3?,n4?pos_) = fac(n1)*(S(R(2),n1)+2*S(R(-2),n1)) -sum_(j,1,n3-1,fac_(j)*fac(n1-j)*sign_(j)/j^2) -sum(j,n2+1,n1,n1-n2-1)*fac(j)*fac_(n1-j)*sign(j)*den(j)*den(j); id X(n1?,n2?,n3?,n4?) = sum`i'(j`i',n3,n2)*fac`i'(0,j`i') *fac`i'(n1,-j`i')*sign(j`i')*den`i'(0,j`i')*den`i'(0,j`i'); repeat id sum(j,n1?,n2?,n3?pos0_) = sum(j,n1,n2-1,n3-1)+replace_(j,n2); id sum(j,n1?,n2?,n3?neg_) = 0; id sum`i'(j`i',0,n?)*fac`i'(m?,j`i')*invfac`i'(0,j`i') *S`i'(R(1),m?,j`i')*S`i'(R(1),m?,j`i') = fac(n+m+1)*invfac(n)*den(m+1)*(den(m+1)*den(m+1) +(S(R(1),n+m+1)-den(m+1))^2) -fac(n+m)*invfac(n)*den(m+1)*den(n+m+1) -sign(m)*fac(m)*den(m+1)*(S(R(1),n+m)+A(1,m,n)); id sum`i'(j`i',0,n?)*den(n1?,-j`i') = X(n,n1,n1-n); id X(n?,n1?,1)*fac`i'(m?,j`i')*invfac`i'(0,j`i')*S`i'(R(1),m?,j`i') = fac(n+m)*invfac(n)*(S(R(1),n+m)^2-S(R(2),m+n) +S(R(2),m)-S(R(1),m+n)*S(R(1),m)); id X(n?,n1?,n2?) = sum`i'(j`i',0,n)*den`i'(n1,-j`i'); id sum`i'(j`i',0,n?)*S`i'(R(1),n1?,-j`i') = X(n,n1,n1-n); id X(n?,n1?,n2?{0,1})*fac`i'(m?,j`i')*invfac`i'(0,j`i') *S`i'(R(1),m?,j`i') = fac(n+m+1)*invfac(n)*den(m+1)*(-S(R(2),n+m+1)+S(R(2),m+1) +(S(R(1),n+m+1)-S(R(1),m+1))*(S(R(1),n+m+1)-den(m+1))); id X(n?,n1?,n2?) = sum`i'(j`i',0,n)*S`i'(R(1),n1,-j`i'); endif; #endprocedure * *--#] sumspec : *--#[ synch : * #procedure synch(i) * * Procedure to synchronize the arguments of den,fac,invfac,bino,S. * * Start with synchronizing products of S functions. * Note that if two S functions have been synchronized they are * brought to the basis. Hence only one will be left. * id S(R,?a) = 1; id S`i'(R,?a) = 1; #call synchss(`i') id S(R,?a) = 1; id S`i'(R,?a) = 1; id Even(N)*sign(N) = Even(N); id Odd(N)*sign(N) = -Odd(N); #if `i' == 0 #call normden(0) #else #do ii = `i',1,-1 #call normden(`ii') #enddo #endif .sort:Synchronize S; #if `i' == 0 #call densplit(0) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #else #do ii = `i',1,-1 #call densplit(`ii') #enddo #endif #call densplit(N) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif .sort:synch-densplit-1; #if `i' == 0 #call theta(0) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #else #do ii = `i',1,-1 #call theta(`ii') #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #enddo #endif #call theta(N) .sort:synch-theta-1; * * First see whether we need to invert the direction of summation * id sum`i'(j`i',x1?,x2?)*den`i'(x3?,-j`i') = X(x3-x2)*sum`i'(j`i',x1,x2)*den`i'(x3,-j`i'); if ( match(X(x1?int_)) ); #call flipj(`i') endif; id X(x1?) = 1; .sort:synch-flip direction; * * Then see whether we need to move the summation a bit. * if ( match(den`i'(x1?pos_,j`i')) ); id,once,den`i'(x1?pos_,j`i') = den`i'(x1,j`i')*X(x1); #call movej(`i',X) id X(x1?) = 1; endif; id S(R,?a) = 1; id S`i'(R,?a) = 1; .sort:synch den`i' shift; * * Now comes the great recursion * #do k1 = 1,1 #do k2 = 1,1 * * Now we look at * 1: combinations of den and S. * #call synchds(`i') id S(R,?a) = 1; id S`i'(R,?a) = 1; * .sort:synch den`i',S`i'; * * 2: combinations of den and fac,invfac. * #call synchdf(`i') id S(R,?a) = 1; id S`i'(R,?a) = 1; * * If there was action we have to restart with den and S. * if ( $syndf > 0 ) redefine k2 "0"; * #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif .sort:synch den`i',fac`i'; #enddo * * Combination of j and fac or invfac * If there is a j there is no den! * if ( count(j`i',1) > 0 ); repeat id j`i'*invfac`i'(n?pos_,j`i') = invfac`i'(n-1,j`i')-n*invfac`i'(n,j`i'); endif; * * 3: combinations of fac,invfac.and S * #call synchfs(`i') id S(R,?a) = 1; id S`i'(R,?a) = 1; * * If there was action, we have to start from the beginning again. * if ( $synfs > 0 ) redefine k1 "0"; #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif * .sort:synch fac`i',S`i'; #if `$synfs' > 0 #if `i' == 0 #call densplit(0) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #else #do ii = `i',1,-1 #call densplit(`ii') #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #enddo #endif #call densplit(N) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif .sort:synch-densplit-2; #if `i' == 0 #call theta(0) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #else #do ii = `i',1,-1 #call theta(`ii') #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif #enddo #endif #call theta(N) #ifdef `EXTRASUMMER' ; `EXTRASUMMER' #endif .sort:synch-theta-2; #endif id S(R,?a) = 1; id S`i'(R,?a) = 1; id sum`i'(j`i',x1?,x2?)*den`i'(x3?,-j`i') = X(x3-x2)*sum`i'(j`i',x1,x2)*den`i'(x3,-j`i'); if ( match(X(x1?int_)) ); #call flipj(`i') else if ( ( count(den`i',1) == 0 ) && ( count(S`i',1) == 1 ) ); id sum`i'(j`i',x1?,x2?)*S`i'(?a,x3?,-j`i') = X(x3-x2)*sum`i'(j`i',x1,x2)*S`i'(?a,x3,-j`i'); if ( match(X(x1?int_)) ); #call flipj(`i') endif; endif; id X(x1?) = 1; #call synchds(`i') id sum`i'(j`i',n1?,n2?) = X(n1,n2,n2-n1); if ( match(X(n1?,n2?,n3?int_)) ); id X(n1?,n2?,n3?neg_) = 0; repeat; id X(n1?,n2?,n3?pos_) = replace_(j`i',n2)+X(n1,n2-1,n3-1); endrepeat; id X(n1?,n2?,0) = replace_(j`i',n2); id S`i'(R(?a),n1?,n2?) = S(R(?a),n1+n2); id bino`i'(n1?,n2?,n3?) = fac_(n1)*invfac_(n2+n3)*invfac_(n1-n2-n3); id fac`i'(n1?,n2?) = fac_(n1+n2); id invfac`i'(n1?,n2?) = invfac_(n1+n2); id sign`i'(n1?) = sign_(n1); id den`i'(n1?,n2?) = den(n1+n2); id fac_(x?) = fac(x); id invfac_(x?) = invfac(x); id sign_(x?) = sign(x); else; id X(n1?,n2?,n3?) = sum`i'(j`i',n1,n2); endif; .sort:synch-flip direction; #enddo * * 4: synchronize with the summation boundaries * also introduces the binomial coefficients * #call adjustsm(`i') #call dosign id Even(N)*sign(N) = Even(N); id Odd(N)*sign(N) = -Odd(N); id sign(j`i') = sign`i'(j`i'); id sign(-j`i') = sign`i'(j`i'); id sign`i'(j`i')*sign`i'(j`i') = 1; * #endprocedure * *--#] synch : *--#[ synchdf : * #procedure synchdf(i) * * Synchronizes combinations of factorials and denominators * den and fac and invfac. * Note: if there is a fac with which den can synchronize, * there cannot be an invfac et vise versa. * The variable $syndf will be 1 if anything relevant happened. * #$syndf = 0; repeat; id,once,den`i'(x1?,x?)*fac`i'(x2?,x?) = f1(1,x1,x2,x,x2-x1); if ( match(f1(1,x1?,x2?,x3?,n?int_)) ); repeat id f1(n1?,x1?,x2?,x?,x3?)*den`i'(x1?,x?) = f1(n1+1,x1,x2,x,x3); id f1(?a) = f2(?a); else; id f1(1,x1?,x2?,x?,x3?) = den`i'(x1,x)*f3(x2,x); endif; endrepeat; id f3(?a) = fac`i'(?a); repeat; id,once,den`i'(x1?,x?)*invfac`i'(x2?,x?) = f1(1,x1,x2,x,x2-x1); if ( match(f1(1,x1?,x2?,x3?,n?int_)) ); repeat id f1(n1?,x1?,x2?,x?,x3?)*den`i'(x1?,x?) = f1(n1+1,x1,x2,x,x3); id f1(?a) = f4(?a); else; id f1(1,x1?,x2?,x?,x3?) = den`i'(x1,x)*f3(x2,x); endif; endrepeat; id f3(?a) = invfac`i'(?a); if ( match(f2(1,x1?,x2?,x?,0)) ); id f2(1,x1?,x2?,x?,0) = fac`i'(x2-1,x); $syndf = 1; endif; id f2(n?,x1?,x2?,x?,0) = den`i'(x1,x)^n*fac`i'(x2,x); id f4(n?,x1?,x2?,x?,0) = den`i'(x1,x)^n*invfac`i'(x2,x); * * f2 contains a combination of den and fac * f4 contains a combination of den and invfac * if ( count(f2,1,f4,1) ); $syndf = 1; #if `i' == 0 Print "sych0: %t"; #endif endif; repeat; id f2(n?pos_,x1?,x2?,x?,n1?pos_) = f2(n-1,x1,x2-1,x,n1-1) + n1*f2(n,x1,x2-1,x,n1-1); id f2(1,x1?,x2?,x?,0) = fac`i'(x2-1,x); id f2(n?,x1?,x2?,x?,0) = den`i'(x1,x)^n*fac`i'(x2,x); id f2(0,x1?,x2?,x?,n1?) = fac`i'(x2,x); endrepeat; repeat; id f2(n?,x1?,x2?,x?,-1) = fac`i'(x1,x)*den`i'(x1,x)^(n+1); id f2(n?pos_,x1?,x2?,x?,n1?neg_) = fac`i'(x2,x)/(-n1-1)^n -sum_(jjj,1,n,f2(jjj,x1,x2+1,x,n1+1)/(-n1-1)^(n+1-jjj)); endrepeat; repeat; id f4(n?,x1?,x2?,x?,-1) = invfac`i'(x1,x)*den`i'(x1,x)^(n-1); id f4(n?pos_,x1?,x2?,x?,n1?neg_) = f4(n-1,x1,x2+1,x,n1+1) + acc1(n1+1)*f4(n,x1,x2+1,x,n1+1); id acc1(n?) = n; id f4(0,x1?,x2?,x?,n1?) = invfac`i'(x2,x); endrepeat; repeat; id f4(n?,x1?,x2?,x?,0) = den`i'(x1,x)^n*invfac`i'(x2,x); id f4(n?pos_,x1?,x2?,x?,n1?pos_) = invfac`i'(x2,x)/n1^n*sign_(n) +sum_(jjj,1,n,f4(jjj,x1,x2-1,x,n1-1)/n1^(n+1-jjj)*sign_(n-jjj)); endrepeat; * #endprocedure * *--#] synchdf : *--#[ synchds : * #procedure synchds(i) * * Procedure synchronizes products of den and S. * The algorithm is in the paper * repeat; if ( count(SS,1) == 0 ); id,once,S`i'(?a,x1?!{x2?},j`i')*den`i'(x2?!{x1?},j`i') = SS(?a,x1,x2,x1-x2,1); if ( match(SS(?a,n?int_,1)) == 0 ); id SS(?a,x1?,x2?,x3?,1) = X(?a,x1,j`i')*den`i'(x2,j`i'); endif; endif; endrepeat; id X(?a) = S`i'(?a); if ( match(SS(?a,n?int_,1)) ); repeat id SS(?a,x2?,x3?,n?)*den`i'(x2?,j`i') = SS(?a,x2,x3,n+1); repeat; repeat; id SS(R(n1?pos_,?a),x1?,x2?,-1,n2?) = +S`i'(R(n1,?a),x2,j`i')*(den`i'(x2,j`i'))^n2 -S`i'(R(?a),x2,j`i')*(den`i'(x2,j`i'))^n1*(den`i'(x2,j`i'))^n2; id SS(R(n1?neg_,?a),x1?,x2?,-1,n2?) = +S`i'(R(n1,?a),x2,j`i')*(den`i'(x2,j`i'))^n2 -sign(x2)*sign`i'(j`i')*S`i'(R(?a),x2,j`i')* (den`i'(x2,j`i'))^(-n1)*(den`i'(x2,j`i'))^n2; id SS(R(?a),x1?,x2?,0,n2?) = S`i'(R(?a),x1,j`i')*(den`i'(x2,j`i'))^n2; id SS(R,x1?,x2?,x3?,n1?) = (den`i'(x2,j`i'))^n1; id SS(R(n1?pos_,?a),x1?,x2?,x3?pos_,n2?) = +SS(R(n1,?a),x1-1,x2,x3-1,n2) +sum_(jjj,1,n2,sign_(n2-jjj)*binom_(n1+n2-1-jjj,n1-1) /x3^(n1+n2-jjj)*SS(R(?a),x1,x2,x3,jjj)) +sum_(jjj,1,n1,sign_(n2)*binom_(n1+n2-1-jjj,n2-1) /x3^(n1+n2-jjj)*(den`i'(x1,j`i'))^jjj*S`i'(R(?a),x1,j`i')); id SS(R(n1?pos_,?a),x1?,x2?,x3?neg_,n2?) = +SS(R(n1,?a),x1+1,x2,x3+1,n2) -sum_(jjj,1,n2,sign_(n2-jjj)*binom_(n1+n2-1-jjj,n1-1) /(x3+1)^(n1+n2-jjj)*SS(R(?a),x1+1,x2,x3+1,jjj)) -sum_(jjj,1,n1,sign_(n2)*binom_(n1+n2-1-jjj,n2-1) /(x3+1)^(n1+n2-jjj)*(den`i'(x1+1,j`i'))^jjj*S`i'(R(?a),x1+1,j`i')); endrepeat; id SS(R(n1?neg_,?a),x1?,x2?,x3?pos_,n2?) = +SS(R(n1,?a),x1-1,x2,x3-1,n2) +sign(x1)*sign`i'(j`i')*sum_(jjj,1,n2,sign_(n2-jjj)* binom_(-n1+n2-1-jjj,-n1-1) /x3^(-n1+n2-jjj)*SS(R(?a),x1,x2,x3,jjj)) +sign(x1)*sign`i'(j`i')*sum_(jjj,1,-n1,sign_(n2)* binom_(-n1+n2-1-jjj,n2-1)/x3^(-n1+n2-jjj)* (den`i'(x1,j`i'))^jjj*S`i'(R(?a),x1,j`i')); id SS(R(n1?neg_,?a),x1?,x2?,x3?neg_,n2?) = +SS(R(n1,?a),x1+1,x2,x3+1,n2) -sign(x1+1)*sign`i'(j`i')*sum_(jjj,1,n2,sign_(n2-jjj)* binom_(-n1+n2-1-jjj,-n1-1) /(x3+1)^(-n1+n2-jjj)*SS(R(?a),x1+1,x2,x3+1,jjj)) -sign(x1+1)*sign`i'(j`i')*sum_(jjj,1,-n1,sign_(n2)* binom_(-n1+n2-1-jjj,n2-1) /(x3+1)^(-n1+n2-jjj)*(den`i'(x1+1,j`i'))^jjj*S`i'(R(?a),x1+1,j`i')); endrepeat; id S`i'(R,n?,j`i') = 1; endif; * #endprocedure * *--#] synchds : *--#[ synchfs : * #procedure synchfs(i) * * Combinations of fac and S or invfac and S. * The variable $synfs will be 1 if anything relevant happened. * #$synfs = 0; repeat; id,once,S`i'(R(?a),x1?,x?)*fac`i'(x2?,x?) = f1(R(?a),x1,x2,x,x2-x1); if ( match(f1(?a,n?int_)) ); id f1(?a) = f2(?a); else; id f1(R(?a),x1?,x2?,x?,x3?) = S`i'(R(?a),x1,x)*f3(x2,x); endif; endrepeat; id f3(?a) = fac`i'(?a); repeat; id,once,S`i'(R(?a),x1?,x?)*invfac`i'(x2?,x?) = f1(R(?a),x1,x2,x,x2-x1); if ( match(f1(?a,n?int_)) ); id f1(?a) = f4(?a); else; id f1(R(?a),x1?,x2?,x?,x3?) = S`i'(R(?a),x1,x)*f3(x2,x); endif; endrepeat; id f3(?a) = invfac`i'(?a); id f2(R(?a),x1?,x2?,x?,0) = S`i'(R(?a),x1,x)*fac`i'(x2,x); id f4(R(?a),x1?,x2?,x?,0) = S`i'(R(?a),x1,x)*invfac`i'(x2,x); if ( count(f2,1,f4,1) ) $synfs = 1; repeat; id f4(R(n1?,?a),x1?,x2?,x?,n?neg_) = f4(R(n1,?a),x1-1,x2,x,n+1) +S`i'(R(?a),x1,x)*invfac`i'(x2,x)*den`i'(x1,x)^(abs_(n1)) *sign(x1)^theta_(-n1)*sign`i'(x)^theta_(-n1); endrepeat; repeat; id f4(R(n1?,?a),x1?,x2?,x?,n?pos_) = f4(R(n1,?a),x1+1,x2,x,n-1) -S`i'(R(?a),x1+1,x)*invfac`i'(x2,x)*den`i'(x1+1,x)^(abs_(n1)) *sign(x1)^theta_(-n1)*sign`i'(x)^theta_(-n1); endrepeat; * * Theta constraint from Sven * id f4(R(?a),x1?,x2?,x?,0) = S`i'(R(?a),x1,x)*invfac`i'(x2,x)*theta_(x1+x-1); *id f4(R(?a),x1?,x2?,x?,0) = S`i'(R(?a),x1,x)*invfac`i'(x2,x); repeat; id f2(R(n1?,?a),x1?,x2?,x?,n?neg_) = f2(R(n1,?a),x1-1,x2,x,n+1) +S`i'(R(?a),x1,x)*fac`i'(x2,x)*den`i'(x1,x)^(abs_(n1)) *sign(x1)^theta_(-n1)*sign`i'(x)^theta_(-n1); endrepeat; repeat; id f2(R(n1?,?a),x1?,x2?,x?,n?pos_) = f2(R(n1,?a),x1+1,x2,x,n-1) -S`i'(R(?a),x1+1,x)*fac`i'(x2,x)*den`i'(x1+1,x)^(abs_(n1)) *sign(x1)^theta_(-n1)*sign`i'(x)^theta_(-n1); endrepeat; * * Theta constraint from Sven * id f2(R(?a),x1?,x2?,x?,0) = S`i'(R(?a),x1,x)*fac`i'(x2,x)*theta_(x1+x-1); *id f2(R(?a),x1?,x2?,x?,0) = S`i'(R(?a),x1,x)*fac`i'(x2,x); id sign`i'(-j`i') = sign`i'(j`i'); id sign`i'(j`i')*sign`i'(j`i') = 1; * #endprocedure * *--#] synchfs : *--#[ synchss : * #procedure synchss(i) * * Synchronization of products of S-functions * repeat; id,once,S`i'(x1?,x2?,x3?) = f1(x1,x2,x3); repeat; id,f1(x1?,x2?,x3?)*S`i'(x4?,x5?,x3?) = f2(x1,x2,x4,x5,x3,x2-x5); if ( match(f2(?a,x?int_)) ); repeat; id f2(R(n1?,?a),x2?,R(n2?,?b),x5?,x3?,x6?pos_) = +f2(R(n1,?a),x2,R(n2,?b),x5+1,x3,x6-1) -f2(R(n1,?a),x2,R(?b),x5+1,x3,x6-1) *den`i'(x5+1,x3)^abs_(n2)*sign(x5+1)^theta_(-n2) *sign`i'(j`i')^theta_(-n2); endrepeat; repeat; id f2(R(n1?,?a),x2?,R(n2?,?b),x5?,x3?,x6?neg_) = +f2(R(n1,?a),x2+1,R(n2,?b),x5,x3,x6+1) -f2(R(?a),x2+1,R(n2,?b),x5,x3,x6+1) *den`i'(x2+1,x3)^abs_(n1)*sign(x2+1)^theta_(-n1) *sign`i'(j`i')^theta_(-n1); endrepeat; id f2(x1?,x2?,x4?,x5?,x3?,n?) = S`i'(x1,x2,x3)*S`i'(x4,x5,x3); id S`i'(R,x1?,x2?) = 1; #call basis2(S`i') else; id f2(x1?,x2?,x4?,x5?,x3?,x6?) = f1(x1,x2,x3)*f3(x4,x5,x3); endif; endrepeat; id f3(x4?,x5?,x3?) = S`i'(x4,x5,x3); id f1(?a) = f4(?a); endrepeat; id f4(?a) = S`i'(?a); #endprocedure * *--#] synchss : *--#[ table1 : * #procedure table1 * * Constants: Sinf is the basic divergence ~ln_(inf) = lim(n->inf)*S_1(n) * ln2 = ln_(2) * File by J. Vermaseren 5-jun-1998 * S Sinf,ln2; CTable,relax,Stab1(-1:1); Fill Stab1(1) = Sinf; Fill Stab1(-1) = -ln2; #endprocedure * *--#] table1 : *--#[ table2 : * #procedure table2 * * New constant: z2 = zeta_2 = pi_^2/6 * File by J. Vermaseren, 5-jun-1998 * S z2; CTable,relax,Stab2(-1:1,-1:1); Fill Stab2(0,1) = z2; Fill Stab2(0,-1) = -z2/2; Fill Stab2(1,1) = + 1/2*z2 + 1/2*Sinf^2; Fill Stab2(1,-1) = - 1/2*ln2^2 - Sinf*ln2; Fill Stab2(-1,1) = - 1/2*z2 + 1/2*ln2^2; Fill Stab2(-1,-1) = + 1/2*z2 + 1/2*ln2^2; #endprocedure * *--#] table2 : *--#[ table3 : * #procedure table3 * * New constant: z3 = zeta_3 * File by J. Vermaseren, 5-jun-1998 * S z3; CTable,relax,Stab3(-1:1,-1:1,-1:1); Fill Stab3(0,0,1) = + z3; Fill Stab3(0,0,-1) = - 3/4*z3; Fill Stab3(0,1,1) = + 2*z3; Fill Stab3(0,1,-1) = - 3/2*z2*ln2 + 1/4*z3; Fill Stab3(0,-1,1) = - 5/8*z3; Fill Stab3(0,-1,-1) = + 3/2*z2*ln2 - 5/8*z3; Fill Stab3(1,0,1) = - z3 + Sinf*z2; Fill Stab3(1,0,-1) = - 1/8*z3 - 1/2*Sinf*z2; Fill Stab3(-1,0,1) = + 1/2*z2*ln2 - z3; Fill Stab3(-1,0,-1) = - z2*ln2 + 13/8*z3; Fill Stab3(1,1,1) = + 1/3*z3 + 1/2*Sinf*z2 + 1/6*Sinf^3; Fill Stab3(1,1,-1) = - 1/2*z2*ln2 - 1/6*ln2^3 - 1/2*Sinf*ln2^2 - 1/2*Sinf^2*ln2; Fill Stab3(1,-1,1) = - 1/2*z2*ln2 + 1/8*z3 + 1/3*ln2^3 - 1/2*Sinf*z2 + 1/2*Sinf*ln2^2; Fill Stab3(1,-1,-1) = + 1/2*z2*ln2 - 7/8*z3 + 1/3*ln2^3 + 1/2*Sinf*z2 + 1/2*Sinf*ln2^2; Fill Stab3(-1,1,1) = + 1/2*z2*ln2 - 7/8*z3 - 1/6*ln2^3; Fill Stab3(-1,1,-1) = + 1/2*z2*ln2 + 1/8*z3 - 1/6*ln2^3; Fill Stab3(-1,-1,1) = - 1/2*z2*ln2 + 7/4*z3 - 1/6*ln2^3; Fill Stab3(-1,-1,-1) = - 1/2*z2*ln2 - 1/4*z3 - 1/6*ln2^3; #endprocedure * *--#] table3 : *--#[ table4 : * #procedure table4 * * New constant: li4half = Li_4(1/2) = -S(R(-1,1,1,1),inf) * File by J. Vermaseren, 5-jun-1998 * S li4half; CTable,relax,Stab4(-1:1,-1:1,-1:1,-1:1); Fill Stab4(-1,-1,-1,-1) = 1/4*z2*ln2^2+9/40*z2^2+1/4*z3*ln2+1/24*ln2^4; Fill Stab4(-1,-1,-1,1) = 1/4*z2*ln2^2-19/40*z2^2+1/4*z3*ln2+1/24*ln2^4; Fill Stab4(-1,-1,0,-1) = -1/4*z2*ln2^2-3/5*z2^2+z3*ln2; Fill Stab4(-1,-1,0,1) = -1/4*z2*ln2^2-3/8*z2^2+z3*ln2+1/8*ln2^4+3*li4half; Fill Stab4(-1,-1,1,-1) = -1/2*z2*ln2^2-6/5*z2^2+7/8*z3*ln2+1/6*ln2^4+3*li4half; Fill Stab4(-1,-1,1,1) = -1/2*z2*ln2^2+7/8*z3*ln2+1/6*ln2^4+3*li4half; Fill Stab4(-1,0,-1,-1) = 1/2*z2*ln2^2-7/5*z2^2+5/8*z3*ln2+1/6*ln2^4+4*li4half; Fill Stab4(-1,0,-1,1) = -3/4*z2*ln2^2-9/40*z2^2+5/8*z3*ln2+1/8*ln2^4+3*li4half; Fill Stab4(-1,0,0,-1) = -1/2*z2*ln2^2-1/5*z2^2+3/4*z3*ln2+1/12*ln2^4+2*li4half; Fill Stab4(-1,0,0,1) = -19/40*z2^2+3/4*z3*ln2; Fill Stab4(-1,0,1,-1) = -1/2*z2*ln2^2+5/4*z2^2-1/4*z3*ln2-1/6*ln2^4-4*li4half; Fill Stab4(-1,0,1,1) = 1/4*z2*ln2^2-1/40*z2^2-1/4*z3*ln2-1/24*ln2^4-li4half; Fill Stab4(-1,1,-1,-1) = -1/4*z2*ln2^2-1/8*z2^2-1/8*z3*ln2+1/24*ln2^4; Fill Stab4(-1,1,-1,1) = -1/4*z2*ln2^2+3/8*z2^2-1/8*z3*ln2+1/24*ln2^4; Fill Stab4(-1,1,0,-1) = -1/5*z2^2+1/8*z3*ln2+1/12*ln2^4+2*li4half; Fill Stab4(-1,1,0,1) = -1/20*z2^2+1/8*z3*ln2-1/24*ln2^4-li4half; Fill Stab4(-1,1,1,-1) = 2/5*z2^2-li4half; Fill Stab4(-1,1,1,1) = -li4half; Fill Stab4(0,-1,-1,-1) = -1/2*z2*ln2^2+7/5*z2^2-21/8*z3*ln2-1/6*ln2^4-4*li4half; Fill Stab4(0,-1,-1,1) = 39/40*z2^2-1/8*ln2^4-3*li4half; Fill Stab4(0,-1,0,-1) = 13/40*z2^2; Fill Stab4(0,-1,0,1) = z2*ln2^2+51/40*z2^2-7/2*z3*ln2-1/6*ln2^4-4*li4half; Fill Stab4(0,-1,1,-1) = 3/4*z2*ln2^2+3/40*z2^2; Fill Stab4(0,-1,1,1) = 1/4*z2*ln2^2+1/8*z2^2-7/8*z3*ln2-1/24*ln2^4-li4half; Fill Stab4(0,0,-1,-1) = 1/2*z2*ln2^2+3/5*z2^2-1/12*ln2^4-2*li4half; Fill Stab4(0,0,-1,1) = -1/2*z2*ln2^2-11/10*z2^2+7/4*z3*ln2+1/12*ln2^4+2*li4half; Fill Stab4(0,0,0,-1) = -7/20*z2^2; Fill Stab4(0,0,0,1) = 2/5*z2^2; Fill Stab4(0,0,1,-1) = 1/8*z2^2-7/4*z3*ln2; Fill Stab4(0,0,1,1) = 1/2*z2^2; Fill Stab4(0,1,-1,-1) = 5/4*z2*ln2^2+1/40*z2^2+1/24*ln2^4+li4half; Fill Stab4(0,1,-1,1) = -1/4*z2*ln2^2-2*z2^2+21/8*z3*ln2+1/6*ln2^4+4*li4half; Fill Stab4(0,1,0,-1) = -z2*ln2^2-17/8*z2^2+7/2*z3*ln2+1/6*ln2^4+4*li4half; Fill Stab4(0,1,0,1) = 7/10*z2^2; Fill Stab4(0,1,1,-1) = -3/2*z2*ln2^2-6/5*z2^2+7/8*z3*ln2+1/8*ln2^4+3*li4half; Fill Stab4(0,1,1,1) = 6/5*z2^2; Fill Stab4(1,-1,-1,-1) = -1/2*z2*ln2*Sinf+1/4*z2*ln2^2+6/5*z2^2-2*z3*ln2 -1/4*z3*Sinf-1/6*ln2^3*Sinf-1/4*ln2^4-3*li4half; Fill Stab4(1,-1,-1,1) = -1/2*z2*ln2*Sinf+1/4*z2*ln2^2+7/4*z3*Sinf -1/6*ln2^3*Sinf-1/4*ln2^4-3*li4half; Fill Stab4(1,-1,0,-1) = -z2*ln2*Sinf+1/4*z2*ln2^2+11/20*z2^2+13/8*z3*Sinf -1/8*ln2^4-3*li4half; Fill Stab4(1,-1,0,1) = 1/2*z2*ln2*Sinf+3/4*z2*ln2^2+7/8*z2^2-21/8*z3*ln2 -z3*Sinf-1/12*ln2^4-2*li4half; Fill Stab4(1,-1,1,-1) = 1/2*z2*ln2*Sinf+1/2*z2*ln2^2-1/20*z2^2+1/8*z3*Sinf -1/6*ln2^3*Sinf-1/8*ln2^4; Fill Stab4(1,-1,1,1) = 1/2*z2*ln2*Sinf+1/2*z2*ln2^2+1/20*z2^2-z3*ln2 -7/8*z3*Sinf-1/6*ln2^3*Sinf-1/8*ln2^4; Fill Stab4(1,0,-1,-1) = 3/2*z2*ln2*Sinf-1/4*z2*ln2^2-1/8*z2^2-5/8*z3*Sinf +1/24*ln2^4+li4half; Fill Stab4(1,0,-1,1) = -3/40*z2^2-5/8*z3*Sinf; Fill Stab4(1,0,0,-1) = 1/2*z2*ln2^2+3/4*z2^2-7/4*z3*ln2-3/4*z3*Sinf-1/12*ln2^4 -2*li4half; Fill Stab4(1,0,0,1) = -1/10*z2^2+z3*Sinf; Fill Stab4(1,0,1,-1) = -3/2*z2*ln2*Sinf+3/4*z2*ln2^2+6/5*z2^2-7/4*z3*ln2 +1/4*z3*Sinf-1/8*ln2^4-3*li4half; Fill Stab4(1,0,1,1) = -6/5*z2^2+2*z3*Sinf; Fill Stab4(1,1,-1,-1) = 1/2*z2*ln2*Sinf+1/4*z2*ln2^2+1/4*z2*Sinf^2+1/4*z2^2 -7/8*z3*Sinf+1/4*ln2^2*Sinf^2+1/3*ln2^3*Sinf+1/6*ln2^4+li4half; Fill Stab4(1,1,-1,1) = -1/2*z2*ln2*Sinf-1/4*z2*ln2^2-1/4*z2*Sinf^2-13/20*z2^2 +z3*ln2+1/8*z3*Sinf+1/4*ln2^2*Sinf^2+1/3*ln2^3*Sinf+1/6*ln2^4+li4half; Fill Stab4(1,1,0,-1) = -1/4*z2*ln2^2-1/4*z2*Sinf^2-13/20*z2^2+7/8*z3*ln2 -1/8*z3*Sinf+1/24*ln2^4+li4half; Fill Stab4(1,1,0,1) = 1/2*z2*Sinf^2+9/10*z2^2-z3*Sinf; Fill Stab4(1,1,1,-1) = -1/2*z2*ln2*Sinf-1/4*z2*ln2^2-1/3*z3*ln2-1/6*ln2*Sinf^3 -1/4*ln2^2*Sinf^2-1/6*ln2^3*Sinf-1/24*ln2^4; Fill Stab4(1,1,1,1) = 1/4*z2*Sinf^2+9/40*z2^2+1/3*z3*Sinf+1/24*Sinf^4; #endprocedure * *--#] table4 : *--#[ table5 : * #procedure table5 * * New constants: li5half = Li_5(1/2) = -S(R(-1,1,1,1,1),inf) * z5 = zeta_5 * File by J. Vermaseren, 5-jun-1998 * S z5,li5half; CTable,relax,Stab5(-1:1,-1:1,-1:1,-1:1,-1:1); Fill Stab5(-1,-1,-1,-1,-1) = -1/8*z2*z3-1/12*z2*ln2^3-9/40*z2^2 *ln2-1/8*z3*ln2^2-3/16*z5-1/120*ln2^5; Fill Stab5(-1,-1,-1,-1,1) = -1/8*z2*z3-1/12*z2*ln2^3-9/40*z2^2* ln2-1/8*z3*ln2^2+29/16*z5-1/120*ln2^5; Fill Stab5(-1,-1,-1,0,-1) = -3/4*z2*z3+1/12*z2*ln2^3+3/8*z2^2* ln2-1/2*z3*ln2^2+29/64*z5-1/40*ln2^5+3*li5half; Fill Stab5(-1,-1,-1,0,1) = -3/8*z2*z3+1/12*z2*ln2^3+3/5*z2^2* ln2-1/2*z3*ln2^2-z5; Fill Stab5(-1,-1,-1,1,-1) = -23/16*z2*z3+5/12*z2*ln2^3+19/40* z2^2*ln2-23/16*z3*ln2^2+375/64*z5-3*ln2*li4half-13/120*ln2^5 -3*li5half; Fill Stab5(-1,-1,-1,1,1) = 9/16*z2*z3+5/12*z2*ln2^3+19/40*z2^2* ln2-23/16*z3*ln2^2+23/64*z5-3*ln2*li4half-13/120*ln2^5-3* li5half; Fill Stab5(-1,-1,0,-1,-1) = -13/8*z2*z3+5/6*z2*ln2^3-41/40*z2^2 *ln2-13/8*z3*ln2^2+845/64*z5-4*ln2*li4half-3/40*ln2^5-11* li5half; Fill Stab5(-1,-1,0,-1,1) = z2*z3+7/12*z2*ln2^3+1/40*z2^2*ln2-13/ 8*z3*ln2^2+101/64*z5-4*ln2*li4half-1/8*ln2^5-5*li5half; Fill Stab5(-1,-1,0,0,-1) = 1/8*z2*z3+19/40*z2^2*ln2-3/8*z3*ln2^2 -15/8*z5; Fill Stab5(-1,-1,0,0,1) = -11/8*z2*z3+1/6*z2*ln2^3+1/5*z2^2*ln2 -3/8*z3*ln2^2+159/64*z5-1/60*ln2^5+2*li5half; Fill Stab5(-1,-1,0,1,-1) = 1/8*z2*z3-1/3*z2*ln2^3+47/40*z2^2*ln2 +1/8*z3*ln2^2-61/8*z5+ln2*li4half-1/40*ln2^5+8*li5half; Fill Stab5(-1,-1,0,1,1) = 1/8*z2*z3+1/12*z2*ln2^3+9/40*z2^2*ln2 +1/8*z3*ln2^2-29/16*z5+ln2*li4half+1/120*ln2^5+4*li5half; Fill Stab5(-1,-1,1,-1,-1) = -7/16*z2*z3+1/6*z2*ln2^3+6/5*z2^2* ln2-7/16*z3*ln2^2-81/64*z5-1/30*ln2^5+3*li5half; Fill Stab5(-1,-1,1,-1,1) = 9/16*z2*z3+1/6*z2*ln2^3+6/5*z2^2*ln2 -7/16*z3*ln2^2-369/64*z5-1/30*ln2^5+3*li5half; Fill Stab5(-1,-1,1,0,-1) = 3/8*z2*z3-1/12*z2*ln2^3+3/5*z2^2*ln2 -1/16*z3*ln2^2-125/32*z5+ln2*li4half+1/30*ln2^5+li5half; Fill Stab5(-1,-1,1,0,1) = -15/16*z2*z3-1/12*z2*ln2^3+3/8*z2^2* ln2-1/16*z3*ln2^2+29/64*z5+ln2*li4half+1/120*ln2^5+4* li5half; Fill Stab5(-1,-1,1,1,-1) = -4*z5+ln2*li4half+4*li5half; Fill Stab5(-1,-1,1,1,1) = ln2*li4half+4*li5half; Fill Stab5(-1,0,-1,-1,-1) = 21/16*z2*z3-17/12*z2*ln2^3+21/8*z2^2* ln2+21/16*z3*ln2^2-911/64*z5+4*ln2*li4half+7/120*ln2^5+13* li5half; Fill Stab5(-1,0,-1,-1,1) = -2/3*z2*ln2^3+27/8*z2^2*ln2-911/64* z5+4*ln2*li4half+7/120*ln2^5+13*li5half; Fill Stab5(-1,0,-1,0,-1) = 5/16*z2*z3-1/3*z2*ln2^3+17/8*z2^2*ln2 -331/32*z5+4*ln2*li4half+1/10*ln2^5+8*li5half; Fill Stab5(-1,0,-1,0,1) = 9/8*z2*z3-2/3*z2*ln2^3-7/10*z2^2*ln2+ 7/4*z3*ln2^2-259/64*z5+4*ln2*li4half+2/15*ln2^5+4*li5half; Fill Stab5(-1,0,-1,1,-1) = 3/4*z2*ln2^3+1/40*z2^2*ln2-99/32*z5+ ln2*li4half+1/60*ln2^5+3*li5half; Fill Stab5(-1,0,-1,1,1) = 7/16*z2*z3-1/6*z2*ln2^3-6/5*z2^2*ln2+ 7/16*z3*ln2^2+81/64*z5+ln2*li4half+1/30*ln2^5+li5half; Fill Stab5(-1,0,0,-1,-1) = 1/2*z2*ln2^3-2/5*z2^2*ln2+15/32*z5-2 *ln2*li4half-1/12*ln2^5; Fill Stab5(-1,0,0,-1,1) = -7/8*z2*z3+1/3*z2*ln2^3-1/2*z2^2*ln2 -7/8*z3*ln2^2+85/16*z5-2*ln2*li4half-1/15*ln2^5-2*li5half; Fill Stab5(-1,0,0,0,-1) = -3/4*z2*z3-2/5*z2^2*ln2+91/32*z5; Fill Stab5(-1,0,0,0,1) = 3/8*z2*z3+7/20*z2^2*ln2-2*z5; Fill Stab5(-1,0,0,1,-1) = -1/3*z2*ln2^3-13/40*z2^2*ln2+27/8*z5 +1/30*ln2^5-4*li5half; Fill Stab5(-1,0,0,1,1) = 7/8*z2*z3+1/6*z2*ln2^3+11/10*z2^2*ln2- 7/8*z3*ln2^2-311/64*z5-1/60*ln2^5+2*li5half; Fill Stab5(-1,0,1,-1,-1) = 7/6*z2*ln2^3-81/20*z2^2*ln2+245/16*z5 -4*ln2*li4half-1/30*ln2^5-16*li5half; Fill Stab5(-1,0,1,-1,1) = -21/16*z2*z3+7/12*z2*ln2^3-49/20*z2^2 *ln2-21/16*z3*ln2^2+521/32*z5-4*ln2*li4half-1/20*ln2^5-14* li5half; Fill Stab5(-1,0,1,0,-1) = -3/2*z2*z3+2/3*z2*ln2^3-13/40*z2^2* ln2-7/4*z3*ln2^2+129/16*z5-4*ln2*li4half-2/15*ln2^5-4* li5half; Fill Stab5(-1,0,1,0,1) = -1/8*z2*z3+1/3*z2*ln2^3-51/40*z2^2*ln2 +227/32*z5-4*ln2*li4half-1/10*ln2^5-8*li5half; Fill Stab5(-1,0,1,1,-1) = -21/16*z2*z3+6/5*z2^2*ln2-21/16*z3* ln2^2+87/32*z5-3*ln2*li4half-1/8*ln2^5; Fill Stab5(-1,0,1,1,1) = 7/8*z2*z3+5/12*z2*ln2^3-1/8*z2^2*ln2-7/ 8*z3*ln2^2+81/64*z5-3*ln2*li4half-11/120*ln2^5-4*li5half; Fill Stab5(-1,1,-1,-1,-1) = 13/8*z2*z3-5/12*z2*ln2^3+1/8*z2^2*ln2 +11/8*z3*ln2^2-369/64*z5+3*ln2*li4half+11/120*ln2^5+3* li5half; Fill Stab5(-1,1,-1,-1,1) = -11/8*z2*z3-5/12*z2*ln2^3+1/8*z2^2* ln2+11/8*z3*ln2^2-81/64*z5+3*ln2*li4half+11/120*ln2^5+3* li5half; Fill Stab5(-1,1,-1,0,-1) = -7/8*z2*z3-1/3*z2*ln2^3+1/20*z2^2* ln2+13/16*z3*ln2^2-33/64*z5+2*ln2*li4half+3/40*ln2^5+ li5half; Fill Stab5(-1,1,-1,0,1) = 31/16*z2*z3-1/3*z2*ln2^3+1/5*z2^2*ln2 +13/16*z3*ln2^2-405/64*z5+2*ln2*li4half+1/20*ln2^5+4* li5half; Fill Stab5(-1,1,-1,1,-1) = -1/16*z2*z3+1/12*z2*ln2^3-3/8*z2^2* ln2+1/16*z3*ln2^2+3/64*z5-1/120*ln2^5; Fill Stab5(-1,1,-1,1,1) = 15/16*z2*z3+1/12*z2*ln2^3-3/8*z2^2*ln2 +1/16*z3*ln2^2-29/64*z5-1/120*ln2^5; Fill Stab5(-1,1,0,-1,-1) = 5/16*z2*z3-1/6*z2*ln2^3+31/20*z2^2*ln2 -5/16*z3*ln2^2-457/64*z5-7/120*ln2^5+7*li5half; Fill Stab5(-1,1,0,-1,1) = 5/16*z2*z3+1/4*z2*ln2^3+9/40*z2^2*ln2 -5/16*z3*ln2^2-29/16*z5-1/40*ln2^5+3*li5half; Fill Stab5(-1,1,0,0,-1) = 9/8*z2*z3-1/6*z2*ln2^3+1/5*z2^2*ln2+1/ 2*z3*ln2^2-153/32*z5+2*ln2*li4half+1/20*ln2^5+4*li5half; Fill Stab5(-1,1,0,0,1) = -7/16*z2*z3-1/3*z2*ln2^3+19/40*z2^2* ln2+1/2*z3*ln2^2-151/64*z5+2*ln2*li4half+1/15*ln2^5+2* li5half; Fill Stab5(-1,1,0,1,-1) = 19/16*z2*z3-1/3*z2*ln2^3-7/5*z2^2*ln2 +23/16*z3*ln2^2+35/32*z5+3*ln2*li4half+19/120*ln2^5-4* li5half; Fill Stab5(-1,1,0,1,1) = -23/16*z2*z3-7/12*z2*ln2^3+1/40*z2^2* ln2+23/16*z3*ln2^2-23/64*z5+3*ln2*li4half+13/120*ln2^5+2* li5half; Fill Stab5(-1,1,1,-1,-1) = 7/16*z2*z3+1/6*z2*ln2^3-2/5*z2^2*ln2 -7/16*z3*ln2^2+27/32*z5-ln2*li4half-1/30*ln2^5-2*li5half; Fill Stab5(-1,1,1,-1,1) = -9/16*z2*z3+1/6*z2*ln2^3-2/5*z2^2*ln2 -7/16*z3*ln2^2+123/32*z5-ln2*li4half-1/30*ln2^5-2*li5half; Fill Stab5(-1,1,1,0,-1) = -3/8*z2*z3+1/6*z2*ln2^3+1/5*z2^2*ln2 -1/2*z3*ln2^2+15/16*z5-ln2*li4half-1/20*ln2^5+li5half; Fill Stab5(-1,1,1,0,1) = 1/2*z2*z3+1/6*z2*ln2^3+1/20*z2^2*ln2-1/ 2*z3*ln2^2-1/32*z5-ln2*li4half-1/40*ln2^5-2*li5half; Fill Stab5(-1,1,1,1,-1) = z5-li5half; Fill Stab5(-1,1,1,1,1) = -li5half; Fill Stab5(0,-1,-1,-1,-1) = 27/16*z2*z3+7/12*z2*ln2^3-11/8*z2^2* ln2+21/16*z3*ln2^2+101/64*z5+1/24*ln2^5-5*li5half; Fill Stab5(0,-1,-1,-1,1) = -21/16*z2*z3+7/12*z2*ln2^3-17/5*z2^2 *ln2+21/16*z3*ln2^2+845/64*z5-3*ln2*li4half-1/30*ln2^5-11* li5half; Fill Stab5(0,-1,-1,0,-1) = -13/16*z2*z3+2/3*z2*ln2^3-17/5*z2^2* ln2+547/32*z5-8*ln2*li4half-1/5*ln2^5-16*li5half; Fill Stab5(0,-1,-1,0,1) = 25/8*z2*z3+3/8*z2^2*ln2-363/64*z5; Fill Stab5(0,-1,-1,1,-1) = -1/3*z2*ln2^3-87/40*z2^2*ln2+221/32* z5-ln2*li4half+1/60*ln2^5-7*li5half; Fill Stab5(0,-1,-1,1,1) = 21/16*z2*z3+9/40*z2^2*ln2-23/64*z5+1/ 40*ln2^5-3*li5half; Fill Stab5(0,-1,0,-1,-1) = -1/3*z2*ln2^3+19/20*z2^2*ln2-123/16* z5+4*ln2*li4half+1/10*ln2^5+8*li5half; Fill Stab5(0,-1,0,-1,1) = 15/16*z2*z3-29/32*z5; Fill Stab5(0,-1,0,0,-1) = 21/8*z2*z3-67/16*z5; Fill Stab5(0,-1,0,0,1) = -3/4*z2*z3+21/32*z5; Fill Stab5(0,-1,0,1,-1) = 11/8*z2*z3-1/3*z2*ln2^3-19/20*z2^2*ln2 +7/4*z3*ln2^2+33/32*z5+1/30*ln2^5-4*li5half; Fill Stab5(0,-1,0,1,1) = -7/4*z2*z3-2/3*z2*ln2^3+7/4*z3*ln2^2 -89/64*z5+4*ln2*li4half+2/15*ln2^5+4*li5half; Fill Stab5(0,-1,1,-1,-1) = -11/12*z2*ln2^3+53/40*z2^2*ln2-457/ 64*z5+3*ln2*li4half+1/15*ln2^5+7*li5half; Fill Stab5(0,-1,1,-1,1) = -3/16*z2*z3-1/4*z2*ln2^3+9/10*z2^2* ln2-29/16*z5-1/40*ln2^5+3*li5half; Fill Stab5(0,-1,1,0,-1) = 1/16*z2*z3+5/8*z5; Fill Stab5(0,-1,1,0,1) = 1/16*z2*z3-53/64*z5; Fill Stab5(0,-1,1,1,-1) = 7/16*z2*z3+1/6*z2*ln2^3-1/20*z2^2*ln2 +7/16*z3*ln2^2+1/8*z5+1/120*ln2^5-li5half; Fill Stab5(0,-1,1,1,1) = -7/16*z2*z3-1/6*z2*ln2^3+7/16*z3*ln2^2 -27/32*z5+ln2*li4half+1/30*ln2^5+li5half; Fill Stab5(0,0,-1,-1,-1) = -1/2*z2*z3-1/2*z2*ln2^3-19/40*z2^2* ln2+15/32*z5+2*ln2*li4half+1/12*ln2^5; Fill Stab5(0,0,-1,-1,1) = -13/8*z2*z3-1/6*z2*ln2^3-1/10*z2^2* ln2+85/16*z5+1/60*ln2^5-2*li5half; Fill Stab5(0,0,-1,0,-1) = -9/4*z2*z3+83/16*z5; Fill Stab5(0,0,-1,0,1) = -5/8*z2*z3+11/32*z5; Fill Stab5(0,0,-1,1,-1) = -3/4*z2*z3+1/3*z2*ln2^3+17/10*z2^2* ln2-7/8*z3*ln2^2-39/16*z5-1/30*ln2^5+4*li5half; Fill Stab5(0,0,-1,1,1) = 3/8*z2*z3+1/3*z2*ln2^3-7/8*z3*ln2^2+15/ 32*z5-2*ln2*li4half-1/15*ln2^5-2*li5half; Fill Stab5(0,0,0,-1,-1) = 3/4*z2*z3+3/4*z2^2*ln2-59/32*z5; Fill Stab5(0,0,0,-1,1) = 1/2*z2*z3-59/32*z5; Fill Stab5(0,0,0,0,-1) = -15/16*z5; Fill Stab5(0,0,0,0,1) = z5; Fill Stab5(0,0,0,1,-1) = -3/8*z2*z3-3/4*z2^2*ln2+17/16*z5; Fill Stab5(0,0,0,1,1) = -z2*z3+3*z5; Fill Stab5(0,0,1,-1,-1) = 15/8*z2*z3+1/6*z2*ln2^3+19/40*z2^2*ln2 +7/8*z3*ln2^2-311/64*z5-1/60*ln2^5+2*li5half; Fill Stab5(0,0,1,-1,1) = -1/16*z2*z3+1/6*z2*ln2^3-49/40*z2^2* ln2+7/8*z3*ln2^2+27/8*z5-2*ln2*li4half-1/20*ln2^5-4*li5half ; Fill Stab5(0,0,1,0,-1) = 1/4*z2*z3-51/32*z5; Fill Stab5(0,0,1,0,1) = 3*z2*z3-9/2*z5; Fill Stab5(0,0,1,1,-1) = -1/16*z2*z3-1/3*z2*ln2^3-3/8*z2^2*ln2 -125/64*z5+2*ln2*li4half+1/15*ln2^5+2*li5half; Fill Stab5(0,0,1,1,1) = z2*z3-1/2*z5; Fill Stab5(0,1,-1,-1,-1) = -3/8*z2*z3-13/12*z2*ln2^3+11/8*z2^2* ln2-61/8*z5+3*ln2*li4half+7/120*ln2^5+8*li5half; Fill Stab5(0,1,-1,-1,1) = -5/12*z2*ln2^3+19/20*z2^2*ln2-29/16* z5-1/30*ln2^5+4*li5half; Fill Stab5(0,1,-1,0,-1) = -z2*z3-3/8*z2^2*ln2+257/64*z5; Fill Stab5(0,1,-1,0,1) = -z2*z3-2/3*z2*ln2^3+17/5*z2^2*ln2- 507/32*z5+8*ln2*li4half+1/5*ln2^5+16*li5half; Fill Stab5(0,1,-1,1,-1) = -21/16*z2*z3+1/3*z2*ln2^3+83/40*z2^2* ln2-21/16*z3*ln2^2-85/64*z5-1/30*ln2^5+4*li5half; Fill Stab5(0,1,-1,1,1) = 17/8*z2^2*ln2-21/16*z3*ln2^2-61/8*z5+ ln2*li4half-1/120*ln2^5+6*li5half; Fill Stab5(0,1,0,-1,-1) = -7/4*z2*z3+1/3*z2*ln2^3+113/40*z2^2* ln2-7/4*z3*ln2^2-89/64*z5-1/30*ln2^5+4*li5half; Fill Stab5(0,1,0,-1,1) = 13/16*z2*z3+2/3*z2*ln2^3-7/4*z3*ln2^2+ 33/32*z5-4*ln2*li4half-2/15*ln2^5-4*li5half; Fill Stab5(0,1,0,0,-1) = -1/8*z2*z3-41/32*z5; Fill Stab5(0,1,0,0,1) = -2*z2*z3+11/2*z5; Fill Stab5(0,1,0,1,-1) = 3/8*z2*z3+1/3*z2*ln2^3-113/40*z2^2*ln2 +125/16*z5-4*ln2*li4half-1/10*ln2^5-8*li5half; Fill Stab5(0,1,0,1,1) = 2*z5; Fill Stab5(0,1,1,-1,-1) = -7/16*z2*z3+11/12*z2*ln2^3+49/40*z2^2 *ln2-7/16*z3*ln2^2-23/64*z5-1/60*ln2^5+2*li5half; Fill Stab5(0,1,1,-1,1) = 5/8*z2*z3+11/12*z2*ln2^3-4/5*z2^2*ln2- 7/16*z3*ln2^2+35/32*z5-3*ln2*li4half-11/120*ln2^5-4*li5half; Fill Stab5(0,1,1,0,-1) = 5/16*z2*z3-177/64*z5; Fill Stab5(0,1,1,0,1) = -z2*z3+9/2*z5; Fill Stab5(0,1,1,1,-1) = -1/3*z2*ln2^3-12/5*z2^2*ln2+4*z5-ln2 *li4half-1/120*ln2^5-4*li5half; Fill Stab5(0,1,1,1,1) = 4*z5; Fill Stab5(1,-1,-1,-1,-1) = z2*z3+1/4*z2*ln2^2*Sinf-39/40*z2^2* ln2+9/40*z2^2*Sinf+1/4*z3*ln2*Sinf+9/8*z3*ln2^2+23/64*z5+1/ 24*ln2^4*Sinf+7/120*ln2^5-3*li5half; Fill Stab5(1,-1,-1,-1,1) = -z2*z3+1/4*z2*ln2^2*Sinf-67/40*z2^2* ln2-19/40*z2^2*Sinf+1/4*z3*ln2*Sinf+9/8*z3*ln2^2+375/64*z5+ 1/24*ln2^4*Sinf+7/120*ln2^5-3*li5half; Fill Stab5(1,-1,-1,0,-1) = -7/8*z2*z3-1/4*z2*ln2^2*Sinf+1/6*z2* ln2^3-59/40*z2^2*ln2-3/5*z2^2*Sinf+z3*ln2*Sinf+1/2*z3*ln2^2 +247/32*z5-3*ln2*li4half-1/12*ln2^5-5*li5half; Fill Stab5(1,-1,-1,0,1) = 7/4*z2*z3-1/4*z2*ln2^2*Sinf-1/6*z2* ln2^3-37/40*z2^2*ln2-3/8*z2^2*Sinf+z3*ln2*Sinf+1/2*z3*ln2^2 +29/64*z5+1/8*ln2^4*Sinf+1/20*ln2^5+3*Sinf*li4half-6* li5half; Fill Stab5(1,-1,-1,1,-1) = -1/2*z2*ln2^2*Sinf-1/4*z2*ln2^3-6/5* z2^2*ln2-6/5*z2^2*Sinf+7/8*z3*ln2*Sinf+7/16*z3*ln2^2+6*z5+1/ 6*ln2^4*Sinf+1/12*ln2^5+3*Sinf*li4half-6*li5half; Fill Stab5(1,-1,-1,1,1) = -1/2*z2*ln2^2*Sinf-1/4*z2*ln2^3+7/8* z3*ln2*Sinf+7/16*z3*ln2^2+1/6*ln2^4*Sinf+1/12*ln2^5+3*Sinf* li4half-6*li5half; Fill Stab5(1,-1,0,-1,-1) = 1/2*z2*ln2^2*Sinf-1/12*z2*ln2^3-91/40* z2^2*ln2-7/5*z2^2*Sinf+5/8*z3*ln2*Sinf+5/16*z3*ln2^2+221/32* z5+ln2*li4half+1/6*ln2^4*Sinf+1/10*ln2^5+4*Sinf*li4half-7* li5half; Fill Stab5(1,-1,0,-1,1) = -3/4*z2*ln2^2*Sinf-1/4*z2*ln2^3+39/40 *z2^2*ln2-9/40*z2^2*Sinf+5/8*z3*ln2*Sinf+5/16*z3*ln2^2-23/64* z5+1/8*ln2^4*Sinf+1/40*ln2^5+3*Sinf*li4half-3*li5half; Fill Stab5(1,-1,0,0,-1) = 13/8*z2*z3-1/2*z2*ln2^2*Sinf-1/6*z2* ln2^3-1/10*z2^2*ln2-1/5*z2^2*Sinf+3/4*z3*ln2*Sinf+3/8*z3* ln2^2-15/8*z5+1/12*ln2^4*Sinf+1/60*ln2^5+2*Sinf*li4half-2* li5half; Fill Stab5(1,-1,0,0,1) = -13/16*z2*z3+1/6*z2*ln2^3-49/40*z2^2* ln2-19/40*z2^2*Sinf+3/4*z3*ln2*Sinf+3/8*z3*ln2^2+47/8*z5-2* ln2*li4half-1/20*ln2^5-4*li5half; Fill Stab5(1,-1,0,1,-1) = 21/16*z2*z3-1/2*z2*ln2^2*Sinf-1/4*z2* ln2^3+21/20*z2^2*ln2+5/4*z2^2*Sinf-1/4*z3*ln2*Sinf+19/16*z3* ln2^2-61/8*z5-1/6*ln2^4*Sinf-1/20*ln2^5-4*Sinf*li4half+6* li5half; Fill Stab5(1,-1,0,1,1) = -21/16*z2*z3+1/4*z2*ln2^2*Sinf-5/12*z2 *ln2^3+1/20*z2^2*ln2-1/40*z2^2*Sinf-1/4*z3*ln2*Sinf+19/16*z3* ln2^2-85/64*z5+3*ln2*li4half-1/24*ln2^4*Sinf+11/120*ln2^5- Sinf*li4half+4*li5half; Fill Stab5(1,-1,1,-1,-1) = -1/4*z2*ln2^2*Sinf-1/4*z2*ln2^3-3/40 *z2^2*ln2-1/8*z2^2*Sinf-1/8*z3*ln2*Sinf-1/16*z3*ln2^2+3/64*z5 +1/24*ln2^4*Sinf+1/30*ln2^5; Fill Stab5(1,-1,1,-1,1) = -1/4*z2*ln2^2*Sinf-1/4*z2*ln2^3+17/40 *z2^2*ln2+3/8*z2^2*Sinf-1/8*z3*ln2*Sinf-1/16*z3*ln2^2-29/64* z5+1/24*ln2^4*Sinf+1/30*ln2^5; Fill Stab5(1,-1,1,0,-1) = 1/8*z2*z3-1/12*z2*ln2^3-3/4*z2^2*ln2- 1/5*z2^2*Sinf+1/8*z3*ln2*Sinf+1/16*z3*ln2^2+123/32*z5+1/12* ln2^4*Sinf+1/24*ln2^5+2*Sinf*li4half-5*li5half; Fill Stab5(1,-1,1,0,1) = -1/16*z2*z3+1/4*z2*ln2^3-37/40*z2^2* ln2-1/20*z2^2*Sinf+1/8*z3*ln2*Sinf+1/16*z3*ln2^2+277/64*z5- 3*ln2*li4half-1/24*ln2^4*Sinf-11/120*ln2^5-Sinf*li4half-4* li5half; Fill Stab5(1,-1,1,1,-1) = 1/2*z2*z3-1/6*z2*ln2^3+7/20*z2^2*ln2+ 2/5*z2^2*Sinf+1/2*z3*ln2^2-63/32*z5+1/40*ln2^5-Sinf*li4half +li5half; Fill Stab5(1,-1,1,1,1) = -1/2*z2*z3-1/6*z2*ln2^3-1/20*z2^2*ln2 +1/2*z3*ln2^2+1/32*z5+1/40*ln2^5-Sinf*li4half+li5half; Fill Stab5(1,0,-1,-1,-1) = -1/2*z2*ln2^2*Sinf+1/2*z2*ln2^3+53/ 40*z2^2*ln2+7/5*z2^2*Sinf-21/8*z3*ln2*Sinf-21/16*z3*ln2^2-99/ 32*z5-ln2*li4half-1/6*ln2^4*Sinf-1/15*ln2^5-4*Sinf*li4half+ 3*li5half; Fill Stab5(1,0,-1,-1,1) = 1/12*z2*ln2^3-43/40*z2^2*ln2+39/40*z2^2 *Sinf+81/64*z5-1/8*ln2^4*Sinf-1/120*ln2^5-3*Sinf*li4half+ li5half; Fill Stab5(1,0,-1,0,-1) = -5/8*z2*z3+13/40*z2^2*Sinf+41/32*z5; Fill Stab5(1,0,-1,0,1) = 5/16*z2*z3+z2*ln2^2*Sinf+2/3*z2*ln2^3+ 51/40*z2^2*Sinf-7/2*z3*ln2*Sinf-7/4*z3*ln2^2+103/32*z5-4*ln2* li4half-1/6*ln2^4*Sinf-2/15*ln2^5-4*Sinf*li4half-4*li5half; Fill Stab5(1,0,-1,1,-1) = 3/4*z2*ln2^2*Sinf-1/12*z2*ln2^3-1/20* z2^2*ln2+3/40*z2^2*Sinf+25/32*z5+1/120*ln2^5-li5half; Fill Stab5(1,0,-1,1,1) = 1/4*z2*ln2^2*Sinf+1/6*z2*ln2^3+1/8*z2^2* Sinf-7/8*z3*ln2*Sinf-7/16*z3*ln2^2+25/32*z5-ln2*li4half-1/ 24*ln2^4*Sinf-1/30*ln2^5-Sinf*li4half-li5half; Fill Stab5(1,0,0,-1,-1) = 7/8*z2*z3+1/2*z2*ln2^2*Sinf-1/6*z2* ln2^3-17/20*z2^2*ln2+3/5*z2^2*Sinf+7/8*z3*ln2^2+15/32*z5-1/ 12*ln2^4*Sinf+1/60*ln2^5-2*Sinf*li4half-2*li5half; Fill Stab5(1,0,0,-1,1) = -7/8*z2*z3-1/2*z2*ln2^2*Sinf-2/3*z2* ln2^3-11/10*z2^2*Sinf+7/4*z3*ln2*Sinf+7/4*z3*ln2^2-39/16*z5 +4*ln2*li4half+1/12*ln2^4*Sinf+2/15*ln2^5+2*Sinf*li4half+4* li5half; Fill Stab5(1,0,0,0,-1) = -1/2*z2*z3-7/20*z2^2*Sinf+29/32*z5; Fill Stab5(1,0,0,0,1) = z2*z3+2/5*z2^2*Sinf-2*z5; Fill Stab5(1,0,0,1,-1) = 1/6*z2*ln2^3+17/20*z2^2*ln2+1/8*z2^2* Sinf-7/4*z3*ln2*Sinf-7/8*z3*ln2^2-125/64*z5-1/60*ln2^5+2* li5half; Fill Stab5(1,0,0,1,1) = 1/2*z2^2*Sinf-1/2*z5; Fill Stab5(1,0,1,-1,-1) = 7/8*z2*z3+5/4*z2*ln2^2*Sinf-1/3*z2* ln2^3-53/40*z2^2*ln2+1/40*z2^2*Sinf+7/8*z3*ln2^2+81/64*z5+1/ 24*ln2^4*Sinf+1/30*ln2^5+Sinf*li4half-4*li5half; Fill Stab5(1,0,1,-1,1) = -7/8*z2*z3-1/4*z2*ln2^2*Sinf-3/4*z2* ln2^3-51/40*z2^2*ln2-2*z2^2*Sinf+21/8*z3*ln2*Sinf+35/16*z3* ln2^2+87/32*z5+3*ln2*li4half+1/6*ln2^4*Sinf+1/8*ln2^5+4* Sinf*li4half; Fill Stab5(1,0,1,0,-1) = -z2*z3-z2*ln2^2*Sinf-2/3*z2*ln2^3-17/ 8*z2^2*Sinf+7/2*z3*ln2*Sinf+7/4*z3*ln2^2-73/64*z5+4*ln2* li4half+1/6*ln2^4*Sinf+2/15*ln2^5+4*Sinf*li4half+4*li5half; Fill Stab5(1,0,1,0,1) = 2*z2*z3+7/10*z2^2*Sinf-11/2*z5; Fill Stab5(1,0,1,1,-1) = -3/2*z2*ln2^2*Sinf-1/4*z2*ln2^3+12/5* z2^2*ln2-6/5*z2^2*Sinf+7/8*z3*ln2*Sinf+7/16*z3*ln2^2-6*z5+3 *ln2*li4half+1/8*ln2^4*Sinf+3/40*ln2^5+3*Sinf*li4half+6* li5half; Fill Stab5(1,0,1,1,1) = 6/5*z2^2*Sinf-6*z5; Fill Stab5(1,1,-1,-1,-1) = -1/8*z2*z3-1/4*z2*ln2*Sinf^2+1/4*z2* ln2^2*Sinf+19/20*z2^2*ln2+6/5*z2^2*Sinf-2*z3*ln2*Sinf-z3* ln2^2-1/8*z3*Sinf^2-4*z5-1/12*ln2^3*Sinf^2-1/4*ln2^4*Sinf-1/ 12*ln2^5-3*Sinf*li4half+4*li5half; Fill Stab5(1,1,-1,-1,1) = 7/8*z2*z3-1/4*z2*ln2*Sinf^2+1/4*z2* ln2^2*Sinf-1/4*z2^2*ln2+7/8*z3*Sinf^2-1/12*ln2^3*Sinf^2-1/4* ln2^4*Sinf-1/12*ln2^5-3*Sinf*li4half+4*li5half; Fill Stab5(1,1,-1,0,-1) = -1/16*z2*z3-1/2*z2*ln2*Sinf^2+1/4*z2* ln2^2*Sinf+1/12*z2*ln2^3-7/20*z2^2*ln2+11/20*z2^2*Sinf+13/16* z3*Sinf^2-1/32*z5-1/8*ln2^4*Sinf-1/40*ln2^5-3*Sinf*li4half+ 3*li5half; Fill Stab5(1,1,-1,0,1) = -1/16*z2*z3+1/4*z2*ln2*Sinf^2+3/4*z2* ln2^2*Sinf+1/6*z2*ln2^3+61/40*z2^2*ln2+7/8*z2^2*Sinf-21/8*z3* ln2*Sinf-21/16*z3*ln2^2-1/2*z3*Sinf^2-39/8*z5+ln2*li4half-1/ 12*ln2^4*Sinf+1/120*ln2^5-2*Sinf*li4half+4*li5half; Fill Stab5(1,1,-1,1,-1) = -7/16*z2*z3+1/4*z2*ln2*Sinf^2+1/2*z2* ln2^2*Sinf+1/4*z2*ln2^3+3/5*z2^2*ln2-1/20*z2^2*Sinf-1/2*z3* ln2^2+1/16*z3*Sinf^2+1/32*z5-1/12*ln2^3*Sinf^2-1/8*ln2^4*Sinf -7/120*ln2^5+li5half; Fill Stab5(1,1,-1,1,1) = 1/16*z2*z3+1/4*z2*ln2*Sinf^2+1/2*z2* ln2^2*Sinf+1/4*z2*ln2^3+7/10*z2^2*ln2+1/20*z2^2*Sinf-z3*ln2* Sinf-z3*ln2^2-7/16*z3*Sinf^2-63/32*z5-1/12*ln2^3*Sinf^2-1/8 *ln2^4*Sinf-7/120*ln2^5+li5half; Fill Stab5(1,1,0,-1,-1) = -3/4*z2*z3+3/4*z2*ln2*Sinf^2-1/4*z2* ln2^2*Sinf+1/12*z2*ln2^3+31/20*z2^2*ln2-1/8*z2^2*Sinf-7/16*z3 *ln2^2-5/16*z3*Sinf^2-27/32*z5+1/24*ln2^4*Sinf-1/120*ln2^5+ Sinf*li4half+li5half; Fill Stab5(1,1,0,-1,1) = 1/8*z2*z3+1/6*z2*ln2^3-3/40*z2^2*Sinf- 7/16*z3*ln2^2-5/16*z3*Sinf^2+1/8*z5-ln2*li4half-1/30*ln2^5- li5half; Fill Stab5(1,1,0,0,-1) = 1/8*z2*z3+1/2*z2*ln2^2*Sinf+1/3*z2*ln2^3 +3/4*z2^2*Sinf-7/4*z3*ln2*Sinf-7/8*z3*ln2^2-3/8*z3*Sinf^2+ 33/32*z5-2*ln2*li4half-1/12*ln2^4*Sinf-1/15*ln2^5-2*Sinf* li4half-2*li5half; Fill Stab5(1,1,0,0,1) = -1/2*z2*z3-1/10*z2^2*Sinf+1/2*z3*Sinf^2 +2*z5; Fill Stab5(1,1,0,1,-1) = 1/8*z2*z3-3/4*z2*ln2*Sinf^2+3/4*z2*ln2^2 *Sinf+5/12*z2*ln2^3-31/20*z2^2*ln2+6/5*z2^2*Sinf-7/4*z3*ln2* Sinf-7/8*z3*ln2^2+1/8*z3*Sinf^2+4*z5-3*ln2*li4half-1/8* ln2^4*Sinf-11/120*ln2^5-3*Sinf*li4half-4*li5half; Fill Stab5(1,1,0,1,1) = z2*z3-6/5*z2^2*Sinf+z3*Sinf^2+4*z5; Fill Stab5(1,1,1,-1,-1) = -13/48*z2*z3+1/4*z2*ln2*Sinf^2+1/4*z2 *ln2^2*Sinf+1/6*z2*ln2^3+1/12*z2*Sinf^3+1/4*z2^2*ln2+1/4*z2^2 *Sinf+1/6*z3*ln2^2-7/16*z3*Sinf^2+1/12*ln2^2*Sinf^3+1/6*ln2^3 *Sinf^2+1/6*ln2^4*Sinf+1/24*ln2^5+Sinf*li4half-li5half; Fill Stab5(1,1,1,-1,1) = -5/48*z2*z3-1/4*z2*ln2*Sinf^2-1/4*z2* ln2^2*Sinf-1/12*z2*Sinf^3-13/20*z2^2*ln2-13/20*z2^2*Sinf+z3* ln2*Sinf+2/3*z3*ln2^2+1/16*z3*Sinf^2+z5+1/12*ln2^2*Sinf^3+1/ 6*ln2^3*Sinf^2+1/6*ln2^4*Sinf+1/24*ln2^5+Sinf*li4half-li5half ; Fill Stab5(1,1,1,0,-1) = -11/48*z2*z3-1/4*z2*ln2^2*Sinf-1/6*z2* ln2^3-1/12*z2*Sinf^3-13/20*z2^2*Sinf+7/8*z3*ln2*Sinf+7/16*z3* ln2^2-1/16*z3*Sinf^2-z5+ln2*li4half+1/24*ln2^4*Sinf+1/30* ln2^5+Sinf*li4half+li5half; Fill Stab5(1,1,1,0,1) = -1/6*z2*z3+1/6*z2*Sinf^3+9/10*z2^2*Sinf -1/2*z3*Sinf^2-z5; Fill Stab5(1,1,1,1,-1) = -1/4*z2*ln2*Sinf^2-1/4*z2*ln2^2*Sinf-1/ 12*z2*ln2^3-9/40*z2^2*ln2-1/3*z3*ln2*Sinf-1/6*z3*ln2^2-1/24* ln2*Sinf^4-1/12*ln2^2*Sinf^3-1/12*ln2^3*Sinf^2-1/24*ln2^4*Sinf -1/120*ln2^5; Fill Stab5(1,1,1,1,1) = 1/6*z2*z3+1/12*z2*Sinf^3+9/40*z2^2*Sinf +1/6*z3*Sinf^2+1/5*z5+1/120*Sinf^5; #endprocedure * *--#] table5 : *--#[ table6 : * #procedure table6 * * New constants: li6half = Li_6(1/2) = -S(R(-1,1,1,1,1,1),inf) * s6 = S(R(-5,-1),inf) * = int(dx,0,1,Li(5,x)/x/(1+x)) * File by J. Vermaseren, 5-jun-1998 * S li6half,s6; CTable,relax,Stab6(-1:1,-1:1,-1:1,-1:1,-1:1,-1:1); Fill Stab6(-1,-1,-1,-1,-1,-1) =1/8*z2*z3*ln2+1/48*z2*ln2^4+9/80* z2^2*ln2^2+61/560*z2^3+1/24*z3*ln2^3+1/32*z3^2+3/16*z5*ln2+ 1/720*ln2^6; Fill Stab6(-1,-1,-1,-1,-1,1) =1/8*z2*z3*ln2+1/48*z2*ln2^4+9/80* z2^2*ln2^2-187/560*z2^3+1/24*z3*ln2^3+1/32*z3^2+3/16*z5*ln2 +1/720*ln2^6; Fill Stab6(-1,-1,-1,-1,0,-1) =3/8*z2*z3*ln2-1/48*z2*ln2^4-3/10* z2^2*ln2^2-57/112*z2^3+1/6*z3*ln2^3+1/4*z3^2+z5*ln2; Fill Stab6(-1,-1,-1,-1,0,1) =3/4*z2*z3*ln2-1/48*z2*ln2^4-3/16* z2^2*ln2^2-99/280*z2^3+1/6*z3*ln2^3+13/64*z3^2+z5*ln2+1/240 *ln2^6+3*li6half-3/4*s6; Fill Stab6(-1,-1,-1,-1,1,-1) =23/16*z2*z3*ln2-5/48*z2*ln2^4+3/2* z2*li4half-21/80*z2^2*ln2^2-11/7*z2^3+23/48*z3*ln2^3+41/64* z3^2-23/64*z5*ln2+3*ln2*li5half+3/2*ln2^2*li4half+31/720* ln2^6+3*li6half-3/4*s6; Fill Stab6(-1,-1,-1,-1,1,1) =23/16*z2*z3*ln2-5/48*z2*ln2^4+3/2* z2*li4half-21/80*z2^2*ln2^2-3/7*z2^3+23/48*z3*ln2^3-87/64* z3^2-23/64*z5*ln2+3*ln2*li5half+3/2*ln2^2*li4half+31/720* ln2^6+3*li6half-3/4*s6; Fill Stab6(-1,-1,-1,0,-1,-1) =2*z2*z3*ln2-1/12*z2*ln2^4+2*z2* li4half-39/40*z2^2*ln2^2-249/70*z2^3+13/24*z3*ln2^3-9/8*z3^2 -101/64*z5*ln2+5*ln2*li5half+2*ln2^2*li4half+23/360*ln2^6+ 16*li6half+4*s6; Fill Stab6(-1,-1,-1,0,-1,1) =13/8*z2*z3*ln2-3/16*z2*ln2^4+2*z2* li4half-49/80*z2^2*ln2^2-65/56*z2^3+13/24*z3*ln2^3-25/8*z3^2 -101/64*z5*ln2+5*ln2*li5half+2*ln2^2*li4half+13/240*ln2^6+9 *li6half+7/4*s6; Fill Stab6(-1,-1,-1,0,0,-1) =11/8*z2*z3*ln2-1/24*z2*ln2^4-1/10* z2^2*ln2^2-123/560*z2^3+1/8*z3*ln2^3+15/8*z5*ln2+1/360*ln2^6 +2*li6half-9/4*s6; Fill Stab6(-1,-1,-1,0,0,1) =-1/8*z2*z3*ln2-19/80*z2^2*ln2^2-71/ 112*z2^3+1/8*z3*ln2^3+11/16*z3^2+15/8*z5*ln2; Fill Stab6(-1,-1,-1,0,1,-1) =-1/2*z2*z3*ln2-1/24*z2*ln2^4-2*z2 *li4half+9/10*z2^2*ln2^2+487/140*z2^3-1/24*z3*ln2^3+243/64* z3^2+61/8*z5*ln2-8*ln2*li5half-2*ln2^2*li4half-17/360*ln2^6 -22*li6half-10*s6; Fill Stab6(-1,-1,-1,0,1,1) =-1/8*z2*z3*ln2+7/48*z2*ln2^4+z2* li4half-21/80*z2^2*ln2^2+163/140*z2^3-1/24*z3*ln2^3+117/64* z3^2+61/8*z5*ln2-8*ln2*li5half-2*ln2^2*li4half-5/144*ln2^6- 13*li6half-19/4*s6; Fill Stab6(-1,-1,-1,1,-1,-1) =23/16*z2*z3*ln2-5/48*z2*ln2^4-19/ 80*z2^2*ln2^2-11/80*z2^3+23/48*z3*ln2^3+167/64*z3^2+369/64*z5 *ln2-3*ln2*li5half+13/720*ln2^6-6*li6half-6*s6; Fill Stab6(-1,-1,-1,1,-1,1) =23/16*z2*z3*ln2-5/48*z2*ln2^4-19/80 *z2^2*ln2^2+2089/1680*z2^3+23/48*z3*ln2^3-25/64*z3^2+369/64* z5*ln2-3*ln2*li5half+13/720*ln2^6-6*li6half-6*s6; Fill Stab6(-1,-1,-1,1,0,-1) =47/16*z2*z3*ln2+7/48*z2*ln2^4+5/2* z2*li4half-13/16*z2^2*ln2^2-41/56*z2^3+1/48*z3*ln2^3-189/128* z3^2+125/32*z5*ln2-ln2*li5half-1/2*ln2^2*li4half-7/720*ln2^6 +2*li6half-9/4*s6; Fill Stab6(-1,-1,-1,1,0,1) =-11/8*z2*z3*ln2-1/24*z2*ln2^4-2*z2 *li4half+1/5*z2^2*ln2^2-7/40*z2^3+1/48*z3*ln2^3+129/64*z3^2 +125/32*z5*ln2-ln2*li5half-1/2*ln2^2*li4half-1/72*ln2^6- li6half-3/2*s6; Fill Stab6(-1,-1,-1,1,1,-1) =-z2*z3*ln2-1/16*z2*ln2^4-1/2*z2* li4half-9/80*z2^2*ln2^2+143/105*z2^3+1/3*z3*ln2^3+23/32*z3^2 +4*z5*ln2-4*ln2*li5half-1/2*ln2^2*li4half+1/240*ln2^6-7* li6half-9/4*s6; Fill Stab6(-1,-1,-1,1,1,1) =-z2*z3*ln2-1/16*z2*ln2^4-1/2*z2* li4half-9/80*z2^2*ln2^2+23/35*z2^3+1/3*z3*ln2^3+55/32*z3^2+ 4*z5*ln2-4*ln2*li5half-1/2*ln2^2*li4half+1/240*ln2^6-7* li6half-9/4*s6; Fill Stab6(-1,-1,0,-1,-1,-1) =-5/12*z2*ln2^4-2*z2*li4half+29/8 *z2^2*ln2^2+421/70*z2^3+39/4*z3^2+911/64*z5*ln2-13*ln2* li5half-2*ln2^2*li4half-1/24*ln2^6-48*li6half-26*s6; Fill Stab6(-1,-1,0,-1,-1,1) =21/16*z2*z3*ln2-1/6*z2*ln2^4-2*z2* li4half+47/20*z2^2*ln2^2+1737/280*z2^3+7/16*z3*ln2^3+417/64* z3^2+911/64*z5*ln2-13*ln2*li5half-2*ln2^2*li4half-1/30*ln2^6 -42*li6half-47/2*s6; Fill Stab6(-1,-1,0,-1,0,-1) =13/4*z2*z3*ln2+1/6*z2*ln2^4+2*z2* li4half-27/80*z2^2*ln2^2+281/240*z2^3+59/64*z3^2+331/32*z5* ln2-8*ln2*li5half-2*ln2^2*li4half-1/30*ln2^6-12*li6half-19/ 2*s6; Fill Stab6(-1,-1,0,-1,0,1) =-27/8*z2*z3*ln2-4*z2*li4half+131/ 80*z2^2*ln2^2+4307/1680*z2^3-7/12*z3*ln2^3+73/16*z3^2+331/32* z5*ln2-8*ln2*li5half-2*ln2^2*li4half-7/180*ln2^6-16*li6half -9*s6; Fill Stab6(-1,-1,0,-1,1,-1) =-21/16*z2*z3*ln2+1/16*z2*ln2^4-9/ 8*z2^2*ln2^2+2/35*z2^3+7/16*z3*ln2^3-165/128*z3^2+99/32*z5* ln2-3*ln2*li5half+7/240*ln2^6+3*li6half+3*s6; Fill Stab6(-1,-1,0,-1,1,1) =-7/4*z2*z3*ln2-7/48*z2*ln2^4-z2* li4half+5/16*z2^2*ln2^2+233/280*z2^3+7/24*z3*ln2^3+241/128* z3^2+99/32*z5*ln2-3*ln2*li5half+11/720*ln2^6-7*li6half-9/4* s6; Fill Stab6(-1,-1,0,0,-1,-1) =-3/2*z2*z3*ln2+1/8*z2*ln2^4+1/40* z2^2*ln2^2+2113/1680*z2^3+1/32*z3^2-15/32*z5*ln2-1/120*ln2^6 -6*li6half+3/4*s6; Fill Stab6(-1,-1,0,0,-1,1) =7/8*z2*z3*ln2+1/24*z2*ln2^4+2*z2* li4half-21/20*z2^2*ln2^2-403/336*z2^3+7/24*z3*ln2^3-1/2*z3^2 -15/32*z5*ln2+1/360*ln2^6+2*li6half+11/4*s6; Fill Stab6(-1,-1,0,0,0,-1) =-3/8*z2*z3*ln2-7/40*z2^2*ln2^2-71/ 112*z2^3+3/4*z3^2+2*z5*ln2; Fill Stab6(-1,-1,0,0,0,1) =3/4*z2*z3*ln2+1/5*z2^2*ln2^2+17/70* z2^3-11/64*z3^2+2*z5*ln2-5/2*s6; Fill Stab6(-1,-1,0,0,1,-1) =3/2*z2*z3*ln2-1/6*z2*ln2^4+27/80* z2^2*ln2^2-295/336*z2^3+7/4*z3^2+311/64*z5*ln2-2*ln2*li5half +1/60*ln2^6-5*s6; Fill Stab6(-1,-1,0,0,1,1) =7/8*z2*z3*ln2-1/12*z2*ln2^4+1/4*z2^2* ln2^2+1801/1680*z2^3+7/24*z3*ln2^3-9/16*z3^2+311/64*z5*ln2- 2*ln2*li5half+1/90*ln2^6-4*li6half-21/4*s6; Fill Stab6(-1,-1,0,1,-1,-1) =17/48*z2*ln2^4+7/2*z2*li4half-263/ 80*z2^2*ln2^2-3643/560*z2^3-39/4*z3^2-245/16*z5*ln2+16*ln2* li5half+7/2*ln2^2*li4half+19/240*ln2^6+48*li6half+26*s6; Fill Stab6(-1,-1,0,1,-1,1) =21/16*z2*z3*ln2-1/48*z2*ln2^4+1/2*z2 *li4half-191/80*z2^2*ln2^2-3331/560*z2^3+7/16*z3*ln2^3-459/64 *z3^2-245/16*z5*ln2+16*ln2*li5half+7/2*ln2^2*li4half+17/240* ln2^6+42*li6half+20*s6; Fill Stab6(-1,-1,0,1,0,-1) =15/8*z2*z3*ln2-1/16*z2*ln2^4+5/2*z2* li4half-27/16*z2^2*ln2^2-1381/420*z2^3+7/12*z3*ln2^3-49/16* z3^2-227/32*z5*ln2+8*ln2*li5half+2*ln2^2*li4half+7/180*ln2^6 +16*li6half+9*s6; Fill Stab6(-1,-1,0,1,0,1) =-1/4*z2*z3*ln2-1/24*z2*ln2^4+z2* li4half+1/10*z2^2*ln2^2-491/336*z2^3-125/64*z3^2-227/32*z5* ln2+8*ln2*li5half+2*ln2^2*li4half+1/30*ln2^6+12*li6half+23/ 4*s6; Fill Stab6(-1,-1,0,1,1,-1) =21/16*z2*z3*ln2-5/12*z2*ln2^4+3/2*z2 *li4half+7/80*z2^2*ln2^2-11/7*z2^3+7/16*z3*ln2^3+39/64*z3^2 -81/64*z5*ln2+4*ln2*li5half+3/2*ln2^2*li4half+1/30*ln2^6+3* li6half-3/4*s6; Fill Stab6(-1,-1,0,1,1,1) =7/8*z2*z3*ln2-1/12*z2*ln2^4+3/2*z2* li4half+9/40*z2^2*ln2^2-3/5*z2^3+7/24*z3*ln2^3-49/32*z3^2- 81/64*z5*ln2+4*ln2*li5half+3/2*ln2^2*li4half+13/360*ln2^6+5* li6half; Fill Stab6(-1,-1,1,-1,-1,-1) =-7/8*z2*z3*ln2+1/12*z2*ln2^4-3/2 *z2*li4half-9/40*z2^2*ln2^2+3/5*z2^3-7/24*z3*ln2^3-15/32*z3^2 +81/64*z5*ln2-3*ln2*li5half-3/2*ln2^2*li4half-13/360*ln2^6; Fill Stab6(-1,-1,1,-1,-1,1) =-7/8*z2*z3*ln2+1/12*z2*ln2^4-3/2* z2*li4half-9/40*z2^2*ln2^2+3/5*z2^3-7/24*z3*ln2^3+49/32*z3^2 +81/64*z5*ln2-3*ln2*li5half-3/2*ln2^2*li4half-13/360*ln2^6; Fill Stab6(-1,-1,1,-1,0,-1) =1/16*z2*z3*ln2+5/48*z2*ln2^4-z2* li4half+1/16*z2^2*ln2^2+1/112*z2^3-13/48*z3*ln2^3+115/128* z3^2+33/64*z5*ln2-ln2*li5half-ln2^2*li4half-7/240*ln2^6+3* li6half-1/2*s6; Fill Stab6(-1,-1,1,-1,0,1) =-5/4*z2*z3*ln2+5/48*z2*ln2^4-z2* li4half-1/20*z2^2*ln2^2+31/70*z2^3-13/48*z3*ln2^3-91/64*z3^2 +33/64*z5*ln2-ln2*li5half-ln2^2*li4half-1/30*ln2^6+7/4*s6; Fill Stab6(-1,-1,1,-1,1,-1) =-9/16*z2*z3*ln2-1/24*z2*ln2^4-3/5 *z2^2*ln2^2-1/56*z2^3+7/48*z3*ln2^3-69/64*z3^2-3/64*z5*ln2+ 1/180*ln2^6+3*li6half+3*s6; Fill Stab6(-1,-1,1,-1,1,1) =-9/16*z2*z3*ln2-1/24*z2*ln2^4-3/5* z2^2*ln2^2-71/168*z2^3+7/48*z3*ln2^3-101/64*z3^2-3/64*z5*ln2 +1/180*ln2^6+3*li6half+3*s6; Fill Stab6(-1,-1,1,0,-1,-1) =-z2*z3*ln2-1/12*z2*ln2^4-3/2*z2* li4half+31/40*z2^2*ln2^2+1943/560*z2^3+5/48*z3*ln2^3+361/128* z3^2+457/64*z5*ln2-7*ln2*li5half-3/2*ln2^2*li4half-1/30*ln2^6 -21*li6half-33/4*s6; Fill Stab6(-1,-1,1,0,-1,1) =5/16*z2*z3*ln2+5/48*z2*ln2^4+3/2*z2* li4half-31/80*z2^2*ln2^2+443/560*z2^3+5/48*z3*ln2^3+181/128* z3^2+457/64*z5*ln2-7*ln2*li5half-3/2*ln2^2*li4half-1/48*ln2^6 -12*li6half-9/2*s6; Fill Stab6(-1,-1,1,0,0,-1) =-9/16*z2*z3*ln2+5/48*z2*ln2^4-1/2* z2*li4half-9/80*z2^2*ln2^2+8/35*z2^3-1/6*z3*ln2^3-25/64*z3^2 +151/64*z5*ln2-2*ln2*li5half-ln2^2*li4half-1/36*ln2^6-2* li6half-1/4*s6; Fill Stab6(-1,-1,1,0,0,1) =-3/8*z2*z3*ln2-2*z2*li4half+2/5* z2^2*ln2^2+201/280*z2^3-1/6*z3*ln2^3+163/128*z3^2+151/64*z5* ln2-2*ln2*li5half-ln2^2*li4half-1/40*ln2^6-5/2*s6; Fill Stab6(-1,-1,1,0,1,-1) =-1/8*z2*z3*ln2+5/24*z2*ln2^4-3/2* z2*li4half-1/10*z2^2*ln2^2-31/35*z2^3-23/48*z3*ln2^3-25/32* z3^2+23/64*z5*ln2-2*ln2*li5half-3/2*ln2^2*li4half-1/30*ln2^6 +9*li6half+3/2*s6; Fill Stab6(-1,-1,1,0,1,1) =-23/16*z2*z3*ln2+5/48*z2*ln2^4-3/2* z2*li4half+21/80*z2^2*ln2^2+3/7*z2^3-23/48*z3*ln2^3+87/64* z3^2+23/64*z5*ln2-2*ln2*li5half-3/2*ln2^2*li4half-31/720* ln2^6+2*li6half+3/4*s6; Fill Stab6(-1,-1,1,1,-1,-1) =7/16*z2*z3*ln2-1/24*z2*ln2^4+1/2*z2 *li4half-1/8*z2^2*ln2^2-18/35*z2^3+7/48*z3*ln2^3-109/64*z3^2 -27/32*z5*ln2+2*ln2*li5half+1/2*ln2^2*li4half+1/72*ln2^6+6* li6half+5/2*s6; Fill Stab6(-1,-1,1,1,-1,1) =7/16*z2*z3*ln2-1/24*z2*ln2^4+1/2*z2* li4half-1/8*z2^2*ln2^2-172/105*z2^3+7/48*z3*ln2^3-45/64*z3^2 -27/32*z5*ln2+2*ln2*li5half+1/2*ln2^2*li4half+1/72*ln2^6+6* li6half+5/2*s6; Fill Stab6(-1,-1,1,1,0,-1) =1/2*z2*z3*ln2+z2*li4half-11/20*z2^2* ln2^2-47/35*z2^3+1/6*z3*ln2^3-3/4*z3^2+1/32*z5*ln2+2*ln2* li5half+1/2*ln2^2*li4half+1/120*ln2^6+3*li6half+2*s6; Fill Stab6(-1,-1,1,1,0,1) =1/2*z2*z3*ln2-1/16*z2*ln2^4-1/2*z2* li4half-1/16*z2^2*ln2^2-1/7*z2^3+1/6*z3*ln2^3-25/32*z3^2+1/ 32*z5*ln2+2*ln2*li5half+1/2*ln2^2*li4half+1/80*ln2^6+6* li6half-1/4*s6; Fill Stab6(-1,-1,1,1,1,-1) =-8/7*z2^3+ln2*li5half+5*li6half; Fill Stab6(-1,-1,1,1,1,1) =ln2*li5half+5*li6half; Fill Stab6(-1,0,-1,-1,-1,-1) =-15/16*z2*z3*ln2+11/12*z2*ln2^4- 161/40*z2^2*ln2^2-186/35*z2^3-7/16*z3*ln2^3-333/32*z3^2-845/ 64*z5*ln2+11*ln2*li5half-1/40*ln2^6+48*li6half+26*s6; Fill Stab6(-1,0,-1,-1,-1,1) =-21/16*z2*z3*ln2+23/48*z2*ln2^4+3/ 2*z2*li4half-271/80*z2^2*ln2^2-3019/560*z2^3-7/16*z3*ln2^3- 417/64*z3^2-845/64*z5*ln2+11*ln2*li5half+3/2*ln2^2*li4half+7/ 240*ln2^6+42*li6half+47/2*s6; Fill Stab6(-1,0,-1,-1,0,-1) =-13/8*z2*z3*ln2-1/6*z2*ln2^4+3/8* z2^2*ln2^2-13/5*z2^3-455/128*z3^2-547/32*z5*ln2+16*ln2* li5half+4*ln2^2*li4half+1/15*ln2^6+24*li6half+13*s6; Fill Stab6(-1,0,-1,-1,0,1) =37/16*z2*z3*ln2+5/12*z2*ln2^4+2*z2* li4half-39/10*z2^2*ln2^2-421/70*z2^3-95/8*z3^2-547/32*z5*ln2 +16*ln2*li5half-1/15*ln2^6+48*li6half+26*s6; Fill Stab6(-1,0,-1,-1,1,-1) =1/12*z2*ln2^4-17/8*z2^2*ln2^2-107/ 40*z2^3-39/8*z3^2-221/32*z5*ln2+7*ln2*li5half-1/40*ln2^6+24 *li6half+13*s6; Fill Stab6(-1,0,-1,-1,1,1) =21/16*z2*z3*ln2+17/48*z2*ln2^4+1/2* z2*li4half-47/16*z2^2*ln2^2-2141/560*z2^3-891/128*z3^2-221/32 *z5*ln2+7*ln2*li5half-1/2*ln2^2*li4half-3/80*ln2^6+30*li6half +31/2*s6; Fill Stab6(-1,0,-1,0,-1,-1) =-15/16*z2*z3*ln2+1/6*z2*ln2^4-4* z2*li4half-73/40*z2^2*ln2^2+183/140*z2^3+25/128*z3^2+123/16* z5*ln2-8*ln2*li5half-4*ln2^2*li4half-1/10*ln2^6; Fill Stab6(-1,0,-1,0,-1,1) =15/16*z2*z3*ln2+1/6*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2+45/56*z2^3+17/16*z3^2+123/16*z5*ln2- 8*ln2*li5half-2*ln2^2*li4half-1/30*ln2^6-12*li6half-9/2*s6; Fill Stab6(-1,0,-1,0,0,-1) =15/8*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2-853/1680*z2^3-15/8*z3^2-21/32*z5*ln2 +s6; Fill Stab6(-1,0,-1,0,0,1) =-3/2*z2*z3*ln2-1/6*z2*ln2^4-4*z2* li4half+z2^2*ln2^2+503/420*z2^3+59/32*z3^2-21/32*z5*ln2-5/2 *s6; Fill Stab6(-1,0,-1,0,1,-1) =-19/16*z2*z3*ln2+113/40*z2^2*ln2^2 +76/35*z2^3-7/12*z3*ln2^3+45/16*z3^2+89/64*z5*ln2-4*ln2* li5half+1/90*ln2^6-16*li6half-8*s6; Fill Stab6(-1,0,-1,0,1,1) =-7/4*z2*z3*ln2+1/6*z2*ln2^4-2*z2* li4half+1/2*z2^2*ln2^2+589/560*z2^3-7/12*z3*ln2^3+99/32*z3^2 +89/64*z5*ln2-4*ln2*li5half-2*ln2^2*li4half-1/18*ln2^6-4* li6half-7/4*s6; Fill Stab6(-1,0,-1,1,-1,-1) =-29/48*z2*ln2^4-2*z2*li4half+19/ 16*z2^2*ln2^2+97/40*z2^3+111/32*z3^2+457/64*z5*ln2-7*ln2* li5half-2*ln2^2*li4half-11/240*ln2^6-15*li6half-37/4*s6; Fill Stab6(-1,0,-1,1,-1,1) =-3/16*z2*z3*ln2-1/2*z2*ln2^4+1/2* z2*li4half+39/20*z2^2*ln2^2+2*z2^3+501/128*z3^2+457/64*z5*ln2 -7*ln2*li5half-1/2*ln2^2*li4half+1/120*ln2^6-21*li6half-10* s6; Fill Stab6(-1,0,-1,1,0,-1) =1/8*z2*z3*ln2+1/48*z2*ln2^4+1/2*z2* li4half-1/8*z2^2*ln2^2-279/560*z2^3-61/128*z3^2+53/64*z5*ln2 +s6; Fill Stab6(-1,0,-1,1,0,1) =1/8*z2*z3*ln2-1/24*z2*ln2^4-z2* li4half+1/4*z2^2*ln2^2+261/560*z2^3+119/128*z3^2+53/64*z5*ln2 -11/4*s6; Fill Stab6(-1,0,-1,1,1,-1) =-7/16*z2*z3*ln2+5/16*z2*ln2^4+29/ 16*z2^2*ln2^2+22/35*z2^3-7/48*z3*ln2^3+107/64*z3^2+27/32*z5* ln2-ln2*li5half-1/720*ln2^6-7*li6half-19/4*s6; Fill Stab6(-1,0,-1,1,1,1) =-7/16*z2*z3*ln2+1/24*z2*ln2^4-1/2* z2*li4half+1/8*z2^2*ln2^2+18/35*z2^3-7/48*z3*ln2^3+109/64* z3^2+27/32*z5*ln2-ln2*li5half-1/2*ln2^2*li4half-1/72*ln2^6- li6half-5/2*s6; Fill Stab6(-1,0,0,-1,-1,-1) =-z2*z3*ln2-1/3*z2*ln2^4+z2* li4half-9/20*z2^2*ln2^2-509/560*z2^3-25/32*z3^2-15/32*z5*ln2 +ln2^2*li4half+1/20*ln2^6+6*li6half+17/4*s6; Fill Stab6(-1,0,0,-1,-1,1) =-13/16*z2*z3*ln2-11/24*z2*ln2^4-2* z2*li4half+149/80*z2^2*ln2^2+27/35*z2^3+77/32*z3^2-15/32*z5* ln2+2*ln2^2*li4half+3/40*ln2^6-6*li6half-17/4*s6; Fill Stab6(-1,0,0,-1,0,-1) =-9/8*z2*z3*ln2-1/24*z2*ln2^4-z2* li4half+1/4*z2^2*ln2^2-89/840*z2^3+3/4*z3^2-11/32*z5*ln2+s6; Fill Stab6(-1,0,0,-1,0,1) =-5/4*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2-179/840*z2^3+5/64*z3^2-11/32*z5*ln2+ 5/2*s6; Fill Stab6(-1,0,0,-1,1,-1) =15/16*z2*z3*ln2+1/8*z2*ln2^4+19/80* z2^2*ln2^2-4/5*z2^3+7/24*z3*ln2^3+5/8*z3^2-15/32*z5*ln2+2* ln2*li5half-1/72*ln2^6+2*li6half-5/4*s6; Fill Stab6(-1,0,0,-1,1,1) =-1/8*z2*z3*ln2-1/12*z2*ln2^4+z2* li4half-1/4*z2^2*ln2^2-29/280*z2^3+7/24*z3*ln2^3-29/32*z3^2 -15/32*z5*ln2+2*ln2*li5half+ln2^2*li4half+1/36*ln2^6+2* li6half+1/2*s6; Fill Stab6(-1,0,0,0,-1,-1) =3/2*z2*z3*ln2+3/4*z2^2*ln2^2-491/840 *z2^3+33/32*z3^2+59/32*z5*ln2-4*s6; Fill Stab6(-1,0,0,0,-1,1) =z2*z3*ln2+53/168*z2^3-5/8*z3^2+59/ 32*z5*ln2-5/2*s6; Fill Stab6(-1,0,0,0,0,-1) =8/35*z2^3+15/16*z5*ln2-s6; Fill Stab6(-1,0,0,0,0,1) =-111/280*z2^3+9/32*z3^2+15/16*z5*ln2; Fill Stab6(-1,0,0,0,1,-1) =-15/8*z2*z3*ln2-3/4*z2^2*ln2^2+47/ 105*z2^3-21/32*z3^2-17/16*z5*ln2+4*s6; Fill Stab6(-1,0,0,0,1,1) =-1/2*z2*z3*ln2-179/840*z2^3+11/64* z3^2-17/16*z5*ln2+3/2*s6; Fill Stab6(-1,0,0,1,-1,-1) =1/2*z2*z3*ln2+1/3*z2*ln2^4+1/5*z2^2* ln2^2-1/2*z3^2-27/8*z5*ln2+4*ln2*li5half-1/30*ln2^6; Fill Stab6(-1,0,0,1,-1,1) =13/8*z2*z3*ln2+1/8*z2*ln2^4+z2* li4half-23/80*z2^2*ln2^2+11/80*z2^3-169/128*z3^2-27/8*z5*ln2 +4*ln2*li5half+ln2^2*li4half+1/120*ln2^6; Fill Stab6(-1,0,0,1,0,-1) =9/4*z2*z3*ln2+121/840*z2^3-33/64*z3^2 +51/32*z5*ln2-7/2*s6; Fill Stab6(-1,0,0,1,0,1) =5/8*z2*z3*ln2-493/1680*z2^3-1/4*z3^2 +51/32*z5*ln2-s6; Fill Stab6(-1,0,0,1,1,-1) =-z2*z3*ln2-1/8*z2*ln2^4-z2*li4half -21/16*z2^2*ln2^2-247/560*z2^3+7/24*z3*ln2^3-217/128*z3^2+ 125/64*z5*ln2-2*ln2*li5half-ln2^2*li4half-1/72*ln2^6+8* li6half+9/2*s6; Fill Stab6(-1,0,0,1,1,1) =-3/8*z2*z3*ln2-1/12*z2*ln2^4+23/80* z2^3+7/24*z3*ln2^3+47/64*z3^2+125/64*z5*ln2-2*ln2*li5half+1/ 90*ln2^6-4*li6half-5/4*s6; Fill Stab6(-1,0,1,-1,-1,-1) =-3/8*z2*z3*ln2-19/24*z2*ln2^4+161/ 40*z2^2*ln2^2+1459/280*z2^3+501/64*z3^2+61/8*z5*ln2-8*ln2* li5half+1/120*ln2^6-42*li6half-20*s6; Fill Stab6(-1,0,1,-1,-1,1) =-41/48*z2*ln2^4-3/2*z2*li4half+463/ 80*z2^2*ln2^2+3293/560*z2^3+39/4*z3^2+61/8*z5*ln2-8*ln2* li5half+3/2*ln2^2*li4half+1/16*ln2^6-48*li6half-26*s6; Fill Stab6(-1,0,1,-1,0,-1) =-1/2*z2*z3*ln2-5/12*z2*ln2^4-2*z2* li4half+39/10*z2^2*ln2^2+1643/280*z2^3+41/4*z3^2+507/32*z5* ln2-16*ln2*li5half+1/15*ln2^6-48*li6half-26*s6; Fill Stab6(-1,0,1,-1,0,1) =-1/2*z2*z3*ln2+1/6*z2*ln2^4-3/8* z2^2*ln2^2+213/70*z2^3+77/16*z3^2+507/32*z5*ln2-16*ln2* li5half-4*ln2^2*li4half-1/15*ln2^6-24*li6half-23/2*s6; Fill Stab6(-1,0,1,-1,1,-1) =21/16*z2*z3*ln2+1/8*z2*ln2^4+93/40* z2^2*ln2^2+3*z2^3+7/16*z3*ln2^3+441/64*z3^2+61/8*z5*ln2-6* ln2*li5half+1/120*ln2^6-30*li6half-35/2*s6; Fill Stab6(-1,0,1,-1,1,1) =-7/48*z2*ln2^4-1/2*z2*li4half+51/80 *z2^2*ln2^2+1991/560*z2^3+7/16*z3*ln2^3+405/128*z3^2+61/8*z5* ln2-6*ln2*li5half-1/2*ln2^2*li4half-1/240*ln2^6-24*li6half- 23/2*s6; Fill Stab6(-1,0,1,0,-1,-1) =11/8*z2*z3*ln2-19/20*z2^2*ln2^2-20/7 *z2^3+7/12*z3*ln2^3-33/32*z3^2-33/32*z5*ln2+4*ln2*li5half-1/ 90*ln2^6+16*li6half+4*s6; Fill Stab6(-1,0,1,0,-1,1) =13/16*z2*z3*ln2-1/6*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2-153/280*z2^3+7/12*z3*ln2^3-303/128* z3^2-33/32*z5*ln2+4*ln2*li5half+2*ln2^2*li4half+1/18*ln2^6+ 4*li6half+s6; Fill Stab6(-1,0,1,0,0,-1) =7/8*z2*z3*ln2+1/6*z2*ln2^4+4*z2* li4half-z2^2*ln2^2-337/420*z2^3-69/64*z3^2+41/32*z5*ln2+3/2 *s6; Fill Stab6(-1,0,1,0,0,1) =-z2*z3*ln2-1/12*z2*ln2^4-2*z2* li4half+1/2*z2^2*ln2^2+17/1680*z2^3+41/32*z3^2+41/32*z5*ln2 -s6; Fill Stab6(-1,0,1,0,1,-1) =3/4*z2*z3*ln2-1/6*z2*ln2^4+4*z2* li4half-1/20*z2^2*ln2^2-97/140*z2^3-61/32*z3^2-125/16*z5*ln2 +8*ln2*li5half+4*ln2^2*li4half+1/10*ln2^6+4*s6; Fill Stab6(-1,0,1,0,1,1) =-1/6*z2*ln2^4-2*z2*li4half+1/2*z2^2* ln2^2-661/560*z2^3-119/64*z3^2-125/16*z5*ln2+8*ln2*li5half+ 2*ln2^2*li4half+1/30*ln2^6+12*li6half+19/4*s6; Fill Stab6(-1,0,1,1,-1,-1) =21/16*z2*z3*ln2+25/48*z2*ln2^4-263/ 80*z2^2*ln2^2-1133/280*z2^3+7/16*z3*ln2^3-237/64*z3^2-35/32* z5*ln2+4*ln2*li5half+1/240*ln2^6+27*li6half+43/4*s6; Fill Stab6(-1,0,1,1,-1,1) =3/2*z2*z3*ln2+1/12*z2*ln2^4+3/2*z2* li4half-53/20*z2^2*ln2^2-71/28*z2^3+7/16*z3*ln2^3-723/128* z3^2-35/32*z5*ln2+4*ln2*li5half+3/2*ln2^2*li4half+7/120*ln2^6 +21*li6half+17/2*s6; Fill Stab6(-1,0,1,1,0,-1) =41/16*z2*z3*ln2+1/8*z2*ln2^4+3*z2* li4half-3/4*z2^2*ln2^2-69/112*z2^3-181/128*z3^2+177/64*z5*ln2 -7/4*s6; Fill Stab6(-1,0,1,1,0,1) =-11/8*z2*z3*ln2-1/16*z2*ln2^4-3/2*z2 *li4half+3/8*z2^2*ln2^2-9/28*z2^3+7/4*z3^2+177/64*z5*ln2-s6; Fill Stab6(-1,0,1,1,1,-1) =-7/8*z2*z3*ln2-5/16*z2*ln2^4+2*z2* li4half+3/16*z2^2*ln2^2+2/35*z2^3+7/24*z3*ln2^3-73/64*z3^2- 4*z5*ln2+4*ln2*li5half+2*ln2^2*li4half+7/144*ln2^6-li6half+ 11/4*s6; Fill Stab6(-1,0,1,1,1,1) =-7/8*z2*z3*ln2-5/24*z2*ln2^4-3/2*z2* li4half+3/8*z2^2*ln2^2-18/35*z2^3+7/24*z3*ln2^3-11/64*z3^2- 4*z5*ln2+4*ln2*li5half+3/2*ln2^2*li4half+13/360*ln2^6+5* li6half+5/2*s6; Fill Stab6(-1,1,-1,-1,-1,-1) =-13/8*z2*z3*ln2+5/48*z2*ln2^4-1/ 16*z2^2*ln2^2-3/80*z2^3-11/24*z3*ln2^3-169/64*z3^2-375/64*z5* ln2+3*ln2*li5half-11/720*ln2^6+6*li6half+6*s6; Fill Stab6(-1,1,-1,-1,-1,1) =-13/8*z2*z3*ln2+5/48*z2*ln2^4-1/ 16*z2^2*ln2^2-1207/1680*z2^3-11/24*z3*ln2^3+23/64*z3^2-375/64 *z5*ln2+3*ln2*li5half-11/720*ln2^6+6*li6half+6*s6; Fill Stab6(-1,1,-1,-1,0,-1) =-13/4*z2*z3*ln2-1/6*z2*ln2^4-3/2* z2*li4half+11/40*z2^2*ln2^2-187/560*z2^3+1/6*z3*ln2^3-35/64* z3^2-247/32*z5*ln2+5*ln2*li5half+3/2*ln2^2*li4half+1/30*ln2^6 +9*li6half+29/4*s6; Fill Stab6(-1,1,-1,-1,0,1) =7/8*z2*z3*ln2-5/48*z2*ln2^4-1/40* z2^2*ln2^2-157/560*z2^3+1/6*z3*ln2^3-97/32*z3^2-247/32*z5*ln2 +5*ln2*li5half+3/2*ln2^2*li4half+7/240*ln2^6+6*li6half+17/4 *s6; Fill Stab6(-1,1,-1,-1,1,-1) =1/16*z2*z3*ln2-7/48*z2*ln2^4-3/2*z2 *li4half+5/16*z2^2*ln2^2-23/35*z2^3-1/48*z3*ln2^3-179/128* z3^2-6*z5*ln2+6*ln2*li5half+3/2*ln2^2*li4half+19/720*ln2^6+ 9*li6half+15/4*s6; Fill Stab6(-1,1,-1,-1,1,1) =1/16*z2*z3*ln2-7/48*z2*ln2^4-3/2*z2* li4half+5/16*z2^2*ln2^2-27/35*z2^3-1/48*z3*ln2^3-243/128*z3^2 -6*z5*ln2+6*ln2*li5half+3/2*ln2^2*li4half+19/720*ln2^6+9* li6half+15/4*s6; Fill Stab6(-1,1,-1,0,-1,-1) =-1/8*z2*z3*ln2-1/4*z2*ln2^4-2*z2* li4half+51/40*z2^2*ln2^2+191/280*z2^3+5/48*z3*ln2^3-5/64*z3^2 -221/32*z5*ln2+7*ln2*li5half+2*ln2^2*li4half+1/40*ln2^6; Fill Stab6(-1,1,-1,0,-1,1) =-5/16*z2*z3*ln2-3/16*z2*ln2^4-2*z2 *li4half+39/80*z2^2*ln2^2-101/140*z2^3+5/48*z3*ln2^3-95/64* z3^2-221/32*z5*ln2+7*ln2*li5half+2*ln2^2*li4half+3/80*ln2^6 +9*li6half+15/4*s6; Fill Stab6(-1,1,-1,0,0,-1) =7/16*z2*z3*ln2-1/24*z2*ln2^4-19/80* z2^2*ln2^2-51/112*z2^3+1/8*z3*ln2^3-5/2*z3^2-47/8*z5*ln2+4* ln2*li5half+ln2^2*li4half+1/60*ln2^6+6*li6half+17/4*s6; Fill Stab6(-1,1,-1,0,0,1) =-2*z2*z3*ln2-1/8*z2*ln2^4-z2* li4half+3/20*z2^2*ln2^2-2/5*z2^3+1/8*z3*ln2^3-93/128*z3^2- 47/8*z5*ln2+4*ln2*li5half+ln2^2*li4half+7/360*ln2^6+8*li6half +11/2*s6; Fill Stab6(-1,1,-1,0,1,-1) =-11/8*z2*z3*ln2+3/8*z2*ln2^4+2*z2* li4half-27/20*z2^2*ln2^2-27/40*z2^3-23/48*z3*ln2^3-163/64* z3^2+85/64*z5*ln2-4*ln2*li5half-2*ln2^2*li4half-1/24*ln2^6+ 6*li6half+6*s6; Fill Stab6(-1,1,-1,0,1,1) =-19/16*z2*z3*ln2+7/48*z2*ln2^4-z2* li4half+11/80*z2^2*ln2^2+61/280*z2^3-23/48*z3*ln2^3+75/32* z3^2+85/64*z5*ln2-4*ln2*li5half-2*ln2^2*li4half-37/720*ln2^6 -li6half+1/4*s6; Fill Stab6(-1,1,-1,1,-1,-1) =1/16*z2*z3*ln2-1/48*z2*ln2^4+3/16* z2^2*ln2^2+53/560*z2^3-1/48*z3*ln2^3+1/128*z3^2-3/64*z5*ln2 +1/720*ln2^6; Fill Stab6(-1,1,-1,1,-1,1) =1/16*z2*z3*ln2-1/48*z2*ln2^4+3/16* z2^2*ln2^2-123/560*z2^3-1/48*z3*ln2^3+1/128*z3^2-3/64*z5*ln2 +1/720*ln2^6; Fill Stab6(-1,1,-1,1,0,-1) =-1/12*z2*ln2^4-z2*li4half+9/40* z2^2*ln2^2-139/280*z2^3+1/48*z3*ln2^3-129/128*z3^2-277/64*z5* ln2+4*ln2*li5half+ln2^2*li4half+11/720*ln2^6+5*li6half+5/2* s6; Fill Stab6(-1,1,-1,1,0,1) =-3/16*z2*z3*ln2+1/24*z2*ln2^4+2*z2* li4half-3/5*z2^2*ln2^2-23/20*z2^3+1/48*z3*ln2^3-63/32*z3^2- 277/64*z5*ln2+4*ln2*li5half+ln2^2*li4half+7/360*ln2^6+8* li6half+11/2*s6; Fill Stab6(-1,1,-1,1,1,-1) =-1/2*z2*z3*ln2+1/16*z2*ln2^4+1/2* z2*li4half+1/16*z2^2*ln2^2+13/105*z2^3-1/6*z3*ln2^3-7/32*z3^2 -1/32*z5*ln2-ln2*li5half-1/2*ln2^2*li4half-1/80*ln2^6- li6half+1/4*s6; Fill Stab6(-1,1,-1,1,1,1) =-1/2*z2*z3*ln2+1/16*z2*ln2^4+1/2*z2 *li4half+1/16*z2^2*ln2^2+1/7*z2^3-1/6*z3*ln2^3+25/32*z3^2-1/ 32*z5*ln2-ln2*li5half-1/2*ln2^2*li4half-1/80*ln2^6-li6half+ 1/4*s6; Fill Stab6(-1,1,0,-1,-1,-1) =21/16*z2*z3*ln2+31/48*z2*ln2^4+2*z2 *li4half-263/80*z2^2*ln2^2-263/80*z2^3-7/16*z3*ln2^3-459/128* z3^2+99/32*z5*ln2-3*ln2*li5half-2*ln2^2*li4half-7/240*ln2^6 +21*li6half+10*s6; Fill Stab6(-1,1,0,-1,-1,1) =19/48*z2*ln2^4+2*z2*li4half-59/20* z2^2*ln2^2-197/80*z2^3-111/32*z3^2+99/32*z5*ln2-3*ln2*li5half -2*ln2^2*li4half-3/80*ln2^6+15*li6half+37/4*s6; Fill Stab6(-1,1,0,-1,0,-1) =-5/16*z2*z3*ln2+1/12*z2*ln2^4-17/ 16*z2^2*ln2^2-178/105*z2^3-37/16*z3^2-103/32*z5*ln2+4*ln2* li5half-1/60*ln2^6+12*li6half+7*s6; Fill Stab6(-1,1,0,-1,0,1) =19/8*z2*z3*ln2+1/3*z2*ln2^4+4*z2* li4half-13/20*z2^2*ln2^2-3571/1680*z2^3-7/12*z3*ln2^3-217/128 *z3^2-103/32*z5*ln2+4*ln2*li5half-1/45*ln2^6+8*li6half+15/4 *s6; Fill Stab6(-1,1,0,-1,1,-1) =-7/24*z2*ln2^4+13/20*z2^2*ln2^2- 103/560*z2^3+9/32*z3^2-25/32*z5*ln2+ln2*li5half-1/120*ln2^6 -3/4*s6; Fill Stab6(-1,1,0,-1,1,1) =7/16*z2*z3*ln2+1/12*z2*ln2^4+z2* li4half+7/20*z2^2*ln2^2-251/560*z2^3-7/48*z3*ln2^3+19/128* z3^2-25/32*z5*ln2+ln2*li5half-1/180*ln2^6+2*li6half-1/4*s6; Fill Stab6(-1,1,0,0,-1,-1) =-11/16*z2*z3*ln2+z2*li4half+7/80* z2^2*ln2^2+41/210*z2^3-7/24*z3*ln2^3-9/64*z3^2+39/16*z5*ln2 -4*ln2*li5half-ln2^2*li4half-1/90*ln2^6-2*li6half-1/4*s6; Fill Stab6(-1,1,0,0,-1,1) =-7/4*z2*z3*ln2-1/12*z2*ln2^4-3*z2* li4half+z2^2*ln2^2+673/420*z2^3+179/64*z3^2+39/16*z5*ln2-4* ln2*li5half-ln2^2*li4half-1/60*ln2^6-6*li6half-4*s6; Fill Stab6(-1,1,0,0,0,-1) =-z2*z3*ln2-1/12*z2*ln2^4-2*z2* li4half+7/10*z2^2*ln2^2+22/35*z2^3+9/8*z3^2-29/32*z5*ln2-s6; Fill Stab6(-1,1,0,0,0,1) =1/2*z2*z3*ln2+1/24*z2*ln2^4+z2*li4half -17/40*z2^2*ln2^2-59/280*z2^3-65/64*z3^2-29/32*z5*ln2+3/2* s6; Fill Stab6(-1,1,0,0,1,-1) =11/16*z2*z3*ln2+5/24*z2*ln2^4-z2* li4half+11/40*z2^2*ln2^2+251/210*z2^3-7/24*z3*ln2^3+211/128* z3^2+125/64*z5*ln2-2*ln2*li5half-ln2^2*li4half-13/360*ln2^6 -8*li6half-4*s6; Fill Stab6(-1,1,0,0,1,1) =1/8*z2*ln2^4+z2*li4half-4/5*z2^2*ln2^2 -43/120*z2^3-67/128*z3^2+125/64*z5*ln2-2*ln2*li5half-ln2^2* li4half-1/40*ln2^6+3/2*s6; Fill Stab6(-1,1,0,1,-1,-1) =-21/16*z2*z3*ln2-1/3*z2*ln2^4-1/2* z2*li4half+29/8*z2^2*ln2^2+2259/560*z2^3-7/16*z3*ln2^3+237/64 *z3^2-87/32*z5*ln2+1/2*ln2^2*li4half-1/60*ln2^6-27*li6half- 43/4*s6; Fill Stab6(-1,1,0,1,-1,1) =-21/8*z2*z3*ln2-5/24*z2*ln2^4-7/2* z2*li4half+233/80*z2^2*ln2^2+417/112*z2^3+681/128*z3^2-87/32* z5*ln2+1/2*ln2^2*li4half-1/120*ln2^6-21*li6half-17/2*s6; Fill Stab6(-1,1,0,1,0,-1) =-37/8*z2*z3*ln2-11/24*z2*ln2^4-7*z2 *li4half+153/80*z2^2*ln2^2+2641/840*z2^3+7/12*z3*ln2^3+499/ 128*z3^2+73/64*z5*ln2-4*ln2*li5half+1/45*ln2^6-8*li6half-19/ 4*s6; Fill Stab6(-1,1,0,1,0,1) =23/16*z2*z3*ln2-1/48*z2*ln2^4+3/2*z2* li4half+21/80*z2^2*ln2^2+611/420*z2^3+5/32*z3^2+73/64*z5*ln2 -4*ln2*li5half+1/60*ln2^6-12*li6half-17/4*s6; Fill Stab6(-1,1,0,1,1,-1) =1/16*z2*ln2^4-9/2*z2*li4half-3/16* z2^2*ln2^2+z2^3+45/32*z3^2+6*z5*ln2-6*ln2*li5half-3/2*ln2^2 *li4half-1/80*ln2^6-15/4*s6; Fill Stab6(-1,1,0,1,1,1) =7/16*z2*z3*ln2+7/48*z2*ln2^4+3/2*z2* li4half-5/16*z2^2*ln2^2+27/35*z2^3-7/48*z3*ln2^3+131/128*z3^2 +6*z5*ln2-6*ln2*li5half-3/2*ln2^2*li4half-19/720*ln2^6-10* li6half-15/4*s6; Fill Stab6(-1,1,1,-1,-1,-1) =7/8*z2*z3*ln2+5/24*z2*ln2^4+3/2*z2* li4half-7/40*z2^2*ln2^2+5/21*z2^3-7/24*z3*ln2^3+75/64*z3^2+ 4*z5*ln2-4*ln2*li5half-3/2*ln2^2*li4half-13/360*ln2^6-6* li6half-5/2*s6; Fill Stab6(-1,1,1,-1,-1,1) =7/8*z2*z3*ln2+5/24*z2*ln2^4+3/2*z2* li4half-7/40*z2^2*ln2^2+11/35*z2^3-7/24*z3*ln2^3+11/64*z3^2 +4*z5*ln2-4*ln2*li5half-3/2*ln2^2*li4half-13/360*ln2^6-6* li6half-5/2*s6; Fill Stab6(-1,1,1,-1,0,-1) =3/8*z2*z3*ln2+3/16*z2*ln2^4+z2* li4half-11/40*z2^2*ln2^2+81/280*z2^3-13/48*z3*ln2^3+85/128* z3^2+39/8*z5*ln2-4*ln2*li5half-3/2*ln2^2*li4half-3/80*ln2^6 -6*li6half-5/2*s6; Fill Stab6(-1,1,1,-1,0,1) =27/16*z2*z3*ln2+5/24*z2*ln2^4+3/2*z2* li4half-19/40*z2^2*ln2^2-17/70*z2^3-13/48*z3*ln2^3+65/64*z3^2 +39/8*z5*ln2-4*ln2*li5half-3/2*ln2^2*li4half-1/30*ln2^6-3* li6half-3*s6; Fill Stab6(-1,1,1,-1,1,-1) =9/16*z2*z3*ln2-1/24*z2*ln2^4+1/5* z2^2*ln2^2+1/120*z2^3+7/48*z3*ln2^3+153/128*z3^2+63/32*z5*ln2 -ln2*li5half+1/180*ln2^6-3*li6half-3*s6; Fill Stab6(-1,1,1,-1,1,1) =9/16*z2*z3*ln2-1/24*z2*ln2^4+1/5*z2^2 *ln2^2+121/280*z2^3+7/48*z3*ln2^3+89/128*z3^2+63/32*z5*ln2- ln2*li5half+1/180*ln2^6-3*li6half-3*s6; Fill Stab6(-1,1,1,0,-1,-1) =1/8*z2*z3*ln2-1/24*z2*ln2^4-1/2*z2* li4half-29/40*z2^2*ln2^2-927/560*z2^3+1/4*z3*ln2^3-107/128* z3^2-1/8*z5*ln2+ln2*li5half+1/2*ln2^2*li4half+1/36*ln2^6+11 *li6half+13/4*s6; Fill Stab6(-1,1,1,0,-1,1) =1/8*z2*z3*ln2-5/48*z2*ln2^4+1/2*z2* li4half-19/80*z2^2*ln2^2-243/560*z2^3+1/4*z3*ln2^3-111/128* z3^2-1/8*z5*ln2+ln2*li5half+1/2*ln2^2*li4half+13/720*ln2^6+ 4*li6half+s6; Fill Stab6(-1,1,1,0,0,-1) =3/2*z2*z3*ln2+1/6*z2*ln2^4+3*z2* li4half-17/20*z2^2*ln2^2-53/35*z2^3-1/6*z3*ln2^3-3/2*z3^2- 33/32*z5*ln2+2*ln2*li5half-1/120*ln2^6+6*li6half+3*s6; Fill Stab6(-1,1,1,0,0,1) =1/16*z2*ln2^4-1/2*z2*li4half-9/80*z2^2 *ln2^2-87/140*z2^3-1/6*z3*ln2^3-19/32*z3^2-33/32*z5*ln2+2* ln2*li5half-1/90*ln2^6+4*li6half+7/4*s6; Fill Stab6(-1,1,1,0,1,-1) =z2*z3*ln2+1/6*z2*ln2^4+7/2*z2*li4half -1/10*z2^2*ln2^2-13/35*z2^3-1/3*z3*ln2^3-3/4*z3^2-4*z5*ln2 +4*ln2*li5half+1/2*ln2^2*li4half-1/60*ln2^6-3*li6half+2*s6; Fill Stab6(-1,1,1,0,1,1) =z2*z3*ln2+1/16*z2*ln2^4-1/2*z2*li4half +9/80*z2^2*ln2^2-23/35*z2^3-1/3*z3*ln2^3-55/32*z3^2-4*z5* ln2+4*ln2*li5half+1/2*ln2^2*li4half-1/240*ln2^6+6*li6half+9/ 4*s6; Fill Stab6(-1,1,1,1,-1,-1) =-7/16*z2*z3*ln2-1/12*z2*ln2^4-1/2* z2*li4half+1/8*z2^2*ln2^2+7/48*z3*ln2^3+49/128*z3^2-z5*ln2+ ln2*li5half+1/2*ln2^2*li4half+1/72*ln2^6; Fill Stab6(-1,1,1,1,-1,1) =-7/16*z2*z3*ln2-1/12*z2*ln2^4-1/2* z2*li4half+1/8*z2^2*ln2^2+2/5*z2^3+7/48*z3*ln2^3-15/128*z3^2 -z5*ln2+ln2*li5half+1/2*ln2^2*li4half+1/72*ln2^6; Fill Stab6(-1,1,1,1,0,-1) =-1/2*z2*z3*ln2-1/12*z2*ln2^4-z2* li4half+3/20*z2^2*ln2^2+3/7*z2^3+1/6*z3*ln2^3+3/8*z3^2+z5* ln2-ln2*li5half+1/120*ln2^6-s6; Fill Stab6(-1,1,1,1,0,1) =-1/2*z2*z3*ln2-1/24*z2*ln2^4-1/40* z2^2*ln2^2+1/5*z2^3+1/6*z3*ln2^3+5/8*z3^2+z5*ln2-ln2* li5half+1/240*ln2^6-3*li6half-1/2*s6; Fill Stab6(-1,1,1,1,1,-1) =8/35*z2^3-li6half; Fill Stab6(-1,1,1,1,1,1) =-li6half; Fill Stab6(0,-1,-1,-1,-1,-1) =-33/16*z2*z3*ln2-5/12*z2*ln2^4+ 11/8*z2^2*ln2^2+20/7*z2^3-7/16*z3*ln2^3+41/32*z3^2-93/64*z5* ln2-3*ln2*li5half+1/360*ln2^6-16*li6half-4*s6; Fill Stab6(0,-1,-1,-1,-1,1) =-27/16*z2*z3*ln2-1/4*z2*ln2^4+93/ 80*z2^2*ln2^2+447/560*z2^3-7/16*z3*ln2^3+105/32*z3^2-1/80* ln2^6-9*li6half-7/4*s6; Fill Stab6(0,-1,-1,-1,0,-1) =-33/8*z2*z3*ln2-3/8*z2^2*ln2^2+7/ 24*z2^3+73/128*z3^2+5*s6; Fill Stab6(0,-1,-1,-1,0,1) =-3/16*z2*z3*ln2-1/3*z2*ln2^4+17/5* z2^2*ln2^2+5687/840*z2^3+55/8*z3^2+31/4*z5*ln2-16*ln2*li5half +1/15*ln2^6-48*li6half-21*s6; Fill Stab6(0,-1,-1,-1,1,-1) =-21/8*z2*z3*ln2-3/8*z2*ln2^4-3*z2 *li4half+279/80*z2^2*ln2^2+1501/560*z2^3-7/16*z3*ln2^3+243/64 *z3^2+3/2*ln2^2*li4half+1/24*ln2^6-15*li6half-15/2*s6; Fill Stab6(0,-1,-1,-1,1,1) =-19/48*z2*ln2^4-3/2*z2*li4half+251/ 80*z2^2*ln2^2+261/80*z2^3-7/16*z3*ln2^3+147/64*z3^2-465/64*z5 *ln2-ln2*li5half+3/2*ln2^2*li4half+11/240*ln2^6-18*li6half- 7*s6; Fill Stab6(0,-1,-1,0,-1,-1) =-15/16*z2*z3*ln2-7/12*z2*ln2^4-2* z2*li4half+171/40*z2^2*ln2^2+239/70*z2^3+649/128*z3^2+4*ln2^2 *li4half+2/15*ln2^6-24*li6half-13*s6; Fill Stab6(0,-1,-1,0,-1,1) =-15/16*z2*z3*ln2-1/3*z2*ln2^4-4*z2 *li4half+z2^2*ln2^2-46/35*z2^3-599/128*z3^2-1457/64*z5*ln2+ 16*ln2*li5half+4*ln2^2*li4half+1/15*ln2^6+24*li6half+13*s6; Fill Stab6(0,-1,-1,0,0,-1) =-9/8*z2*z3*ln2-1/12*z2*ln2^4-2*z2* li4half+1/2*z2^2*ln2^2+559/336*z2^3-15/8*z3^2-155/16*z5*ln2 +4*s6; Fill Stab6(0,-1,-1,0,0,1) =-9/8*z2*z3*ln2+1/6*z2*ln2^4+4*z2* li4half-z2^2*ln2^2-1279/1680*z2^3-53/64*z3^2+5*s6; Fill Stab6(0,-1,-1,0,1,-1) =-57/16*z2*z3*ln2+1/3*z2*ln2^4-151/ 40*z2^2*ln2^2-162/35*z2^3-11*z3^2-1271/64*z5*ln2+16*ln2* li5half-1/15*ln2^6+48*li6half+30*s6; Fill Stab6(0,-1,-1,0,1,1) =3/8*z2*z3*ln2+1/16*z2*ln2^4+3/2*z2* li4half-3/8*z2^2*ln2^2-117/112*z2^3+127/64*z3^2+3/2*s6; Fill Stab6(0,-1,-1,1,-1,-1) =13/48*z2*ln2^4+1/2*z2*li4half+63/40 *z2^2*ln2^2+143/140*z2^3+45/32*z3^2+1/2*ln2^2*li4half+1/120* ln2^6-9*li6half-15/4*s6; Fill Stab6(0,-1,-1,1,-1,1) =3/16*z2*z3*ln2+11/48*z2*ln2^4-1/2*z2 *li4half+13/16*z2^2*ln2^2+129/560*z2^3-93/16*z5*ln2+3*ln2* li5half+1/2*ln2^2*li4half-1/240*ln2^6; Fill Stab6(0,-1,-1,1,0,-1) =-3/16*z2*z3*ln2-11/48*z2*ln2^4-3/2 *z2*li4half+83/40*z2^2*ln2^2+761/210*z2^3+557/128*z3^2+155/64 *z5*ln2-8*ln2*li5half+1/30*ln2^6-24*li6half-23/2*s6; Fill Stab6(0,-1,-1,1,0,1) =-3/16*z2*z3*ln2+3/16*z2*ln2^4+9/2* z2*li4half-21/16*z2^2*ln2^2-613/840*z2^3-247/128*z3^2+21/4*s6; Fill Stab6(0,-1,-1,1,1,-1) =-21/16*z2*z3*ln2-1/12*z2*ln2^4-21/ 16*z2^2*ln2^2+18/35*z2^3-107/64*z3^2-155/32*z5*ln2+ln2* li5half-1/180*ln2^6+2*li6half+19/4*s6; Fill Stab6(0,-1,-1,1,1,1) =1/16*z2*ln2^4+3/2*z2*li4half-39/80* z2^2*ln2^2-2/35*z2^3+1/32*z3^2-1/240*ln2^6-3*li6half+9/4*s6; Fill Stab6(0,-1,0,-1,-1,-1) =39/8*z2*z3*ln2+5/12*z2*ln2^4+4*z2* li4half-39/20*z2^2*ln2^2-813/280*z2^3-173/64*z3^2-2*ln2^2* li4half-1/15*ln2^6+12*li6half+9/2*s6; Fill Stab6(0,-1,0,-1,-1,1) =1/4*z2*ln2^4+2*z2*li4half-39/40*z2^2 *ln2^2-233/280*z2^3-25/128*z3^2+403/64*z5*ln2-4*ln2*li5half -2*ln2^2*li4half-1/20*ln2^6; Fill Stab6(0,-1,0,-1,0,-1) =-109/560*z2^3; Fill Stab6(0,-1,0,-1,0,1) =21/4*z2*z3*ln2+1/4*z2*ln2^4+6*z2* li4half-3/2*z2^2*ln2^2-1003/560*z2^3-35/32*z3^2; Fill Stab6(0,-1,0,-1,1,-1) =-15/16*z2*z3*ln2-1/12*z2*ln2^4+19/ 40*z2^2*ln2^2+61/35*z2^3+113/64*z3^2+31/16*z5*ln2-4*ln2* li5half+1/60*ln2^6-12*li6half-9/2*s6; Fill Stab6(0,-1,0,-1,1,1) =21/16*z2*z3*ln2+1/16*z2*ln2^4+3/2*z2* li4half-3/8*z2^2*ln2^2-55/112*z2^3+45/128*z3^2; Fill Stab6(0,-1,0,0,-1,-1) =-27/8*z2*z3*ln2+25/24*z2^3-51/32* z3^2-155/32*z5*ln2+5*s6; Fill Stab6(0,-1,0,0,-1,1) =-21/8*z2*z3*ln2-1/8*z2*ln2^4-3*z2* li4half+3/4*z2^2*ln2^2+193/420*z2^3+179/64*z3^2; Fill Stab6(0,-1,0,0,0,-1) =-47/840*z2^3+3/4*z3^2; Fill Stab6(0,-1,0,0,0,1) =143/168*z2^3-33/16*z3^2-31/4*z5*ln2+ 4*s6; Fill Stab6(0,-1,0,0,1,-1) =27/8*z2*z3*ln2-127/336*z2^3+15/64* z3^2-5/2*s6; Fill Stab6(0,-1,0,0,1,1) =23/120*z2^3-23/32*z3^2-93/32*z5*ln2+ 3/2*s6; Fill Stab6(0,-1,0,1,-1,-1) =-11/8*z2*z3*ln2+19/20*z2^2*ln2^2+ 20/7*z2^3-7/12*z3*ln2^3+33/32*z3^2-31/32*z5*ln2-4*ln2*li5half +1/90*ln2^6-16*li6half-4*s6; Fill Stab6(0,-1,0,1,-1,1) =-91/16*z2*z3*ln2-1/6*z2*ln2^4-6*z2* li4half+79/40*z2^2*ln2^2+109/56*z2^3-7/12*z3*ln2^3+513/128* z3^2-1/180*ln2^6-4*li6half-s6; Fill Stab6(0,-1,0,1,0,-1) =-35/4*z2*z3*ln2-5/12*z2*ln2^4-10*z2 *li4half+5/2*z2^2*ln2^2+45/16*z2^3+63/16*z3^2; Fill Stab6(0,-1,0,1,0,1) =7/4*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2+37/80*z2^3-13/4*z3^2-31/4*z5*ln2+4* s6; Fill Stab6(0,-1,0,1,1,-1) =-41/16*z2*z3*ln2+1/16*z2*ln2^4-13/2 *z2*li4half+23/20*z2^2*ln2^2+51/80*z2^3-7/12*z3*ln2^3+83/128* z3^2-2*ln2^2*li4half-13/180*ln2^6+8*li6half+5/4*s6; Fill Stab6(0,-1,0,1,1,1) =7/4*z2*z3*ln2+1/3*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2+411/560*z2^3-7/12*z3*ln2^3-7/4*z3^2- 279/64*z5*ln2-4*ln2*li5half-2*ln2^2*li4half-1/18*ln2^6-4* li6half+9/4*s6; Fill Stab6(0,-1,1,-1,-1,-1) =69/16*z2*z3*ln2+11/16*z2*ln2^4+3*z2 *li4half-21/10*z2^2*ln2^2-92/35*z2^3-321/128*z3^2-3/2*ln2^2* li4half-11/240*ln2^6+12*li6half+9/2*s6; Fill Stab6(0,-1,1,-1,-1,1) =5/8*z2*ln2^4+3/2*z2*li4half-219/80* z2^2*ln2^2-491/140*z2^3-501/128*z3^2+279/64*z5*ln2+3*ln2* li5half-3/2*ln2^2*li4half-7/120*ln2^6+21*li6half+33/4*s6; Fill Stab6(0,-1,1,-1,0,-1) =5/24*z2*ln2^4+z2*li4half-39/20*z2^2* ln2^2-769/210*z2^3-569/128*z3^2-155/64*z5*ln2+8*ln2*li5half -1/30*ln2^6+24*li6half+21/2*s6; Fill Stab6(0,-1,1,-1,0,1) =63/16*z2*z3*ln2+1/24*z2*ln2^4+z2* li4half-1/16*z2^2*ln2^2-241/336*z2^3+91/128*z3^2-13/4*s6; Fill Stab6(0,-1,1,-1,1,-1) =3/16*z2*z3*ln2-1/48*z2*ln2^4-123/80* z2^2*ln2^2-8/5*z2^3-211/128*z3^2+31/64*z5*ln2+ln2*li5half+1/ 144*ln2^6+11*li6half+17/4*s6; Fill Stab6(0,-1,1,-1,1,1) =3/2*z2*z3*ln2+1/16*z2*ln2^4-27/80* z2^2*ln2^2-247/280*z2^3-57/128*z3^2+1/120*ln2^6+6*li6half+3/ 4*s6; Fill Stab6(0,-1,1,0,-1,-1) =25/128*z3^2-93/64*z5*ln2; Fill Stab6(0,-1,1,0,-1,1) =9/80*z2^3+25/128*z3^2; Fill Stab6(0,-1,1,0,0,-1) =21/8*z2*z3*ln2+1/8*z2*ln2^4+3*z2* li4half-3/4*z2^2*ln2^2-37/42*z2^3-3/8*z3^2; Fill Stab6(0,-1,1,0,0,1) =-493/1680*z2^3+7/64*z3^2+31/16*z5* ln2-s6; Fill Stab6(0,-1,1,0,1,-1) =63/16*z2*z3*ln2+3/16*z2*ln2^4+9/2*z2* li4half-9/8*z2^2*ln2^2-771/560*z2^3-151/128*z3^2+3/4*s6; Fill Stab6(0,-1,1,0,1,1) =-75/112*z2^3+65/128*z3^2+465/64*z5* ln2-15/4*s6; Fill Stab6(0,-1,1,1,-1,-1) =-7/16*z2*z3*ln2-13/48*z2*ln2^4+11/ 16*z2^2*ln2^2+481/280*z2^3-7/48*z3*ln2^3+177/128*z3^2-31/32* z5*ln2-3*ln2*li5half+7/720*ln2^6-11*li6half-13/4*s6; Fill Stab6(0,-1,1,1,-1,1) =-31/16*z2*z3*ln2-1/6*z2*ln2^4-3/2* z2*li4half+17/20*z2^2*ln2^2+293/280*z2^3-7/48*z3*ln2^3+181/ 128*z3^2-1/180*ln2^6-4*li6half-s6; Fill Stab6(0,-1,1,1,0,-1) =-35/16*z2*z3*ln2-5/48*z2*ln2^4-5/2* z2*li4half+5/8*z2^2*ln2^2+17/21*z2^3+131/128*z3^2; Fill Stab6(0,-1,1,1,0,1) =7/16*z2*z3*ln2+1/48*z2*ln2^4+1/2*z2* li4half-1/8*z2^2*ln2^2+13/60*z2^3-17/16*z3^2-155/32*z5*ln2+ 5/2*s6; Fill Stab6(0,-1,1,1,1,-1) =7/16*z2*z3*ln2+1/8*z2*ln2^4-1/2*z2* li4half+1/10*z2^2*ln2^2-6/35*z2^3-7/48*z3*ln2^3-17/128*z3^2 -1/2*ln2^2*li4half-13/720*ln2^6+2*li6half+1/2*s6; Fill Stab6(0,-1,1,1,1,1) =7/16*z2*z3*ln2+1/12*z2*ln2^4+1/2*z2* li4half-1/8*z2^2*ln2^2-7/48*z3*ln2^3-49/128*z3^2-ln2*li5half -1/2*ln2^2*li4half-1/72*ln2^6-li6half; Fill Stab6(0,0,-1,-1,-1,-1) =3/2*z2*z3*ln2+1/4*z2*ln2^4-z2* li4half+29/40*z2^2*ln2^2+503/1680*z2^3+15/16*z3^2-ln2^2* li4half-2/45*ln2^6-2*li6half-11/4*s6; Fill Stab6(0,0,-1,-1,-1,1) =13/48*z2*ln2^4-1/2*z2*li4half-1/4* z2^2*ln2^2-1151/840*z2^3-1/32*z3^2+279/64*z5*ln2+2*ln2* li5half-ln2^2*li4half-1/20*ln2^6+6*li6half-3/4*s6; Fill Stab6(0,0,-1,-1,0,-1) =-1/24*z2*ln2^4-z2*li4half+1/4*z2^2 *ln2^2-591/560*z2^3+9/4*z3^2+155/16*z5*ln2-6*s6; Fill Stab6(0,0,-1,-1,0,1) =-1/4*z2*ln2^4-6*z2*li4half+3/2*z2^2 *ln2^2+327/280*z2^3+11/4*z3^2-5*s6; Fill Stab6(0,0,-1,-1,1,-1) =39/16*z2*z3*ln2+z2*li4half-31/80* z2^2*ln2^2-209/336*z2^3+173/64*z3^2+31/4*z5*ln2-2*ln2*li5half +1/120*ln2^6-6*li6half-31/4*s6; Fill Stab6(0,0,-1,-1,1,1) =-1/12*z2*ln2^4-3*z2*li4half+4/5* z2^2*ln2^2+83/60*z2^3+17/64*z3^2-1/360*ln2^6-2*li6half-3*s6; Fill Stab6(0,0,-1,0,-1,-1) =27/8*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2-403/240*z2^3+51/32*z3^2+155/32*z5*ln2 -5*s6; Fill Stab6(0,0,-1,0,-1,1) =643/840*z2^3-109/64*z3^2; Fill Stab6(0,0,-1,0,0,-1) =4/35*z2^3+9/32*z3^2; Fill Stab6(0,0,-1,0,0,1) =-439/280*z2^3+81/32*z3^2+93/8*z5*ln2 -6*s6; Fill Stab6(0,0,-1,0,1,-1) =15/8*z2*z3*ln2+1/6*z2*ln2^4+4*z2* li4half-z2^2*ln2^2-11/12*z2^3-99/64*z3^2+5/2*s6; Fill Stab6(0,0,-1,0,1,1) =-683/840*z2^3+59/64*z3^2+217/32*z5* ln2-7/2*s6; Fill Stab6(0,0,-1,1,-1,-1) =11/16*z2*z3*ln2-3/16*z2*ln2^4+1/2*z2 *li4half-97/80*z2^2*ln2^2-121/168*z2^3+7/24*z3*ln2^3+9/64* z3^2+155/64*z5*ln2-2*ln2*li5half+7/360*ln2^6+2*li6half+1/4* s6; Fill Stab6(0,0,-1,1,-1,1) =7/8*z2*z3*ln2-1/24*z2*ln2^4+2*z2* li4half-7/5*z2^2*ln2^2-137/210*z2^3+7/24*z3*ln2^3-193/64*z3^2 +1/120*ln2^6+6*li6half+4*s6; Fill Stab6(0,0,-1,1,0,-1) =7/4*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2-9/56*z2^3-21/16*z3^2; Fill Stab6(0,0,-1,1,0,1) =-7/8*z2*z3*ln2-1/24*z2*ln2^4-z2* li4half+1/4*z2^2*ln2^2-83/280*z2^3+5/4*z3^2+31/16*z5*ln2-s6; Fill Stab6(0,0,-1,1,1,-1) =5/8*z2*z3*ln2-1/24*z2*ln2^4+2*z2* li4half+7/20*z2^2*ln2^2+337/840*z2^3+7/24*z3*ln2^3+9/64*z3^2 +ln2^2*li4half+1/30*ln2^6-6*li6half-3/2*s6; Fill Stab6(0,0,-1,1,1,1) =-7/8*z2*z3*ln2-1/6*z2*ln2^4-z2* li4half+1/4*z2^2*ln2^2-85/168*z2^3+7/24*z3*ln2^3+41/64*z3^2 +31/32*z5*ln2+2*ln2*li5half+ln2^2*li4half+1/36*ln2^6+2* li6half-1/2*s6; Fill Stab6(0,0,0,-1,-1,-1) =-9/8*z2*z3*ln2-3/4*z2^2*ln2^2+1381/ 1680*z2^3-57/32*z3^2-155/32*z5*ln2+4*s6; Fill Stab6(0,0,0,-1,-1,1) =1/12*z2*ln2^4+2*z2*li4half-7/8*z2^2* ln2^2-59/420*z2^3-z3^2+5/2*s6; Fill Stab6(0,0,0,-1,0,-1) =193/420*z2^3-3/4*z3^2; Fill Stab6(0,0,0,-1,0,1) =743/840*z2^3-9/4*z3^2-31/4*z5*ln2+4* s6; Fill Stab6(0,0,0,-1,1,-1) =-3/2*z2*z3*ln2-1/12*z2*ln2^4-2*z2* li4half+7/8*z2^2*ln2^2+115/168*z2^3+3/8*z3^2; Fill Stab6(0,0,0,-1,1,1) =113/840*z2^3-5/8*z3^2-93/32*z5*ln2+3/ 2*s6; Fill Stab6(0,0,0,0,-1,-1) =s6; Fill Stab6(0,0,0,0,-1,1) =-11/20*z2^3+3/4*z3^2+31/16*z5*ln2- s6; Fill Stab6(0,0,0,0,0,-1) =-31/140*z2^3; Fill Stab6(0,0,0,0,0,1) =8/35*z2^3; Fill Stab6(0,0,0,0,1,-1) =7/40*z2^3-9/32*z3^2-31/16*z5*ln2; Fill Stab6(0,0,0,0,1,1) =2/5*z2^3-1/2*z3^2; Fill Stab6(0,0,0,1,-1,-1) =9/8*z2*z3*ln2+3/4*z2^2*ln2^2-11/42* z2^3+53/64*z3^2-3/2*s6; Fill Stab6(0,0,0,1,-1,1) =-1/24*z2*ln2^4-z2*li4half+5/8*z2^2* ln2^2-607/840*z2^3+15/8*z3^2+155/32*z5*ln2-4*s6; Fill Stab6(0,0,0,1,0,-1) =-1069/840*z2^3+33/16*z3^2+31/4*z5* ln2-4*s6; Fill Stab6(0,0,0,1,0,1) =-8/105*z2^3+z3^2; Fill Stab6(0,0,0,1,1,-1) =3/2*z2*z3*ln2+1/24*z2*ln2^4+z2*li4half -5/8*z2^2*ln2^2-149/168*z2^3+49/64*z3^2+93/32*z5*ln2-5/2*s6; Fill Stab6(0,0,0,1,1,1) =89/210*z2^3-1/2*z3^2; Fill Stab6(0,0,1,-1,-1,-1) =-19/8*z2*z3*ln2-1/6*z2*ln2^4-19/40 *z2^2*ln2^2+937/840*z2^3-7/24*z3*ln2^3-35/16*z3^2-279/64*z5* ln2-2*ln2*li5half+1/60*ln2^6+5*s6; Fill Stab6(0,0,1,-1,-1,1) =-7/8*z2*z3*ln2+1/24*z2*ln2^4+3*z2* li4half-83/80*z2^2*ln2^2-317/210*z2^3-7/24*z3*ln2^3+9/16*z3^2 +1/180*ln2^6+4*li6half+21/4*s6; Fill Stab6(0,0,1,-1,0,-1) =-7/4*z2*z3*ln2+1/6*z2*ln2^4+4*z2* li4half-z2^2*ln2^2-183/280*z2^3-29/64*z3^2+5*s6; Fill Stab6(0,0,1,-1,0,1) =7/8*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2+27/35*z2^3-4*z3^2-155/16*z5*ln2+6*s6; Fill Stab6(0,0,1,-1,1,-1) =-25/16*z2*z3*ln2-1/8*z2*ln2^4-z2* li4half+137/80*z2^2*ln2^2+2363/1680*z2^3-7/24*z3*ln2^3+223/ 128*z3^2+ln2^2*li4half+11/360*ln2^6-8*li6half-3*s6; Fill Stab6(0,0,1,-1,1,1) =7/8*z2*z3*ln2-1/16*z2*ln2^4+1/2*z2* li4half+39/80*z2^2*ln2^2+677/1680*z2^3-7/24*z3*ln2^3-251/128* z3^2-31/4*z5*ln2+2*ln2*li5half+ln2^2*li4half+1/40*ln2^6+5/2 *s6; Fill Stab6(0,0,1,0,-1,-1) =-3/4*z2*z3*ln2-1/6*z2*ln2^4-4*z2* li4half+z2^2*ln2^2+13/12*z2^3+23/32*z3^2-3/2*s6; Fill Stab6(0,0,1,0,-1,1) =677/1680*z2^3-85/64*z3^2-155/32*z5*ln2 +5/2*s6; Fill Stab6(0,0,1,0,0,-1) =377/280*z2^3-105/32*z3^2-93/8*z5*ln2 +6*s6; Fill Stab6(0,0,1,0,0,1) =4/35*z2^3+1/2*z3^2; Fill Stab6(0,0,1,0,1,-1) =-9/2*z2*z3*ln2-1/12*z2*ln2^4-2*z2* li4half+1/2*z2^2*ln2^2+589/336*z2^3-41/32*z3^2-217/32*z5*ln2 +5*s6; Fill Stab6(0,0,1,0,1,1) =-143/210*z2^3+3*z3^2; Fill Stab6(0,0,1,1,-1,-1) =3/16*z2*z3*ln2+1/6*z2*ln2^4-2*z2* li4half+37/40*z2^2*ln2^2+67/120*z2^3+67/128*z3^2-ln2^2* li4half-1/24*ln2^6-3/2*s6; Fill Stab6(0,0,1,1,-1,1) =1/4*z2*ln2^4-17/40*z2^2*ln2^2-205/168* z2^3-183/128*z3^2-155/64*z5*ln2+2*ln2*li5half-ln2^2*li4half -17/360*ln2^6+8*li6half+4*s6; Fill Stab6(0,0,1,1,0,-1) =-27/560*z2^3-31/64*z3^2-31/16*z5*ln2 +s6; Fill Stab6(0,0,1,1,0,1) =11/35*z2^3; Fill Stab6(0,0,1,1,1,-1) =-3/2*z2*z3*ln2-5/48*z2*ln2^4-1/2*z2* li4half-1/16*z2^2*ln2^2+107/105*z2^3+7/32*z3^2-31/32*z5*ln2 -2*ln2*li5half+1/90*ln2^6-4*li6half-1/4*s6; Fill Stab6(0,0,1,1,1,1) =2/105*z2^3+z3^2; Fill Stab6(0,1,-1,-1,-1,-1) =3/4*z2*z3*ln2+13/24*z2*ln2^4-3/2*z2 *li4half-z2^2*ln2^2-659/560*z2^3-121/64*z3^2-3/2*ln2^2* li4half-2/45*ln2^6+13*li6half+19/4*s6; Fill Stab6(0,1,-1,-1,-1,1) =3/8*z2*z3*ln2+2/3*z2*ln2^4+3/2*z2* li4half-221/80*z2^2*ln2^2-134/35*z2^3-247/64*z3^2+93/64*z5* ln2+3*ln2*li5half-3/2*ln2^2*li4half-41/720*ln2^6+22*li6half +10*s6; Fill Stab6(0,1,-1,-1,0,-1) =3/2*z2*z3*ln2+19/48*z2*ln2^4+3/2*z2* li4half-151/40*z2^2*ln2^2-2533/336*z2^3-8*z3^2-31/4*z5*ln2+ 16*ln2*li5half-1/15*ln2^6+48*li6half+21*s6; Fill Stab6(0,1,-1,-1,0,1) =3/2*z2*z3*ln2-1/8*z2*ln2^4-3*z2* li4half+9/8*z2^2*ln2^2+59/84*z2^3+7/4*z3^2-5*s6; Fill Stab6(0,1,-1,-1,1,-1) =63/16*z2*z3*ln2+5/24*z2*ln2^4+9/2*z2 *li4half-43/16*z2^2*ln2^2-149/35*z2^3-39/64*z3^2+465/64*z5* ln2+ln2*li5half+1/120*ln2^6+12*li6half+3/4*s6; Fill Stab6(0,1,-1,-1,1,1) =21/16*z2*z3*ln2+5/48*z2*ln2^4-29/80* z2^2*ln2^2-6/35*z2^3-137/64*z3^2+7/720*ln2^6+7*li6half+3/4* s6; Fill Stab6(0,1,-1,0,-1,-1) =39/8*z2*z3*ln2-1/12*z2*ln2^4+6*z2* li4half+91/40*z2^2*ln2^2+177/70*z2^3+347/32*z3^2+1457/64*z5* ln2-16*ln2*li5half+1/15*ln2^6-48*li6half-30*s6; Fill Stab6(0,1,-1,0,-1,1) =15/16*z2*z3*ln2+303/280*z2^3-137/64* z3^2-3/2*s6; Fill Stab6(0,1,-1,0,0,-1) =9/8*z2*z3*ln2-1/6*z2*ln2^4-4*z2* li4half+z2^2*ln2^2+139/120*z2^3+41/32*z3^2-5*s6; Fill Stab6(0,1,-1,0,0,1) =9/8*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-1/2*z2^2*ln2^2-1811/840*z2^3+57/32*z3^2+155/16*z5*ln2 -4*s6; Fill Stab6(0,1,-1,0,1,-1) =-3/8*z2*z3*ln2+1/3*z2*ln2^4-4*z2* li4half-111/40*z2^2*ln2^2-47/28*z2^3-137/32*z3^2-4*ln2^2* li4half-2/15*ln2^6+24*li6half+23/2*s6; Fill Stab6(0,1,-1,0,1,1) =-3/8*z2*z3*ln2+13/48*z2*ln2^4+5/2*z2 *li4half-5/8*z2^2*ln2^2+919/560*z2^3+139/32*z3^2+1271/64*z5* ln2-16*ln2*li5half-4*ln2^2*li4half-1/15*ln2^6-24*li6half-23/ 2*s6; Fill Stab6(0,1,-1,1,-1,-1) =21/16*z2*z3*ln2-5/16*z2*ln2^4-3/8* z2^2*ln2^2-11/80*z2^3+7/16*z3*ln2^3+165/64*z3^2+93/16*z5*ln2 -3*ln2*li5half+1/60*ln2^6-6*li6half-6*s6; Fill Stab6(0,1,-1,1,-1,1) =9/8*z2*z3*ln2-7/48*z2*ln2^4-47/80* z2^2*ln2^2+113/140*z2^3+7/16*z3*ln2^3-37/16*z3^2+1/720*ln2^6 +li6half-1/4*s6; Fill Stab6(0,1,-1,1,0,-1) =45/16*z2*z3*ln2+1/12*z2*ln2^4+2*z2* li4half-5/16*z2^2*ln2^2+1/105*z2^3-191/128*z3^2-7/4*s6; Fill Stab6(0,1,-1,1,0,1) =-9/8*z2*z3*ln2+1/16*z2*ln2^4-5/2*z2* li4half-43/40*z2^2*ln2^2-5777/1680*z2^3-133/64*z3^2-155/64*z5 *ln2+8*ln2*li5half-1/30*ln2^6+24*li6half+9*s6; Fill Stab6(0,1,-1,1,1,-1) =1/12*z2*ln2^4-1/2*z2*li4half-77/80* z2^2*ln2^2-45/112*z2^3+7/16*z3*ln2^3-31/16*z3^2-1/2*ln2^2* li4half-1/90*ln2^6+7*li6half+4*s6; Fill Stab6(0,1,-1,1,1,1) =-21/16*z2*z3*ln2-1/48*z2*ln2^4-z2* li4half-13/16*z2^2*ln2^2-559/560*z2^3+7/16*z3*ln2^3+1/2*z3^2 +155/32*z5*ln2-ln2*li5half-1/2*ln2^2*li4half-1/144*ln2^6+4* li6half+s6; Fill Stab6(0,1,0,-1,-1,-1) =-25/8*z2*z3*ln2-1/4*z2*ln2^4-6*z2* li4half-53/40*z2^2*ln2^2-1/14*z2^3+7/12*z3*ln2^3-69/32*z3^2 -403/64*z5*ln2+4*ln2*li5half-1/90*ln2^6+16*li6half+8*s6; Fill Stab6(0,1,0,-1,-1,1) =7/4*z2*z3*ln2-1/12*z2*ln2^4-113/80* z2^2*ln2^2+101/280*z2^3+7/12*z3*ln2^3-99/32*z3^2+1/180*ln2^6 +4*li6half+7/4*s6; Fill Stab6(0,1,0,-1,0,-1) =7/2*z2*z3*ln2+1/6*z2*ln2^4+4*z2* li4half-z2^2*ln2^2-41/140*z2^3-91/32*z3^2; Fill Stab6(0,1,0,-1,0,1) =-7*z2*z3*ln2-1/3*z2*ln2^4-8*z2* li4half+2*z2^2*ln2^2+73/35*z2^3+35/16*z3^2; Fill Stab6(0,1,0,-1,1,-1) =-13/16*z2*z3*ln2-1/4*z2*ln2^4+2*z2* li4half+73/80*z2^2*ln2^2+67/70*z2^3+7/12*z3*ln2^3+7/128*z3^2 +2*ln2^2*li4half+13/180*ln2^6-8*li6half-5/4*s6; Fill Stab6(0,1,0,-1,1,1) =-49/16*z2*z3*ln2-19/48*z2*ln2^4-7/2* z2*li4half+7/8*z2^2*ln2^2-69/560*z2^3+7/12*z3*ln2^3+137/128* z3^2-31/16*z5*ln2+4*ln2*li5half+2*ln2^2*li4half+1/18*ln2^6+ 4*li6half+s6; Fill Stab6(0,1,0,0,-1,-1) =-15/8*z2*z3*ln2+389/840*z2^3-59/64* z3^2+7/2*s6; Fill Stab6(0,1,0,0,-1,1) =21/8*z2*z3*ln2+1/8*z2*ln2^4+3*z2* li4half-3/4*z2^2*ln2^2-253/120*z2^3+71/64*z3^2+155/32*z5*ln2 -5/2*s6; Fill Stab6(0,1,0,0,0,-1) =-1223/840*z2^3+9/4*z3^2+31/4*z5*ln2 -4*s6; Fill Stab6(0,1,0,0,0,1) =74/105*z2^3-z3^2; Fill Stab6(0,1,0,0,1,-1) =15/8*z2*z3*ln2-295/336*z2^3+55/32*z3^2 +93/32*z5*ln2-5*s6; Fill Stab6(0,1,0,0,1,1) =29/21*z2^3-3*z3^2; Fill Stab6(0,1,0,1,-1,-1) =-3/8*z2*z3*ln2-1/6*z2*ln2^4+2*z2* li4half+93/40*z2^2*ln2^2+661/560*z2^3+119/64*z3^2+2*ln2^2* li4half+1/15*ln2^6-12*li6half-19/4*s6; Fill Stab6(0,1,0,1,-1,1) =63/16*z2*z3*ln2+4*z2*li4half+33/80* z2^2*ln2^2-1453/560*z2^3+5/4*z3^2+31/32*z5*ln2+4*ln2*li5half +2*ln2^2*li4half+1/20*ln2^6-4*s6; Fill Stab6(0,1,0,1,0,-1) =21/4*z2*z3*ln2+1/4*z2*ln2^4+6*z2* li4half-3/2*z2^2*ln2^2-1943/560*z2^3+17/16*z3^2+31/4*z5*ln2 -4*s6; Fill Stab6(0,1,0,1,0,1) =31/70*z2^3; Fill Stab6(0,1,0,1,1,-1) =69/16*z2*z3*ln2+13/48*z2*ln2^4+9/2*z2* li4half-203/80*z2^2*ln2^2-149/35*z2^3-41/64*z3^2+279/64*z5* ln2+4*ln2*li5half-1/60*ln2^6+12*li6half+3/4*s6; Fill Stab6(0,1,0,1,1,1) =8/7*z2^3-2*z3^2; Fill Stab6(0,1,1,-1,-1,-1) =-31/8*z2*z3*ln2-11/16*z2*ln2^4-9/2 *z2*li4half+6/5*z2^2*ln2^2+23/7*z2^3+7/48*z3*ln2^3+25/32*z3^2 -279/64*z5*ln2-3*ln2*li5half+1/80*ln2^6-9*li6half-3/2*s6; Fill Stab6(0,1,1,-1,-1,1) =7/16*z2*z3*ln2-1/3*z2*ln2^4-11/80* z2^2*ln2^2+6/35*z2^3+7/48*z3*ln2^3+137/64*z3^2-1/360*ln2^6- 2*li6half-3/4*s6; Fill Stab6(0,1,1,-1,0,-1) =7/8*z2*z3*ln2+1/24*z2*ln2^4+z2* li4half-7/16*z2^2*ln2^2-47/420*z2^3+129/128*z3^2-1/4*s6; Fill Stab6(0,1,1,-1,0,1) =-35/8*z2*z3*ln2-5/16*z2*ln2^4-7/2*z2 *li4half+103/40*z2^2*ln2^2+7837/1680*z2^3+177/64*z3^2+155/64* z5*ln2-8*ln2*li5half+1/30*ln2^6-24*li6half-8*s6; Fill Stab6(0,1,1,-1,1,-1) =-5/8*z2*z3*ln2-13/48*z2*ln2^4+3/2* z2*li4half+17/16*z2^2*ln2^2+55/56*z2^3+7/48*z3*ln2^3+37/64* z3^2+3/2*ln2^2*li4half+37/720*ln2^6-8*li6half-5/4*s6; Fill Stab6(0,1,1,-1,1,1) =-31/16*z2*z3*ln2-23/48*z2*ln2^4-3/2* z2*li4half+147/80*z2^2*ln2^2+25/14*z2^3+7/48*z3*ln2^3+81/64* z3^2-31/64*z5*ln2-ln2*li5half+3/2*ln2^2*li4half+1/18*ln2^6- 11*li6half-17/4*s6; Fill Stab6(0,1,1,0,-1,-1) =-21/16*z2*z3*ln2+75/112*z2^3-225/ 128*z3^2+15/4*s6; Fill Stab6(0,1,1,0,-1,1) =-15/28*z2^3-9/128*z3^2+93/64*z5*ln2 -3/4*s6; Fill Stab6(0,1,1,0,0,-1) =-21/8*z2*z3*ln2-1/8*z2*ln2^4-3*z2* li4half+3/4*z2^2*ln2^2+769/840*z2^3-17/32*z3^2-31/16*z5*ln2 +s6; Fill Stab6(0,1,1,0,0,1) =17/42*z2^3+1/2*z3^2; Fill Stab6(0,1,1,0,1,-1) =-21/8*z2*z3*ln2-3/16*z2*ln2^4-9/2*z2 *li4half+9/8*z2^2*ln2^2+9/5*z2^3+15/32*z3^2-465/64*z5*ln2; Fill Stab6(0,1,1,0,1,1) =2*z3^2; Fill Stab6(0,1,1,1,-1,-1) =13/48*z2*ln2^4+1/2*z2*li4half+27/16* z2^2*ln2^2+44/35*z2^3-1/32*z3^2+1/2*ln2^2*li4half+1/80*ln2^6 -6*li6half-9/4*s6; Fill Stab6(0,1,1,1,-1,1) =3/2*z2*z3*ln2+7/24*z2*ln2^4+z2*li4half +11/20*z2^2*ln2^2-71/35*z2^3+3/4*z3^2+31/32*z5*ln2+3*ln2* li5half+1/2*ln2^2*li4half+3*li6half-2*s6; Fill Stab6(0,1,1,1,0,-1) =21/16*z2*z3*ln2+1/16*z2*ln2^4+3/2*z2* li4half-3/8*z2^2*ln2^2-26/15*z2^3+45/64*z3^2+155/32*z5*ln2- 5/2*s6; Fill Stab6(0,1,1,1,0,1) =118/105*z2^3-z3^2; Fill Stab6(0,1,1,1,1,-1) =-1/12*z2*ln2^4-6/5*z2^2*ln2^2-8/7* z2^3+ln2*li5half-1/720*ln2^6+5*li6half; Fill Stab6(0,1,1,1,1,1) =8/7*z2^3; Fill Stab6(1,-1,-1,-1,-1,-1) =-9/8*z2*z3*ln2-1/8*z2*z3*Sinf-1/ 12*z2*ln2^3*Sinf-1/48*z2*ln2^4-9/40*z2^2*ln2*Sinf+3/8*z2^2* ln2^2+34/35*z2^3-1/8*z3*ln2^2*Sinf-5/12*z3*ln2^3-27/64*z3^2 -2*z5*ln2-3/16*z5*Sinf-1/120*ln2^5*Sinf-1/90*ln2^6-3* li6half+3/4*s6; Fill Stab6(1,-1,-1,-1,-1,1) =-9/8*z2*z3*ln2-1/8*z2*z3*Sinf-1/ 12*z2*ln2^3*Sinf-1/48*z2*ln2^4-9/40*z2^2*ln2*Sinf+3/8*z2^2* ln2^2-6/35*z2^3-1/8*z3*ln2^2*Sinf-5/12*z3*ln2^3+101/64*z3^2 +29/16*z5*Sinf-1/120*ln2^5*Sinf-1/90*ln2^6-3*li6half+3/4*s6; Fill Stab6(1,-1,-1,-1,0,-1) =-5/2*z2*z3*ln2-3/4*z2*z3*Sinf+1/ 12*z2*ln2^3*Sinf+1/16*z2*ln2^4+3/8*z2^2*ln2*Sinf+13/20*z2^2* ln2^2+241/280*z2^3-1/2*z3*ln2^2*Sinf-1/3*z3*ln2^3+35/16*z3^2 +29/64*z5*Sinf-1/40*ln2^5*Sinf-1/80*ln2^6+3*Sinf*li5half-9* li6half; Fill Stab6(1,-1,-1,-1,0,1) =1/2*z2*z3*ln2-3/8*z2*z3*Sinf+1/12*z2 *ln2^3*Sinf-1/48*z2*ln2^4+3/5*z2^2*ln2*Sinf+83/80*z2^2*ln2^2+ 859/560*z2^3-1/2*z3*ln2^2*Sinf-1/3*z3*ln2^3+55/64*z3^2-93/64* z5*ln2-z5*Sinf-3*ln2*li5half+1/72*ln2^6-8*li6half-15/4*s6; Fill Stab6(1,-1,-1,-1,1,-1) =-7/16*z2*z3*ln2-23/16*z2*z3*Sinf+ 5/12*z2*ln2^3*Sinf+7/24*z2*ln2^4+19/40*z2^2*ln2*Sinf+43/40*z2^2 *ln2^2-29/60*z2^3-23/16*z3*ln2^2*Sinf-31/24*z3*ln2^3+177/128* z3^2+375/64*z5*Sinf-3*ln2*Sinf*li4half-3/2*ln2^2*li4half-13/ 120*ln2^5*Sinf-5/72*ln2^6-3*Sinf*li5half; Fill Stab6(1,-1,-1,-1,1,1) =25/16*z2*z3*ln2+9/16*z2*z3*Sinf+5/12 *z2*ln2^3*Sinf+7/24*z2*ln2^4+19/40*z2^2*ln2*Sinf+43/40*z2^2* ln2^2+29/60*z2^3-23/16*z3*ln2^2*Sinf-31/24*z3*ln2^3-79/128* z3^2-11/2*z5*ln2+23/64*z5*Sinf-3*ln2*Sinf*li4half-3/2*ln2^2* li4half-13/120*ln2^5*Sinf-5/72*ln2^6-3*Sinf*li5half; Fill Stab6(1,-1,-1,0,-1,-1) =z2*z3*ln2-13/8*z2*z3*Sinf+5/6*z2* ln2^3*Sinf+5/16*z2*ln2^4+3/2*z2*li4half-41/40*z2^2*ln2*Sinf- 91/80*z2^2*ln2^2-261/80*z2^3-13/8*z3*ln2^2*Sinf-13/12*z3*ln2^3 -7/4*z3^2+845/64*z5*Sinf-4*ln2*Sinf*li4half-1/2*ln2^2*li4half -3/40*ln2^5*Sinf+1/240*ln2^6-11*Sinf*li5half+18*li6half+7* s6; Fill Stab6(1,-1,-1,0,-1,1) =z2*z3*ln2+z2*z3*Sinf+7/12*z2*ln2^3* Sinf+1/4*z2*ln2^4-3/2*z2*li4half+1/40*z2^2*ln2*Sinf+29/80* z2^2*ln2^2-493/560*z2^3-13/8*z3*ln2^2*Sinf-13/12*z3*ln2^3-13/ 4*z3^2-93/8*z5*ln2+101/64*z5*Sinf-4*ln2*Sinf*li4half+6*ln2* li5half-1/2*ln2^2*li4half-1/8*ln2^5*Sinf-1/20*ln2^6-5*Sinf* li5half+15*li6half+15/2*s6; Fill Stab6(1,-1,-1,0,0,-1) =-3/8*z2*z3*ln2+1/8*z2*z3*Sinf-5/48 *z2*ln2^4-3/2*z2*li4half+19/40*z2^2*ln2*Sinf+49/40*z2^2*ln2^2 +1091/560*z2^3-3/8*z3*ln2^2*Sinf-1/4*z3*ln2^3+25/64*z3^2- 279/64*z5*ln2-15/8*z5*Sinf-2*ln2*li5half+1/120*ln2^6-6* li6half-7/4*s6; Fill Stab6(1,-1,-1,0,0,1) =-3/8*z2*z3*ln2-11/8*z2*z3*Sinf+1/6* z2*ln2^3*Sinf+5/24*z2*ln2^4+3*z2*li4half+1/5*z2^2*ln2*Sinf-3/ 5*z2^2*ln2^2-199/280*z2^3-3/8*z3*ln2^2*Sinf-1/4*z3*ln2^3+55/ 64*z3^2+159/64*z5*Sinf-1/60*ln2^5*Sinf-1/180*ln2^6+2*Sinf* li5half-4*li6half+9/4*s6; Fill Stab6(1,-1,-1,0,1,-1) =-5/2*z2*z3*ln2+1/8*z2*z3*Sinf-1/3* z2*ln2^3*Sinf-1/24*z2*ln2^4+47/40*z2^2*ln2*Sinf+29/20*z2^2* ln2^2+86/35*z2^3+1/8*z3*ln2^2*Sinf+1/12*z3*ln2^3+25/64*z3^2 -93/16*z5*ln2-61/8*z5*Sinf+ln2*Sinf*li4half+4*ln2*li5half+1/ 2*ln2^2*li4half-1/40*ln2^5*Sinf-7/240*ln2^6+8*Sinf*li5half-12 *li6half-3/4*s6; Fill Stab6(1,-1,-1,0,1,1) =1/8*z2*z3*ln2+1/8*z2*z3*Sinf+1/12*z2* ln2^3*Sinf+1/48*z2*ln2^4+9/40*z2^2*ln2*Sinf-3/8*z2^2*ln2^2+6/ 35*z2^3+1/8*z3*ln2^2*Sinf+1/12*z3*ln2^3+123/64*z3^2-29/16*z5* Sinf+ln2*Sinf*li4half+1/2*ln2^2*li4half+1/120*ln2^5*Sinf+1/90 *ln2^6+4*Sinf*li5half-7*li6half-3/4*s6; Fill Stab6(1,-1,-1,1,-1,-1) =-7/16*z2*z3*ln2-7/16*z2*z3*Sinf+1/ 6*z2*ln2^3*Sinf+5/48*z2*ln2^4+6/5*z2^2*ln2*Sinf+6/5*z2^2*ln2^2 +27/35*z2^3-7/16*z3*ln2^2*Sinf-7/24*z3*ln2^3+229/128*z3^2- 81/64*z5*Sinf-1/30*ln2^5*Sinf-7/360*ln2^6+3*Sinf*li5half-9* li6half-15/4*s6; Fill Stab6(1,-1,-1,1,-1,1) =9/16*z2*z3*ln2+9/16*z2*z3*Sinf+1/6* z2*ln2^3*Sinf+5/48*z2*ln2^4+6/5*z2^2*ln2*Sinf+6/5*z2^2*ln2^2+ 13/7*z2^3-7/16*z3*ln2^2*Sinf-7/24*z3*ln2^3+165/128*z3^2-9/2* z5*ln2-369/64*z5*Sinf-1/30*ln2^5*Sinf-7/360*ln2^6+3*Sinf* li5half-9*li6half-15/4*s6; Fill Stab6(1,-1,-1,1,0,-1) =-1/16*z2*z3*ln2+3/8*z2*z3*Sinf-1/ 12*z2*ln2^3*Sinf-3/16*z2*ln2^4-3/2*z2*li4half+3/5*z2^2*ln2*Sinf +113/80*z2^2*ln2^2+86/35*z2^3-1/16*z3*ln2^2*Sinf-1/24*z3* ln2^3+97/64*z3^2-279/64*z5*ln2-125/32*z5*Sinf+ln2*Sinf* li4half-3*ln2*li5half+1/2*ln2^2*li4half+1/30*ln2^5*Sinf+1/30* ln2^6+Sinf*li5half-9*li6half-15/4*s6; Fill Stab6(1,-1,-1,1,0,1) =-1/16*z2*z3*ln2-15/16*z2*z3*Sinf-1/ 12*z2*ln2^3*Sinf+1/12*z2*ln2^4+3*z2*li4half+3/8*z2^2*ln2*Sinf -1/10*z2^2*ln2^2-1/16*z3*ln2^2*Sinf-1/24*z3*ln2^3+63/128*z3^2 +29/64*z5*Sinf+ln2*Sinf*li4half+1/2*ln2^2*li4half+1/120*ln2^5 *Sinf+1/144*ln2^6+4*Sinf*li5half-10*li6half; Fill Stab6(1,-1,-1,1,1,-1) =16/7*z2^3-4*z5*ln2-4*z5*Sinf+ln2* Sinf*li4half+1/2*ln2^2*li4half+4*Sinf*li5half-10*li6half; Fill Stab6(1,-1,-1,1,1,1) =ln2*Sinf*li4half+1/2*ln2^2*li4half+4* Sinf*li5half-10*li6half; Fill Stab6(1,-1,0,-1,-1,-1) =21/16*z2*z3*ln2+21/16*z2*z3*Sinf-17/ 12*z2*ln2^3*Sinf-25/48*z2*ln2^4-1/2*z2*li4half+21/8*z2^2*ln2* Sinf+301/80*z2^2*ln2^2+2141/560*z2^3+21/16*z3*ln2^2*Sinf+7/8* z3*ln2^3+597/128*z3^2-911/64*z5*Sinf+4*ln2*Sinf*li4half+3/2* ln2^2*li4half+7/120*ln2^5*Sinf+1/48*ln2^6+13*Sinf*li5half-30* li6half-31/2*s6; Fill Stab6(1,-1,0,-1,-1,1) =-2/3*z2*ln2^3*Sinf-11/48*z2*ln2^4+ 1/2*z2*li4half+27/8*z2^2*ln2*Sinf+269/80*z2^2*ln2^2+227/80*z2^3 +39/8*z3^2-911/64*z5*Sinf+4*ln2*Sinf*li4half+3/2*ln2^2* li4half+7/120*ln2^5*Sinf+7/240*ln2^6+13*Sinf*li5half-24* li6half-13*s6; Fill Stab6(1,-1,0,-1,0,-1) =5/16*z2*z3*Sinf-1/3*z2*ln2^3*Sinf-11/ 48*z2*ln2^4-3/2*z2*li4half+17/8*z2^2*ln2*Sinf+23/16*z2^2*ln2^2 +977/1680*z2^3+77/128*z3^2-403/64*z5*ln2-331/32*z5*Sinf+4* ln2*Sinf*li4half+4*ln2*li5half+2*ln2^2*li4half+1/10*ln2^5*Sinf +1/20*ln2^6+8*Sinf*li5half-3/2*s6; Fill Stab6(1,-1,0,-1,0,1) =7/4*z2*z3*ln2+9/8*z2*z3*Sinf-2/3*z2* ln2^3*Sinf-7/24*z2*ln2^4+3*z2*li4half-7/10*z2^2*ln2*Sinf-11/ 10*z2^2*ln2^2-167/840*z2^3+7/4*z3*ln2^2*Sinf+7/6*z3*ln2^3-3/2 *z3^2-259/64*z5*Sinf+4*ln2*Sinf*li4half+2*ln2^2*li4half+2/15* ln2^5*Sinf+7/90*ln2^6+4*Sinf*li5half-4*li6half+3/4*s6; Fill Stab6(1,-1,0,-1,1,-1) =3/4*z2*ln2^3*Sinf+11/48*z2*ln2^4+1/ 40*z2^2*ln2*Sinf-45/16*z2^2*ln2^2-16/35*z2^3-45/16*z3^2-279/ 64*z5*ln2-99/32*z5*Sinf+ln2*Sinf*li4half+2*ln2*li5half+1/2* ln2^2*li4half+1/60*ln2^5*Sinf+1/60*ln2^6+3*Sinf*li5half+9* li6half+15/2*s6; Fill Stab6(1,-1,0,-1,1,1) =7/16*z2*z3*ln2+7/16*z2*z3*Sinf-1/6*z2 *ln2^3*Sinf-5/48*z2*ln2^4-6/5*z2^2*ln2*Sinf-3/5*z2^2*ln2^2-6/ 35*z2^3+7/16*z3*ln2^2*Sinf+7/24*z3*ln2^3-229/128*z3^2+81/64* z5*Sinf+ln2*Sinf*li4half+1/2*ln2^2*li4half+1/30*ln2^5*Sinf+7/ 360*ln2^6+Sinf*li5half-li6half+15/4*s6; Fill Stab6(1,-1,0,0,-1,-1) =-39/16*z2*z3*ln2+1/2*z2*ln2^3*Sinf +7/24*z2*ln2^4-2/5*z2^2*ln2*Sinf-19/16*z2^2*ln2^2+31/168*z2^3 -173/64*z3^2-155/32*z5*ln2+15/32*z5*Sinf-2*ln2*Sinf*li4half +2*ln2*li5half-ln2^2*li4half-1/12*ln2^5*Sinf-1/20*ln2^6+6* li6half+31/4*s6; Fill Stab6(1,-1,0,0,-1,1) =-7/8*z2*z3*ln2-7/8*z2*z3*Sinf+1/3* z2*ln2^3*Sinf+5/24*z2*ln2^4-1/2*z2^2*ln2*Sinf-1/4*z2^2*ln2^2- 5/6*z2^3-7/8*z3*ln2^2*Sinf-7/12*z3*ln2^3+81/64*z3^2+85/16*z5* Sinf-2*ln2*Sinf*li4half-ln2^2*li4half-1/15*ln2^5*Sinf-7/180* ln2^6-2*Sinf*li5half+2*li6half+3*s6; Fill Stab6(1,-1,0,0,0,-1) =-3/4*z2*z3*Sinf+1/12*z2*ln2^4+2*z2* li4half-2/5*z2^2*ln2*Sinf-7/10*z2^2*ln2^2-27/35*z2^3+1/4*z3^2 +91/32*z5*Sinf+5/2*s6; Fill Stab6(1,-1,0,0,0,1) =3/8*z2*z3*Sinf-1/24*z2*ln2^4-z2* li4half+7/20*z2^2*ln2*Sinf+17/40*z2^2*ln2^2+123/140*z2^3-15/ 16*z3^2-155/32*z5*ln2-2*z5*Sinf+s6; Fill Stab6(1,-1,0,0,1,-1) =39/16*z2*z3*ln2-1/3*z2*ln2^3*Sinf-5/ 24*z2*ln2^4+z2*li4half-13/40*z2^2*ln2*Sinf+23/40*z2^2*ln2^2- 1139/1680*z2^3+55/128*z3^2+27/8*z5*Sinf+ln2^2*li4half+1/30* ln2^5*Sinf+1/24*ln2^6-4*Sinf*li5half-5/2*s6; Fill Stab6(1,-1,0,0,1,1) =7/8*z2*z3*ln2+7/8*z2*z3*Sinf+1/6*z2* ln2^3*Sinf+1/24*z2*ln2^4-z2*li4half+11/10*z2^2*ln2*Sinf+4/5* z2^2*ln2^2-893/1680*z2^3-7/8*z3*ln2^2*Sinf-7/12*z3*ln2^3-223/ 128*z3^2-527/64*z5*ln2-311/64*z5*Sinf+6*ln2*li5half+ln2^2* li4half-1/60*ln2^5*Sinf+1/360*ln2^6+2*Sinf*li5half+8*li6half +3*s6; Fill Stab6(1,-1,0,1,-1,-1) =-21/16*z2*z3*ln2+7/6*z2*ln2^3*Sinf +11/24*z2*ln2^4-81/20*z2^2*ln2*Sinf-87/20*z2^2*ln2^2-3*z2^3 -7/16*z3*ln2^3-441/64*z3^2-31/32*z5*ln2+245/16*z5*Sinf-4* ln2*Sinf*li4half-2*ln2*li5half-2*ln2^2*li4half-1/30*ln2^5*Sinf -1/40*ln2^6-16*Sinf*li5half+30*li6half+35/2*s6; Fill Stab6(1,-1,0,1,-1,1) =-21/8*z2*z3*ln2-21/16*z2*z3*Sinf+7/ 12*z2*ln2^3*Sinf+3/8*z2*ln2^4-49/20*z2^2*ln2*Sinf-29/40*z2^2* ln2^2-1041/280*z2^3-21/16*z3*ln2^2*Sinf-21/16*z3*ln2^3-111/ 128*z3^2+521/32*z5*Sinf-4*ln2*Sinf*li4half-2*ln2^2*li4half-1/ 20*ln2^5*Sinf-1/20*ln2^6-14*Sinf*li5half+24*li6half+23/2*s6; Fill Stab6(1,-1,0,1,0,-1) =-35/8*z2*z3*ln2-3/2*z2*z3*Sinf+2/3* z2*ln2^3*Sinf+1/4*z2*ln2^4-4*z2*li4half-13/40*z2^2*ln2*Sinf+ 67/80*z2^2*ln2^2+29/168*z2^3-7/4*z3*ln2^2*Sinf-7/6*z3*ln2^3+ 285/128*z3^2+129/16*z5*Sinf-4*ln2*Sinf*li4half-2*ln2^2*li4half -2/15*ln2^5*Sinf-7/90*ln2^6-4*Sinf*li5half+4*li6half+7/2*s6; Fill Stab6(1,-1,0,1,0,1) =21/16*z2*z3*ln2-1/8*z2*z3*Sinf+1/3*z2* ln2^3*Sinf+1/4*z2*ln2^4+2*z2*li4half-51/40*z2^2*ln2*Sinf-91/ 80*z2^2*ln2^2+19/84*z2^3-145/64*z3^2-31/32*z5*ln2+227/32*z5* Sinf-4*ln2*Sinf*li4half-4*ln2*li5half-2*ln2^2*li4half-1/10* ln2^5*Sinf-1/20*ln2^6-8*Sinf*li5half+5/2*s6; Fill Stab6(1,-1,0,1,1,-1) =-21/16*z2*z3*Sinf+3/8*z2*ln2^4-3/2* z2*li4half+6/5*z2^2*ln2*Sinf+3/2*z2^2*ln2^2+173/560*z2^3-21/ 16*z3*ln2^2*Sinf-21/16*z3*ln2^3+69/32*z3^2+87/32*z5*Sinf-3* ln2*Sinf*li4half-3*ln2^2*li4half-1/8*ln2^5*Sinf-31/240*ln2^6- 3*li6half-9/4*s6; Fill Stab6(1,-1,0,1,1,1) =35/16*z2*z3*ln2+7/8*z2*z3*Sinf+5/12*z2 *ln2^3*Sinf+1/2*z2*ln2^4+3/2*z2*li4half-1/8*z2^2*ln2*Sinf-7/ 16*z2^2*ln2^2+163/560*z2^3-7/8*z3*ln2^2*Sinf-49/48*z3*ln2^3- 209/128*z3^2-93/64*z5*ln2+81/64*z5*Sinf-3*ln2*Sinf*li4half-4* ln2*li5half-3*ln2^2*li4half-11/120*ln2^5*Sinf-67/720*ln2^6-4* Sinf*li5half-li6half+s6; Fill Stab6(1,-1,1,-1,-1,-1) =13/8*z2*z3*ln2+13/8*z2*z3*Sinf-5/12 *z2*ln2^3*Sinf-11/48*z2*ln2^4+1/8*z2^2*ln2*Sinf+1/10*z2^2*ln2^2 +47/105*z2^3+11/8*z3*ln2^2*Sinf+11/12*z3*ln2^3-13/64*z3^2- 369/64*z5*Sinf+3*ln2*Sinf*li4half+3/2*ln2^2*li4half+11/120* ln2^5*Sinf+37/720*ln2^6+3*Sinf*li5half-3*li6half-3*s6; Fill Stab6(1,-1,1,-1,-1,1) =-11/8*z2*z3*ln2-11/8*z2*z3*Sinf-5/ 12*z2*ln2^3*Sinf-11/48*z2*ln2^4+1/8*z2^2*ln2*Sinf+1/10*z2^2* ln2^2+3/70*z2^3+11/8*z3*ln2^2*Sinf+11/12*z3*ln2^3+83/64*z3^2 +9/2*z5*ln2-81/64*z5*Sinf+3*ln2*Sinf*li4half+3/2*ln2^2* li4half+11/120*ln2^5*Sinf+37/720*ln2^6+3*Sinf*li5half-3* li6half-3*s6; Fill Stab6(1,-1,1,-1,0,-1) =-13/16*z2*z3*ln2-7/8*z2*z3*Sinf-1/ 3*z2*ln2^3*Sinf-13/48*z2*ln2^4+1/20*z2^2*ln2*Sinf+39/80*z2^2* ln2^2+389/560*z2^3+13/16*z3*ln2^2*Sinf+13/24*z3*ln2^3+69/32* z3^2+93/16*z5*ln2-33/64*z5*Sinf+2*ln2*Sinf*li4half-3*ln2* li5half+ln2^2*li4half+3/40*ln2^5*Sinf+1/18*ln2^6+Sinf*li5half -8*li6half-11/2*s6; Fill Stab6(1,-1,1,-1,0,1) =29/16*z2*z3*ln2+31/16*z2*z3*Sinf-1/3* z2*ln2^3*Sinf-3/16*z2*ln2^4+1/5*z2^2*ln2*Sinf+19/40*z2^2*ln2^2 +341/280*z2^3+13/16*z3*ln2^2*Sinf+13/24*z3*ln2^3+89/128*z3^2 -405/64*z5*Sinf+2*ln2*Sinf*li4half+ln2^2*li4half+1/20*ln2^5* Sinf+7/240*ln2^6+4*Sinf*li5half-9*li6half-21/4*s6; Fill Stab6(1,-1,1,-1,1,-1) =-1/16*z2*z3*ln2-1/16*z2*z3*Sinf+1/ 12*z2*ln2^3*Sinf+1/12*z2*ln2^4-3/8*z2^2*ln2*Sinf-2/5*z2^2*ln2^2 +1/16*z3*ln2^2*Sinf+1/24*z3*ln2^3+1/128*z3^2+1/2*z5*ln2+3/ 64*z5*Sinf-1/120*ln2^5*Sinf-1/144*ln2^6; Fill Stab6(1,-1,1,-1,1,1) =15/16*z2*z3*ln2+15/16*z2*z3*Sinf+1/12 *z2*ln2^3*Sinf+1/12*z2*ln2^4-3/8*z2^2*ln2*Sinf-2/5*z2^2*ln2^2 +1/16*z3*ln2^2*Sinf+1/24*z3*ln2^3-63/128*z3^2-29/64*z5*Sinf -1/120*ln2^5*Sinf-1/144*ln2^6; Fill Stab6(1,-1,1,0,-1,-1) =1/8*z2*z3*ln2+5/16*z2*z3*Sinf-1/6*z2 *ln2^3*Sinf+1/16*z2*ln2^4+31/20*z2^2*ln2*Sinf+73/40*z2^2*ln2^2 +8/5*z2^3-5/16*z3*ln2^2*Sinf-5/24*z3*ln2^3+201/128*z3^2-341/ 64*z5*ln2-457/64*z5*Sinf+4*ln2*li5half-7/120*ln2^5*Sinf-7/144 *ln2^6+7*Sinf*li5half-11*li6half-17/4*s6; Fill Stab6(1,-1,1,0,-1,1) =5/16*z2*z3*ln2+5/16*z2*z3*Sinf+1/4*z2 *ln2^3*Sinf+1/8*z2*ln2^4+9/40*z2^2*ln2*Sinf-3/8*z2^2*ln2^2+ 113/140*z2^3-5/16*z3*ln2^2*Sinf-5/24*z3*ln2^3+47/128*z3^2-29/ 16*z5*Sinf-1/40*ln2^5*Sinf-1/120*ln2^6+3*Sinf*li5half-6* li6half-3/4*s6; Fill Stab6(1,-1,1,0,0,-1) =5/4*z2*z3*ln2+9/8*z2*z3*Sinf-1/6*z2* ln2^3*Sinf-1/24*z2*ln2^4+2*z2*li4half+1/5*z2^2*ln2*Sinf-7/20* z2^2*ln2^2+13/35*z2^3+1/2*z3*ln2^2*Sinf+1/3*z3*ln2^3-1/8*z3^2 -153/32*z5*Sinf+2*ln2*Sinf*li4half+ln2^2*li4half+1/20*ln2^5* Sinf+1/30*ln2^6+4*Sinf*li5half-6*li6half-3/2*s6; Fill Stab6(1,-1,1,0,0,1) =-1/2*z2*z3*ln2-7/16*z2*z3*Sinf-1/3* z2*ln2^3*Sinf-7/24*z2*ln2^4-z2*li4half+19/40*z2^2*ln2*Sinf+11/ 10*z2^2*ln2^2+31/28*z2^3+1/2*z3*ln2^2*Sinf+1/3*z3*ln2^3+267/ 128*z3^2+155/64*z5*ln2-151/64*z5*Sinf+2*ln2*Sinf*li4half-2* ln2*li5half+ln2^2*li4half+1/15*ln2^5*Sinf+17/360*ln2^6+2*Sinf *li5half-8*li6half-11/2*s6; Fill Stab6(1,-1,1,0,1,-1) =11/8*z2*z3*ln2+19/16*z2*z3*Sinf-1/3* z2*ln2^3*Sinf-5/12*z2*ln2^4+3/2*z2*li4half-7/5*z2^2*ln2*Sinf- 121/80*z2^2*ln2^2-479/280*z2^3+23/16*z3*ln2^2*Sinf+23/24*z3* ln2^3-177/64*z3^2+35/32*z5*Sinf+3*ln2*Sinf*li4half+3*ln2^2* li4half+19/120*ln2^5*Sinf+101/720*ln2^6-4*Sinf*li5half+11* li6half+17/4*s6; Fill Stab6(1,-1,1,0,1,1) =-23/16*z2*z3*ln2-23/16*z2*z3*Sinf-7/ 12*z2*ln2^3*Sinf-23/48*z2*ln2^4-3/2*z2*li4half+1/40*z2^2*ln2* Sinf+29/80*z2^2*ln2^2-55/56*z2^3+23/16*z3*ln2^2*Sinf+23/24*z3 *ln2^3-21/64*z3^2-93/64*z5*ln2-23/64*z5*Sinf+3*ln2*Sinf* li4half+6*ln2*li5half+3*ln2^2*li4half+13/120*ln2^5*Sinf+31/ 360*ln2^6+2*Sinf*li5half+8*li6half+5/4*s6; Fill Stab6(1,-1,1,1,-1,-1) =-1/16*z2*z3*ln2+7/16*z2*z3*Sinf+1/ 6*z2*ln2^3*Sinf+7/48*z2*ln2^4-2/5*z2^2*ln2*Sinf-3/8*z2^2*ln2^2 +1/60*z2^3-7/16*z3*ln2^2*Sinf-11/24*z3*ln2^3-167/128*z3^2-3 *z5*ln2+27/32*z5*Sinf-ln2*Sinf*li4half-1/2*ln2^2*li4half-1/30 *ln2^5*Sinf-17/720*ln2^6-2*Sinf*li5half+3*li6half+3*s6; Fill Stab6(1,-1,1,1,-1,1) =-17/16*z2*z3*ln2-9/16*z2*z3*Sinf+1/ 6*z2*ln2^3*Sinf+7/48*z2*ln2^4-2/5*z2^2*ln2*Sinf-3/8*z2^2*ln2^2 -71/140*z2^3-7/16*z3*ln2^2*Sinf-11/24*z3*ln2^3+25/128*z3^2+ 123/32*z5*Sinf-ln2*Sinf*li4half-1/2*ln2^2*li4half-1/30*ln2^5* Sinf-17/720*ln2^6-2*Sinf*li5half+3*li6half+3*s6; Fill Stab6(1,-1,1,1,0,-1) =-11/8*z2*z3*ln2-3/8*z2*z3*Sinf+1/6* z2*ln2^3*Sinf+1/12*z2*ln2^4-z2*li4half+1/5*z2^2*ln2*Sinf+29/ 40*z2^2*ln2^2+34/35*z2^3-1/2*z3*ln2^2*Sinf-1/3*z3*ln2^3+7/4* z3^2+15/16*z5*Sinf-ln2*Sinf*li4half-1/2*ln2^2*li4half-1/20* ln2^5*Sinf-7/240*ln2^6+Sinf*li5half-6*li6half-3/2*s6; Fill Stab6(1,-1,1,1,0,1) =z2*z3*ln2+1/2*z2*z3*Sinf+1/6*z2*ln2^3* Sinf+1/16*z2*ln2^4+1/2*z2*li4half+1/20*z2^2*ln2*Sinf+29/80* z2^2*ln2^2+11/14*z2^3-1/2*z3*ln2^2*Sinf-1/3*z3*ln2^3+3/32* z3^2-31/32*z5*ln2-1/32*z5*Sinf-ln2*Sinf*li4half-3*ln2*li5half -1/2*ln2^2*li4half-1/40*ln2^5*Sinf-1/360*ln2^6-2*Sinf*li5half -5*li6half-7/4*s6; Fill Stab6(1,-1,1,1,1,-1) =1/2*z2*z3*ln2+1/24*z2*ln2^4+1/40*z2^2 *ln2^2-13/35*z2^3-1/6*z3*ln2^3-1/8*z3^2+z5*Sinf-1/240*ln2^6 -Sinf*li5half+2*li6half+1/2*s6; Fill Stab6(1,-1,1,1,1,1) =1/2*z2*z3*ln2+1/24*z2*ln2^4+1/40*z2^2* ln2^2-1/5*z2^3-1/6*z3*ln2^3-5/8*z3^2-z5*ln2-1/240*ln2^6- Sinf*li5half+2*li6half+1/2*s6; Fill Stab6(1,0,-1,-1,-1,-1) =21/16*z2*z3*ln2+27/16*z2*z3*Sinf+7/ 12*z2*ln2^3*Sinf-1/4*z2*ln2^4+1/2*z2*li4half-11/8*z2^2*ln2*Sinf -29/20*z2^2*ln2^2-431/560*z2^3+21/16*z3*ln2^2*Sinf+7/8*z3* ln2^3-269/128*z3^2+101/64*z5*Sinf+1/2*ln2^2*li4half+1/24* ln2^5*Sinf+11/360*ln2^6-5*Sinf*li5half+7*li6half+9/4*s6; Fill Stab6(1,0,-1,-1,-1,1) =-21/16*z2*z3*ln2-21/16*z2*z3*Sinf+ 7/12*z2*ln2^3*Sinf-5/24*z2*ln2^4-1/2*z2*li4half-17/5*z2^2*ln2* Sinf-47/40*z2^2*ln2^2+3/560*z2^3+21/16*z3*ln2^2*Sinf+7/8*z3* ln2^3+165/128*z3^2+93/8*z5*ln2+845/64*z5*Sinf-3*ln2*Sinf* li4half-6*ln2*li5half-ln2^2*li4half-1/30*ln2^5*Sinf+1/240* ln2^6-11*Sinf*li5half-3*li6half-3*s6; Fill Stab6(1,0,-1,-1,0,-1) =-13/16*z2*z3*Sinf+2/3*z2*ln2^3*Sinf +11/48*z2*ln2^4+3/2*z2*li4half-17/5*z2^2*ln2*Sinf-3/8*z2^2* ln2^2+989/560*z2^3+659/128*z3^2+1457/64*z5*ln2+547/32*z5*Sinf -8*ln2*Sinf*li4half-16*ln2*li5half-4*ln2^2*li4half-1/5*ln2^5* Sinf-1/15*ln2^6-16*Sinf*li5half-24*li6half-14*s6; Fill Stab6(1,0,-1,-1,0,1) =25/8*z2*z3*Sinf-1/8*z2*ln2^4-3*z2* li4half+3/8*z2^2*ln2*Sinf+3/4*z2^2*ln2^2+31/28*z2^3+1/16*z3^2 -363/64*z5*Sinf-7/2*s6; Fill Stab6(1,0,-1,-1,1,-1) =-1/3*z2*ln2^3*Sinf-1/48*z2*ln2^4- 87/40*z2^2*ln2*Sinf+139/80*z2^2*ln2^2+16/35*z2^3+45/16*z3^2+ 465/64*z5*ln2+221/32*z5*Sinf-ln2*Sinf*li4half-4*ln2*li5half-1/ 2*ln2^2*li4half+1/60*ln2^5*Sinf-7*Sinf*li5half-9*li6half-15/2 *s6; Fill Stab6(1,0,-1,-1,1,1) =21/16*z2*z3*Sinf-1/48*z2*ln2^4+9/40* z2^2*ln2*Sinf+43/80*z2^2*ln2^2+6/35*z2^3+131/128*z3^2-23/64* z5*Sinf+1/40*ln2^5*Sinf+1/720*ln2^6-3*Sinf*li5half+li6half- 15/4*s6; Fill Stab6(1,0,-1,0,-1,-1) =15/16*z2*z3*ln2-1/3*z2*ln2^3*Sinf-1/ 12*z2*ln2^4+19/20*z2^2*ln2*Sinf-61/35*z2^3-113/64*z3^2-217/32 *z5*ln2-123/16*z5*Sinf+4*ln2*Sinf*li4half+8*ln2*li5half+2* ln2^2*li4half+1/10*ln2^5*Sinf+1/30*ln2^6+8*Sinf*li5half+12* li6half+9/2*s6; Fill Stab6(1,0,-1,0,-1,1) =15/16*z2*z3*Sinf+17/56*z2^3-115/128* z3^2-29/32*z5*Sinf; Fill Stab6(1,0,-1,0,0,-1) =21/8*z2*z3*Sinf+403/840*z2^3-89/64* z3^2-67/16*z5*Sinf; Fill Stab6(1,0,-1,0,0,1) =-3/4*z2*z3*Sinf-1033/1680*z2^3+69/64 *z3^2+155/32*z5*ln2+21/32*z5*Sinf-5/2*s6; Fill Stab6(1,0,-1,0,1,-1) =13/16*z2*z3*ln2+11/8*z2*z3*Sinf-1/3* z2*ln2^3*Sinf-1/3*z2*ln2^4+2*z2*li4half-19/20*z2^2*ln2*Sinf-1/ 2*z2^2*ln2^2+87/280*z2^3+7/4*z3*ln2^2*Sinf+7/6*z3*ln2^3-109/ 128*z3^2+33/32*z5*Sinf+2*ln2^2*li4half+1/30*ln2^5*Sinf+7/90* ln2^6-4*Sinf*li5half-4*li6half-s6; Fill Stab6(1,0,-1,0,1,1) =-7/4*z2*z3*ln2-7/4*z2*z3*Sinf-2/3*z2 *ln2^3*Sinf-7/12*z2*ln2^4-2*z2*li4half+1/2*z2^2*ln2^2-67/70* z2^3+7/4*z3*ln2^2*Sinf+7/6*z3*ln2^3-7/128*z3^2-155/64*z5*ln2 -89/64*z5*Sinf+4*ln2*Sinf*li4half+8*ln2*li5half+4*ln2^2* li4half+2/15*ln2^5*Sinf+1/9*ln2^6+4*Sinf*li5half+8*li6half+ 5/4*s6; Fill Stab6(1,0,-1,1,-1,-1) =-11/12*z2*ln2^3*Sinf-1/24*z2*ln2^4 +53/40*z2^2*ln2*Sinf+11/16*z2^2*ln2^2+41/280*z2^3-9/32*z3^2 -341/64*z5*ln2-457/64*z5*Sinf+3*ln2*Sinf*li4half+4*ln2* li5half+3/2*ln2^2*li4half+1/15*ln2^5*Sinf+7/240*ln2^6+7*Sinf* li5half+3/4*s6; Fill Stab6(1,0,-1,1,-1,1) =-3/16*z2*z3*Sinf-1/4*z2*ln2^3*Sinf+ 1/24*z2*ln2^4+9/10*z2^2*ln2*Sinf-41/80*z2^2*ln2^2+101/280*z2^3 -5/128*z3^2-29/16*z5*Sinf-1/40*ln2^5*Sinf-1/360*ln2^6+3* Sinf*li5half-2*li6half+1/4*s6; Fill Stab6(1,0,-1,1,0,-1) =1/16*z2*z3*Sinf+11/280*z2^3+1/128* z3^2+5/8*z5*Sinf; Fill Stab6(1,0,-1,1,0,1) =1/16*z2*z3*Sinf+61/560*z2^3-35/128* z3^2-93/64*z5*ln2-53/64*z5*Sinf+3/4*s6; Fill Stab6(1,0,-1,1,1,-1) =7/16*z2*z3*ln2+7/16*z2*z3*Sinf+1/6*z2 *ln2^3*Sinf-5/48*z2*ln2^4+1/2*z2*li4half-1/20*z2^2*ln2*Sinf-3/ 20*z2^2*ln2^2-17/280*z2^3+7/16*z3*ln2^2*Sinf+7/24*z3*ln2^3-49/ 128*z3^2+1/8*z5*Sinf+1/2*ln2^2*li4half+1/120*ln2^5*Sinf+1/48* ln2^6-Sinf*li5half; Fill Stab6(1,0,-1,1,1,1) =-7/16*z2*z3*ln2-7/16*z2*z3*Sinf-1/6* z2*ln2^3*Sinf-7/48*z2*ln2^4-1/2*z2*li4half+1/8*z2^2*ln2^2-9/ 40*z2^3+7/16*z3*ln2^2*Sinf+7/24*z3*ln2^3-17/128*z3^2-31/32*z5 *ln2-27/32*z5*Sinf+ln2*Sinf*li4half+2*ln2*li5half+ln2^2* li4half+1/30*ln2^5*Sinf+1/36*ln2^6+Sinf*li5half+2*li6half+1/ 2*s6; Fill Stab6(1,0,0,-1,-1,-1) =-7/8*z2*z3*ln2-1/2*z2*z3*Sinf-1/2* z2*ln2^3*Sinf-1/24*z2*ln2^4-19/40*z2^2*ln2*Sinf+17/20*z2^2* ln2^2+4/5*z2^3-7/24*z3*ln2^3-3/4*z3^2-155/32*z5*ln2+15/32* z5*Sinf+2*ln2*Sinf*li4half+2*ln2*li5half+ln2^2*li4half+1/12* ln2^5*Sinf+1/45*ln2^6-2*li6half+5/4*s6; Fill Stab6(1,0,0,-1,-1,1) =-7/8*z2*z3*ln2-13/8*z2*z3*Sinf-1/6* z2*ln2^3*Sinf+1/24*z2*ln2^4-1/10*z2^2*ln2*Sinf+17/40*z2^2*ln2^2 -9/28*z2^3-7/24*z3*ln2^3+81/32*z3^2+85/16*z5*Sinf+1/60* ln2^5*Sinf-1/360*ln2^6-2*Sinf*li5half-2*li6half-1/2*s6; Fill Stab6(1,0,0,-1,0,-1) =-7/4*z2*z3*ln2-9/4*z2*z3*Sinf-1/12* z2*ln2^4-2*z2*li4half+1/2*z2^2*ln2^2-13/420*z2^3+163/64*z3^2 +83/16*z5*Sinf; Fill Stab6(1,0,0,-1,0,1) =7/8*z2*z3*ln2-5/8*z2*z3*Sinf+1/24*z2* ln2^4+z2*li4half-1/4*z2^2*ln2^2+179/420*z2^3-121/64*z3^2- 155/32*z5*ln2+11/32*z5*Sinf+5/2*s6; Fill Stab6(1,0,0,-1,1,-1) =-3/4*z2*z3*Sinf+1/3*z2*ln2^3*Sinf+7/ 24*z2*ln2^4-2*z2*li4half+17/10*z2^2*ln2*Sinf+3/40*z2^2*ln2^2- 19/35*z2^3-7/8*z3*ln2^2*Sinf-7/8*z3*ln2^3+1/4*z3^2-39/16*z5* Sinf-2*ln2^2*li4half-1/30*ln2^5*Sinf-3/40*ln2^6+4*Sinf* li5half+6*li6half+3/2*s6; Fill Stab6(1,0,0,-1,1,1) =7/4*z2*z3*ln2+3/8*z2*z3*Sinf+1/3*z2* ln2^3*Sinf+11/24*z2*ln2^4+2*z2*li4half-1/2*z2^2*ln2^2+19/35* z2^3-7/8*z3*ln2^2*Sinf-7/8*z3*ln2^3-3/8*z3^2+93/32*z5*ln2+ 15/32*z5*Sinf-2*ln2*Sinf*li4half-6*ln2*li5half-3*ln2^2*li4half -1/15*ln2^5*Sinf-1/12*ln2^6-2*Sinf*li5half-6*li6half-3/2*s6; Fill Stab6(1,0,0,0,-1,-1) =3/2*z2*z3*ln2+3/4*z2*z3*Sinf+3/4*z2^2 *ln2*Sinf-71/840*z2^3-1/8*z3^2-59/32*z5*Sinf-3/2*s6; Fill Stab6(1,0,0,0,-1,1) =1/2*z2*z3*Sinf+11/168*z2^3-1/4*z3^2- 59/32*z5*Sinf; Fill Stab6(1,0,0,0,0,-1) =23/70*z2^3-3/4*z3^2-31/16*z5*ln2-15/ 16*z5*Sinf+s6; Fill Stab6(1,0,0,0,0,1) =-6/35*z2^3+1/2*z3^2+z5*Sinf; Fill Stab6(1,0,0,0,1,-1) =-3/2*z2*z3*ln2-3/8*z2*z3*Sinf-3/4* z2^2*ln2*Sinf+43/84*z2^3-55/64*z3^2-31/16*z5*ln2+17/16*z5* Sinf+5/2*s6; Fill Stab6(1,0,0,0,1,1) =-z2*z3*Sinf-11/21*z2^3+3/2*z3^2+3* z5*Sinf; Fill Stab6(1,0,0,1,-1,-1) =7/8*z2*z3*ln2+15/8*z2*z3*Sinf+1/6*z2* ln2^3*Sinf-1/12*z2*ln2^4+19/40*z2^2*ln2*Sinf-17/20*z2^2*ln2^2 -23/80*z2^3+7/8*z3*ln2^2*Sinf+7/12*z3*ln2^3-111/64*z3^2-311/ 64*z5*Sinf-1/60*ln2^5*Sinf+1/180*ln2^6+2*Sinf*li5half+4* li6half+5/4*s6; Fill Stab6(1,0,0,1,-1,1) =-7/8*z2*z3*ln2-1/16*z2*z3*Sinf+1/6* z2*ln2^3*Sinf-1/12*z2*ln2^4-49/40*z2^2*ln2*Sinf-17/40*z2^2* ln2^2+97/112*z2^3+7/8*z3*ln2^2*Sinf+7/12*z3*ln2^3+243/128* z3^2+527/64*z5*ln2+27/8*z5*Sinf-2*ln2*Sinf*li4half-6*ln2* li5half-ln2^2*li4half-1/20*ln2^5*Sinf-1/360*ln2^6-4*Sinf* li5half-8*li6half-9/2*s6; Fill Stab6(1,0,0,1,0,-1) =1/4*z2*z3*Sinf-59/210*z2^3+19/32*z3^2 +93/32*z5*ln2-51/32*z5*Sinf-3/2*s6; Fill Stab6(1,0,0,1,0,1) =3*z2*z3*Sinf+17/42*z2^3-3/2*z3^2-9/2* z5*Sinf; Fill Stab6(1,0,0,1,1,-1) =-1/16*z2*z3*Sinf-1/3*z2*ln2^3*Sinf-1/ 12*z2*ln2^4-3/8*z2^2*ln2*Sinf+17/40*z2^2*ln2^2-1/128*z3^2-93/ 64*z5*ln2-125/64*z5*Sinf+2*ln2*Sinf*li4half+2*ln2*li5half+ ln2^2*li4half+1/15*ln2^5*Sinf+1/40*ln2^6+2*Sinf*li5half; Fill Stab6(1,0,0,1,1,1) =z2*z3*Sinf-1/2*z3^2-1/2*z5*Sinf; Fill Stab6(1,0,1,-1,-1,-1) =-7/8*z2*z3*ln2-3/8*z2*z3*Sinf-13/ 12*z2*ln2^3*Sinf+1/48*z2*ln2^4+11/8*z2^2*ln2*Sinf+53/40*z2^2* ln2^2+34/35*z2^3-7/24*z3*ln2^3-25/64*z3^2-93/16*z5*ln2-61/8 *z5*Sinf+3*ln2*Sinf*li4half+4*ln2*li5half+3/2*ln2^2*li4half+7/ 120*ln2^5*Sinf+1/40*ln2^6+8*Sinf*li5half-3*li6half+3/4*s6; Fill Stab6(1,0,1,-1,-1,1) =-7/8*z2*z3*ln2-5/12*z2*ln2^3*Sinf+5/ 48*z2*ln2^4+19/20*z2^2*ln2*Sinf+1/8*z2^2*ln2^2-7/24*z3*ln2^3+ 49/32*z3^2-29/16*z5*Sinf-1/30*ln2^5*Sinf-1/144*ln2^6+4*Sinf* li5half-5*li6half; Fill Stab6(1,0,1,-1,0,-1) =-7/4*z2*z3*ln2-z2*z3*Sinf+1/24*z2* ln2^4+z2*li4half-3/8*z2^2*ln2*Sinf-1/4*z2^2*ln2^2-43/56*z2^3 +39/64*z3^2+257/64*z5*Sinf+7/2*s6; Fill Stab6(1,0,1,-1,0,1) =7/8*z2*z3*ln2-z2*z3*Sinf-2/3*z2*ln2^3* Sinf-3/16*z2*ln2^4-1/2*z2*li4half+17/5*z2^2*ln2*Sinf+1/8*z2^2 *ln2^2-1213/560*z2^3-81/16*z3^2-1271/64*z5*ln2-507/32*z5*Sinf +8*ln2*Sinf*li4half+16*ln2*li5half+4*ln2^2*li4half+1/5*ln2^5* Sinf+1/15*ln2^6+16*Sinf*li5half+24*li6half+25/2*s6; Fill Stab6(1,0,1,-1,1,-1) =-7/16*z2*z3*ln2-21/16*z2*z3*Sinf+1/ 3*z2*ln2^3*Sinf+7/24*z2*ln2^4-3/2*z2*li4half+83/40*z2^2*ln2* Sinf+79/80*z2^2*ln2^2-163/560*z2^3-21/16*z3*ln2^2*Sinf-7/6*z3 *ln2^3+209/128*z3^2-85/64*z5*Sinf-3/2*ln2^2*li4half-1/30* ln2^5*Sinf-11/180*ln2^6+4*Sinf*li5half+li6half-s6; Fill Stab6(1,0,1,-1,1,1) =35/16*z2*z3*ln2+5/12*z2*ln2^4+3/2*z2* li4half+17/8*z2^2*ln2*Sinf+21/80*z2^2*ln2^2-173/560*z2^3-21/ 16*z3*ln2^2*Sinf-7/6*z3*ln2^3-89/64*z3^2-403/64*z5*ln2-61/8* z5*Sinf+ln2*Sinf*li4half+2*ln2*li5half-ln2^2*li4half-1/120* ln2^5*Sinf-13/240*ln2^6+6*Sinf*li5half+3*li6half+9/4*s6; Fill Stab6(1,0,1,0,-1,-1) =5/4*z2*z3*ln2-7/4*z2*z3*Sinf+1/3*z2* ln2^3*Sinf+1/3*z2*ln2^4-2*z2*li4half+113/40*z2^2*ln2*Sinf+1/2 *z2^2*ln2^2-411/560*z2^3-7/4*z3*ln2^2*Sinf-7/6*z3*ln2^3+7/4* z3^2-89/64*z5*Sinf-2*ln2^2*li4half-1/30*ln2^5*Sinf-7/90*ln2^6 +4*Sinf*li5half+4*li6half-9/4*s6; Fill Stab6(1,0,1,0,-1,1) =7/4*z2*z3*ln2+13/16*z2*z3*Sinf+2/3*z2* ln2^3*Sinf+7/12*z2*ln2^4+2*z2*li4half-1/2*z2^2*ln2^2+93/80* z2^3-7/4*z3*ln2^2*Sinf-7/6*z3*ln2^3-13/128*z3^2+155/64*z5*ln2 +33/32*z5*Sinf-4*ln2*Sinf*li4half-8*ln2*li5half-4*ln2^2* li4half-2/15*ln2^5*Sinf-1/9*ln2^6-4*Sinf*li5half-8*li6half- 5/4*s6; Fill Stab6(1,0,1,0,0,-1) =-1/8*z2*z3*Sinf+13/12*z2^3-103/64* z3^2-217/32*z5*ln2-41/32*z5*Sinf+7/2*s6; Fill Stab6(1,0,1,0,0,1) =-2*z2*z3*Sinf-29/30*z2^3+2*z3^2+11/ 2*z5*Sinf; Fill Stab6(1,0,1,0,1,-1) =-3*z2*z3*ln2+3/8*z2*z3*Sinf+1/3*z2* ln2^3*Sinf+1/12*z2*ln2^4-113/40*z2^2*ln2*Sinf+86/35*z2^3+27/ 64*z3^2+93/16*z5*ln2+125/16*z5*Sinf-4*ln2*Sinf*li4half-8*ln2* li5half-2*ln2^2*li4half-1/10*ln2^5*Sinf-1/30*ln2^6-8*Sinf* li5half-12*li6half-3/4*s6; Fill Stab6(1,0,1,0,1,1) =-8/7*z2^3+2*z3^2+2*z5*Sinf; Fill Stab6(1,0,1,1,-1,-1) =-7/16*z2*z3*ln2-7/16*z2*z3*Sinf+11/ 12*z2*ln2^3*Sinf+5/48*z2*ln2^4-3/2*z2*li4half+49/40*z2^2*ln2* Sinf-119/80*z2^2*ln2^2-48/35*z2^3-7/16*z3*ln2^2*Sinf-7/24*z3* ln2^3-131/128*z3^2-23/64*z5*Sinf-3/2*ln2^2*li4half-1/60*ln2^5 *Sinf-7/144*ln2^6+2*Sinf*li5half+10*li6half+15/4*s6; Fill Stab6(1,0,1,1,-1,1) =7/16*z2*z3*ln2+5/8*z2*z3*Sinf+11/12*z2 *ln2^3*Sinf+5/16*z2*ln2^4+3/2*z2*li4half-4/5*z2^2*ln2*Sinf- 177/80*z2^2*ln2^2+4/5*z2^3-7/16*z3*ln2^2*Sinf-7/24*z3*ln2^3- 97/64*z3^2+93/64*z5*ln2+35/32*z5*Sinf-3*ln2*Sinf*li4half-6* ln2*li5half-3*ln2^2*li4half-11/120*ln2^5*Sinf-3/40*ln2^6-4* Sinf*li5half+15/4*s6; Fill Stab6(1,0,1,1,0,-1) =5/16*z2*z3*Sinf+7/5*z2^3-165/128*z3^2 -465/64*z5*ln2-177/64*z5*Sinf+15/4*s6; Fill Stab6(1,0,1,1,0,1) =-z2*z3*Sinf-38/35*z2^3+1/2*z3^2+9/2 *z5*Sinf; Fill Stab6(1,0,1,1,1,-1) =-1/3*z2*ln2^3*Sinf-12/5*z2^2*ln2*Sinf +6/5*z2^2*ln2^2+16/7*z2^3+4*z5*Sinf-ln2*Sinf*li4half-4*ln2* li5half-1/2*ln2^2*li4half-1/120*ln2^5*Sinf-1/720*ln2^6-4*Sinf *li5half-10*li6half; Fill Stab6(1,0,1,1,1,1) =-16/7*z2^3+4*z5*Sinf; Fill Stab6(1,1,-1,-1,-1,-1) =9/8*z2*z3*ln2+z2*z3*Sinf+1/8*z2* ln2^2*Sinf^2-39/40*z2^2*ln2*Sinf-77/80*z2^2*ln2^2+9/80*z2^2* Sinf^2-61/112*z2^3+1/8*z3*ln2*Sinf^2+9/8*z3*ln2^2*Sinf+17/24* z3*ln2^3-55/32*z3^2+23/64*z5*Sinf+1/48*ln2^4*Sinf^2+7/120* ln2^5*Sinf+17/720*ln2^6-3*Sinf*li5half+7*li6half+9/4*s6; Fill Stab6(1,1,-1,-1,-1,1) =-7/8*z2*z3*ln2-z2*z3*Sinf+1/8*z2* ln2^2*Sinf^2-67/40*z2^2*ln2*Sinf-21/16*z2^2*ln2^2-19/80*z2^2* Sinf^2-2687/1680*z2^3+1/8*z3*ln2*Sinf^2+9/8*z3*ln2^2*Sinf+17/ 24*z3*ln2^3-23/32*z3^2+11/2*z5*ln2+375/64*z5*Sinf+1/48*ln2^4* Sinf^2+7/120*ln2^5*Sinf+17/720*ln2^6-3*Sinf*li5half+7*li6half +9/4*s6; Fill Stab6(1,1,-1,-1,0,-1) =1/2*z2*z3*ln2-7/8*z2*z3*Sinf-1/8*z2* ln2^2*Sinf^2+1/6*z2*ln2^3*Sinf+1/4*z2*ln2^4+3/2*z2*li4half-59/ 40*z2^2*ln2*Sinf-15/8*z2^2*ln2^2-3/10*z2^2*Sinf^2-193/70*z2^3 +1/2*z3*ln2*Sinf^2+1/2*z3*ln2^2*Sinf+1/6*z3*ln2^3-73/64*z3^2 +465/64*z5*ln2+247/32*z5*Sinf-3*ln2*Sinf*li4half+ln2*li5half -3/2*ln2^2*li4half-1/12*ln2^5*Sinf-41/720*ln2^6-5*Sinf* li5half+10*li6half+11/4*s6; Fill Stab6(1,1,-1,-1,0,1) =1/2*z2*z3*ln2+7/4*z2*z3*Sinf-1/8*z2* ln2^2*Sinf^2-1/6*z2*ln2^3*Sinf-1/8*z2*ln2^4-3/2*z2*li4half-37/ 40*z2^2*ln2*Sinf+7/80*z2^2*ln2^2-3/16*z2^2*Sinf^2-137/560*z2^3 +1/2*z3*ln2*Sinf^2+1/2*z3*ln2^2*Sinf+1/6*z3*ln2^3-31/32*z3^2 +29/64*z5*Sinf+1/16*ln2^4*Sinf^2+1/20*ln2^5*Sinf+1/80*ln2^6 -6*Sinf*li5half+3/2*Sinf^2*li4half+9*li6half+1/4*s6; Fill Stab6(1,1,-1,-1,1,-1) =7/16*z2*z3*ln2-1/4*z2*ln2^2*Sinf^2-1/ 4*z2*ln2^3*Sinf+3/2*z2*li4half-6/5*z2^2*ln2*Sinf-17/20*z2^2* ln2^2-3/5*z2^2*Sinf^2-101/35*z2^3+7/16*z3*ln2*Sinf^2+7/16*z3* ln2^2*Sinf+7/48*z3*ln2^3+6*z5*ln2+6*z5*Sinf+1/12*ln2^4*Sinf^2 +1/12*ln2^5*Sinf+1/36*ln2^6-6*Sinf*li5half+3/2*Sinf^2*li4half +10*li6half; Fill Stab6(1,1,-1,-1,1,1) =7/16*z2*z3*ln2-1/4*z2*ln2^2*Sinf^2-1/ 4*z2*ln2^3*Sinf+3/2*z2*li4half-1/4*z2^2*ln2^2+7/16*z3*ln2* Sinf^2+7/16*z3*ln2^2*Sinf+7/48*z3*ln2^3+1/12*ln2^4*Sinf^2+1/ 12*ln2^5*Sinf+1/36*ln2^6-6*Sinf*li5half+3/2*Sinf^2*li4half+10 *li6half; Fill Stab6(1,1,-1,0,-1,-1) =13/8*z2*z3*ln2+1/4*z2*ln2^2*Sinf^2-1/ 12*z2*ln2^3*Sinf-1/12*z2*ln2^4+2*z2*li4half-91/40*z2^2*ln2*Sinf +3/40*z2^2*ln2^2-7/10*z2^2*Sinf^2-17/14*z2^3+5/16*z3*ln2* Sinf^2+5/16*z3*ln2^2*Sinf+5/48*z3*ln2^3+107/64*z3^2+465/64*z5 *ln2+221/32*z5*Sinf+ln2*Sinf*li4half-4*ln2*li5half+1/2*ln2^2* li4half+1/12*ln2^4*Sinf^2+1/10*ln2^5*Sinf+37/720*ln2^6-7*Sinf *li5half+2*Sinf^2*li4half-2*li6half-19/4*s6; Fill Stab6(1,1,-1,0,-1,1) =5/16*z2*z3*ln2-3/8*z2*ln2^2*Sinf^2-1/ 4*z2*ln2^3*Sinf+3/2*z2*li4half+39/40*z2^2*ln2*Sinf+9/80*z2^2* ln2^2-9/80*z2^2*Sinf^2-31/560*z2^3+5/16*z3*ln2*Sinf^2+5/16*z3 *ln2^2*Sinf+5/48*z3*ln2^3-1/32*z3^2-23/64*z5*Sinf+1/16*ln2^4* Sinf^2+1/40*ln2^5*Sinf+1/240*ln2^6-3*Sinf*li5half+3/2*Sinf^2* li4half+3*li6half-9/4*s6; Fill Stab6(1,1,-1,0,0,-1) =3/8*z2*z3*ln2+13/8*z2*z3*Sinf-1/4*z2* ln2^2*Sinf^2-1/6*z2*ln2^3*Sinf-1/8*z2*ln2^4-2*z2*li4half-1/10 *z2^2*ln2*Sinf+9/20*z2^2*ln2^2-1/10*z2^2*Sinf^2+93/140*z2^3+3/ 8*z3*ln2*Sinf^2+3/8*z3*ln2^2*Sinf+1/8*z3*ln2^3-1/2*z3^2-15/8* z5*Sinf+1/24*ln2^4*Sinf^2+1/60*ln2^5*Sinf+1/360*ln2^6-2*Sinf* li5half+Sinf^2*li4half+2*li6half-2*s6; Fill Stab6(1,1,-1,0,0,1) =3/8*z2*z3*ln2-13/16*z2*z3*Sinf+1/6*z2* ln2^3*Sinf+7/48*z2*ln2^4+3/2*z2*li4half-49/40*z2^2*ln2*Sinf- 79/80*z2^2*ln2^2-19/80*z2^2*Sinf^2-691/560*z2^3+3/8*z3*ln2* Sinf^2+3/8*z3*ln2^2*Sinf+1/8*z3*ln2^3+101/128*z3^2+31/4*z5* ln2+47/8*z5*Sinf-2*ln2*Sinf*li4half-2*ln2*li5half-ln2^2* li4half-1/20*ln2^5*Sinf-1/40*ln2^6-4*Sinf*li5half-3/2*s6; Fill Stab6(1,1,-1,0,1,-1) =-1/8*z2*z3*ln2+21/16*z2*z3*Sinf-1/4 *z2*ln2^2*Sinf^2-1/4*z2*ln2^3*Sinf-7/48*z2*ln2^4-5/2*z2*li4half +21/20*z2^2*ln2*Sinf-9/16*z2^2*ln2^2+5/8*z2^2*Sinf^2+909/560* z2^3-1/8*z3*ln2*Sinf^2+19/16*z3*ln2^2*Sinf+5/6*z3*ln2^3-1/2* z3^2-61/8*z5*Sinf-1/2*ln2^2*li4half-1/12*ln2^4*Sinf^2-1/20* ln2^5*Sinf-19/720*ln2^6+6*Sinf*li5half-2*Sinf^2*li4half-4* li6half-s6; Fill Stab6(1,1,-1,0,1,1) =-23/16*z2*z3*ln2-21/16*z2*z3*Sinf+1/ 8*z2*ln2^2*Sinf^2-5/12*z2*ln2^3*Sinf-13/48*z2*ln2^4+1/20*z2^2* ln2*Sinf+1/40*z2^2*ln2^2-1/80*z2^2*Sinf^2+109/280*z2^3-1/8*z3 *ln2*Sinf^2+19/16*z3*ln2^2*Sinf+5/6*z3*ln2^3+31/16*z3^2+403/ 64*z5*ln2-85/64*z5*Sinf+3*ln2*Sinf*li4half-2*ln2*li5half+ ln2^2*li4half-1/48*ln2^4*Sinf^2+11/120*ln2^5*Sinf+7/144*ln2^6 +4*Sinf*li5half-1/2*Sinf^2*li4half-7*li6half-4*s6; Fill Stab6(1,1,-1,1,-1,-1) =7/16*z2*z3*ln2-1/8*z2*ln2^2*Sinf^2-1/ 4*z2*ln2^3*Sinf-1/8*z2*ln2^4-3/40*z2^2*ln2*Sinf-27/80*z2^2* ln2^2-1/16*z2^2*Sinf^2-649/1680*z2^3-1/16*z3*ln2*Sinf^2-1/16* z3*ln2^2*Sinf+7/48*z3*ln2^3+7/32*z3^2+1/2*z5*ln2+3/64*z5*Sinf +1/48*ln2^4*Sinf^2+1/30*ln2^5*Sinf+11/720*ln2^6+li6half-1/4 *s6; Fill Stab6(1,1,-1,1,-1,1) =7/16*z2*z3*ln2-1/8*z2*ln2^2*Sinf^2-1/ 4*z2*ln2^3*Sinf-1/8*z2*ln2^4+17/40*z2^2*ln2*Sinf-7/80*z2^2* ln2^2+3/16*z2^2*Sinf^2+137/560*z2^3-1/16*z3*ln2*Sinf^2-1/16* z3*ln2^2*Sinf+7/48*z3*ln2^3-25/32*z3^2-29/64*z5*Sinf+1/48* ln2^4*Sinf^2+1/30*ln2^5*Sinf+11/720*ln2^6+li6half-1/4*s6; Fill Stab6(1,1,-1,1,0,-1) =17/16*z2*z3*ln2+1/8*z2*z3*Sinf-1/12* z2*ln2^3*Sinf+z2*li4half-3/4*z2^2*ln2*Sinf-9/20*z2^2*ln2^2-1/ 10*z2^2*Sinf^2-151/140*z2^3+1/16*z3*ln2*Sinf^2+1/16*z3*ln2^2* Sinf+1/48*z3*ln2^3-13/8*z3^2+123/32*z5*Sinf+1/24*ln2^4*Sinf^2 +1/24*ln2^5*Sinf+1/90*ln2^6-5*Sinf*li5half+Sinf^2*li4half+8 *li6half+2*s6; Fill Stab6(1,1,-1,1,0,1) =-7/16*z2*z3*ln2-1/16*z2*z3*Sinf+1/4* z2*ln2^3*Sinf+3/16*z2*ln2^4-1/2*z2*li4half-37/40*z2^2*ln2*Sinf -11/10*z2^2*ln2^2-1/40*z2^2*Sinf^2-181/140*z2^3+1/16*z3*ln2* Sinf^2+1/16*z3*ln2^2*Sinf+1/48*z3*ln2^3-153/128*z3^2+31/64*z5 *ln2+277/64*z5*Sinf-3*ln2*Sinf*li4half+ln2*li5half-3/2*ln2^2* li4half-1/48*ln2^4*Sinf^2-11/120*ln2^5*Sinf-7/120*ln2^6-4* Sinf*li5half-1/2*Sinf^2*li4half+9*li6half+9/2*s6; Fill Stab6(1,1,-1,1,1,-1) =1/2*z2*z3*Sinf-1/6*z2*ln2^3*Sinf-1/8* z2*ln2^4-1/2*z2*li4half+7/20*z2^2*ln2*Sinf-1/20*z2^2*ln2^2+1/ 5*z2^2*Sinf^2+51/140*z2^3+1/2*z3*ln2^2*Sinf+1/2*z3*ln2^3-1/2* z3^2-63/32*z5*Sinf+1/40*ln2^5*Sinf+1/72*ln2^6+Sinf*li5half- 1/2*Sinf^2*li4half; Fill Stab6(1,1,-1,1,1,1) =-z2*z3*ln2-1/2*z2*z3*Sinf-1/6*z2* ln2^3*Sinf-1/8*z2*ln2^4-1/2*z2*li4half-1/20*z2^2*ln2*Sinf-1/4 *z2^2*ln2^2-23/140*z2^3+1/2*z3*ln2^2*Sinf+1/2*z3*ln2^3+1/2* z3^2+2*z5*ln2+1/32*z5*Sinf+1/40*ln2^5*Sinf+1/72*ln2^6+Sinf* li5half-1/2*Sinf^2*li4half; Fill Stab6(1,1,0,-1,-1,-1) =-7/8*z2*z3*ln2-1/4*z2*ln2^2*Sinf^2 +1/2*z2*ln2^3*Sinf+1/16*z2*ln2^4-2*z2*li4half+53/40*z2^2*ln2* Sinf-21/20*z2^2*ln2^2+7/10*z2^2*Sinf^2+1/14*z2^3-21/16*z3*ln2 *Sinf^2-21/16*z3*ln2^2*Sinf-7/24*z3*ln2^3-107/64*z3^2-279/64* z5*ln2-99/32*z5*Sinf-ln2*Sinf*li4half+2*ln2*li5half-1/2*ln2^2 *li4half-1/12*ln2^4*Sinf^2-1/15*ln2^5*Sinf-1/36*ln2^6+3*Sinf* li5half-2*Sinf^2*li4half+7*li6half+19/4*s6; Fill Stab6(1,1,0,-1,-1,1) =7/16*z2*z3*ln2+1/12*z2*ln2^3*Sinf-1/ 12*z2*ln2^4-3/2*z2*li4half-43/40*z2^2*ln2*Sinf-2/5*z2^2*ln2^2 +39/80*z2^2*Sinf^2+209/560*z2^3+7/48*z3*ln2^3-109/64*z3^2+ 81/64*z5*Sinf-1/16*ln2^4*Sinf^2-1/120*ln2^5*Sinf+1/720*ln2^6+ Sinf*li5half-3/2*Sinf^2*li4half+li6half+5/2*s6; Fill Stab6(1,1,0,-1,0,-1) =7/8*z2*z3*ln2-5/8*z2*z3*Sinf+1/24*z2* ln2^4+z2*li4half-1/4*z2^2*ln2^2+13/80*z2^2*Sinf^2-157/1680* z2^3-51/128*z3^2+41/32*z5*Sinf; Fill Stab6(1,1,0,-1,0,1) =-35/16*z2*z3*ln2+5/16*z2*z3*Sinf+1/2 *z2*ln2^2*Sinf^2+2/3*z2*ln2^3*Sinf+7/48*z2*ln2^4-5/2*z2*li4half +5/8*z2^2*ln2^2+51/80*z2^2*Sinf^2+1153/840*z2^3-7/4*z3*ln2* Sinf^2-7/4*z3*ln2^2*Sinf-7/12*z3*ln2^3+109/128*z3^2+31/16*z5* ln2+103/32*z5*Sinf-4*ln2*Sinf*li4half-4*ln2*li5half-2*ln2^2* li4half-1/12*ln2^4*Sinf^2-2/15*ln2^5*Sinf-1/18*ln2^6-4*Sinf* li5half-2*Sinf^2*li4half-4*li6half-s6; Fill Stab6(1,1,0,-1,1,-1) =-7/16*z2*z3*ln2+3/8*z2*ln2^2*Sinf^2 -1/12*z2*ln2^3*Sinf-1/16*z2*ln2^4+1/2*z2*li4half-1/20*z2^2* ln2*Sinf+13/20*z2^2*ln2^2+3/80*z2^2*Sinf^2+21/80*z2^3+7/48*z3 *ln2^3+17/128*z3^2+25/32*z5*Sinf+1/2*ln2^2*li4half+1/120* ln2^5*Sinf+13/720*ln2^6-Sinf*li5half-2*li6half-1/2*s6; Fill Stab6(1,1,0,-1,1,1) =-7/8*z2*z3*ln2+1/8*z2*ln2^2*Sinf^2+1/ 6*z2*ln2^3*Sinf-1/24*z2*ln2^4-z2*li4half+1/4*z2^2*ln2^2+1/16* z2^2*Sinf^2+69/560*z2^3-7/16*z3*ln2*Sinf^2-7/16*z3*ln2^2*Sinf +49/128*z3^2+25/32*z5*Sinf-ln2*Sinf*li4half-1/48*ln2^4*Sinf^2 -1/30*ln2^5*Sinf-Sinf*li5half-1/2*Sinf^2*li4half; Fill Stab6(1,1,0,0,-1,-1) =-5/8*z2*z3*ln2+7/8*z2*z3*Sinf+1/4* z2*ln2^2*Sinf^2-1/6*z2*ln2^3*Sinf-5/24*z2*ln2^4-17/20*z2^2*ln2* Sinf+3/10*z2^2*Sinf^2+509/840*z2^3+7/8*z3*ln2^2*Sinf+7/12*z3* ln2^3-41/64*z3^2+15/32*z5*Sinf+ln2^2*li4half-1/24*ln2^4* Sinf^2+1/60*ln2^5*Sinf+7/180*ln2^6-2*Sinf*li5half-Sinf^2* li4half-2*li6half+1/2*s6; Fill Stab6(1,1,0,0,-1,1) =-7/8*z2*z3*Sinf-1/4*z2*ln2^2*Sinf^2- 2/3*z2*ln2^3*Sinf-3/8*z2*ln2^4-11/20*z2^2*Sinf^2-227/168*z2^3 +7/8*z3*ln2*Sinf^2+7/4*z3*ln2^2*Sinf+7/8*z3*ln2^3-9/64*z3^2 -93/32*z5*ln2-39/16*z5*Sinf+4*ln2*Sinf*li4half+6*ln2*li5half +3*ln2^2*li4half+1/24*ln2^4*Sinf^2+2/15*ln2^5*Sinf+1/12*ln2^6 +4*Sinf*li5half+Sinf^2*li4half+6*li6half+3/2*s6; Fill Stab6(1,1,0,0,0,-1) =-1/2*z2*z3*Sinf-7/40*z2^2*Sinf^2-167/ 280*z2^3+7/8*z3^2+93/32*z5*ln2+29/32*z5*Sinf-3/2*s6; Fill Stab6(1,1,0,0,0,1) =z2*z3*Sinf+1/5*z2^2*Sinf^2+37/70*z2^3 -z3^2-2*z5*Sinf; Fill Stab6(1,1,0,0,1,-1) =5/8*z2*z3*ln2+1/6*z2*ln2^3*Sinf+1/12* z2*ln2^4+17/20*z2^2*ln2*Sinf+1/16*z2^2*Sinf^2-1271/1680*z2^3- 7/8*z3*ln2*Sinf^2-7/8*z3*ln2^2*Sinf-7/24*z3*ln2^3-7/32*z3^2- 93/64*z5*ln2-125/64*z5*Sinf+2*ln2*li5half-1/60*ln2^5*Sinf-1/ 90*ln2^6+2*Sinf*li5half+4*li6half+1/4*s6; Fill Stab6(1,1,0,0,1,1) =1/4*z2^2*Sinf^2+53/84*z2^3-z3^2-1/2* z5*Sinf; Fill Stab6(1,1,0,1,-1,-1) =7/8*z2*z3*ln2+7/8*z2*z3*Sinf+5/8*z2* ln2^2*Sinf^2-1/3*z2*ln2^3*Sinf-3/16*z2*ln2^4+2*z2*li4half-53/ 40*z2^2*ln2*Sinf+21/20*z2^2*ln2^2+1/80*z2^2*Sinf^2+59/112*z2^3 +7/8*z3*ln2^2*Sinf+7/12*z3*ln2^3+11/64*z3^2+81/64*z5*Sinf+3/ 2*ln2^2*li4half+1/48*ln2^4*Sinf^2+1/30*ln2^5*Sinf+1/18*ln2^6- 4*Sinf*li5half+1/2*Sinf^2*li4half-5*li6half-5/2*s6; Fill Stab6(1,1,0,1,-1,1) =7/16*z2*z3*ln2-7/8*z2*z3*Sinf-1/8*z2* ln2^2*Sinf^2-3/4*z2*ln2^3*Sinf-5/12*z2*ln2^4+1/2*z2*li4half- 51/40*z2^2*ln2*Sinf+13/20*z2^2*ln2^2-z2^2*Sinf^2-51/35*z2^3+ 21/16*z3*ln2*Sinf^2+35/16*z3*ln2^2*Sinf+49/48*z3*ln2^3+73/64* z3^2+93/64*z5*ln2+87/32*z5*Sinf+3*ln2*Sinf*li4half+4*ln2* li5half+3*ln2^2*li4half+1/12*ln2^4*Sinf^2+1/8*ln2^5*Sinf+67/ 720*ln2^6+2*Sinf^2*li4half+li6half-11/4*s6; Fill Stab6(1,1,0,1,0,-1) =7/4*z2*z3*ln2-z2*z3*Sinf-1/2*z2*ln2^2* Sinf^2-2/3*z2*ln2^3*Sinf-1/6*z2*ln2^4+2*z2*li4half-1/2*z2^2* ln2^2-17/16*z2^2*Sinf^2-4393/1680*z2^3+7/4*z3*ln2*Sinf^2+7/4* z3*ln2^2*Sinf+7/12*z3*ln2^3+23/32*z3^2+279/64*z5*ln2-73/64*z5 *Sinf+4*ln2*Sinf*li4half+4*ln2*li5half+2*ln2^2*li4half+1/12* ln2^4*Sinf^2+2/15*ln2^5*Sinf+1/18*ln2^6+4*Sinf*li5half+2* Sinf^2*li4half+4*li6half-9/4*s6; Fill Stab6(1,1,0,1,0,1) =2*z2*z3*Sinf+7/20*z2^2*Sinf^2+443/420* z2^3-z3^2-11/2*z5*Sinf; Fill Stab6(1,1,0,1,1,-1) =7/16*z2*z3*ln2-3/4*z2*ln2^2*Sinf^2-1/4 *z2*ln2^3*Sinf-1/48*z2*ln2^4+3/2*z2*li4half+12/5*z2^2*ln2*Sinf -23/20*z2^2*ln2^2-3/5*z2^2*Sinf^2-101/35*z2^3+7/16*z3*ln2* Sinf^2+7/16*z3*ln2^2*Sinf+7/48*z3*ln2^3-6*z5*Sinf+3*ln2*Sinf* li4half+6*ln2*li5half+3/2*ln2^2*li4half+1/16*ln2^4*Sinf^2+3/ 40*ln2^5*Sinf+19/720*ln2^6+6*Sinf*li5half+3/2*Sinf^2*li4half+ 10*li6half; Fill Stab6(1,1,0,1,1,1) =3/5*z2^2*Sinf^2+101/35*z2^3-6*z5*Sinf; Fill Stab6(1,1,1,-1,-1,-1) =-7/6*z2*z3*ln2-1/8*z2*z3*Sinf-1/12 *z2*ln2*Sinf^3+1/8*z2*ln2^2*Sinf^2-5/48*z2*ln2^4-3/2*z2*li4half +19/20*z2^2*ln2*Sinf+29/40*z2^2*ln2^2+3/5*z2^2*Sinf^2+61/35* z2^3-z3*ln2*Sinf^2-z3*ln2^2*Sinf-7/18*z3*ln2^3-1/24*z3*Sinf^3 -1/12*z3^2-4*z5*ln2-4*z5*Sinf-1/36*ln2^3*Sinf^3-1/8*ln2^4* Sinf^2-1/12*ln2^5*Sinf-1/48*ln2^6+4*Sinf*li5half-3/2*Sinf^2* li4half-5*li6half; Fill Stab6(1,1,1,-1,-1,1) =-1/6*z2*z3*ln2+7/8*z2*z3*Sinf-1/12* z2*ln2*Sinf^3+1/8*z2*ln2^2*Sinf^2-5/48*z2*ln2^4-3/2*z2*li4half -1/4*z2^2*ln2*Sinf+1/8*z2^2*ln2^2-1/18*z3*ln2^3+7/24*z3* Sinf^3+7/12*z3^2-1/36*ln2^3*Sinf^3-1/8*ln2^4*Sinf^2-1/12* ln2^5*Sinf-1/48*ln2^6+4*Sinf*li5half-3/2*Sinf^2*li4half-5* li6half; Fill Stab6(1,1,1,-1,0,-1) =-1/3*z2*z3*ln2-1/16*z2*z3*Sinf-1/6* z2*ln2*Sinf^3+1/8*z2*ln2^2*Sinf^2+1/12*z2*ln2^3*Sinf-1/2*z2* li4half-7/20*z2^2*ln2*Sinf-1/20*z2^2*ln2^2+11/40*z2^2*Sinf^2+ 11/40*z2^3+13/48*z3*Sinf^3+19/24*z3^2-1/32*z5*Sinf-1/16*ln2^4 *Sinf^2-1/40*ln2^5*Sinf-1/240*ln2^6+3*Sinf*li5half-3/2*Sinf^2 *li4half-3*li6half+1/2*s6; Fill Stab6(1,1,1,-1,0,1) =-55/48*z2*z3*ln2-1/16*z2*z3*Sinf+1/ 12*z2*ln2*Sinf^3+3/8*z2*ln2^2*Sinf^2+1/6*z2*ln2^3*Sinf-1/24*z2* ln2^4-3/2*z2*li4half+61/40*z2^2*ln2*Sinf+91/80*z2^2*ln2^2+7/ 16*z2^2*Sinf^2+661/560*z2^3-21/16*z3*ln2*Sinf^2-21/16*z3*ln2^2* Sinf-7/16*z3*ln2^3-1/6*z3*Sinf^3-179/384*z3^2-155/32*z5*ln2 -39/8*z5*Sinf+ln2*Sinf*li4half+ln2*li5half+1/2*ln2^2*li4half -1/24*ln2^4*Sinf^2+1/120*ln2^5*Sinf+7/720*ln2^6+4*Sinf* li5half-Sinf^2*li4half-2*li6half+1/2*s6; Fill Stab6(1,1,1,-1,1,-1) =-1/3*z2*z3*ln2-7/16*z2*z3*Sinf+1/12 *z2*ln2*Sinf^3+1/4*z2*ln2^2*Sinf^2+1/4*z2*ln2^3*Sinf+1/16*z2* ln2^4+3/5*z2^2*ln2*Sinf+5/8*z2^2*ln2^2-1/40*z2^2*Sinf^2+7/40* z2^3-1/2*z3*ln2^2*Sinf-7/18*z3*ln2^3+1/48*z3*Sinf^3+2/3*z3^2 +1/32*z5*Sinf-1/36*ln2^3*Sinf^3-1/16*ln2^4*Sinf^2-7/120*ln2^5 *Sinf-1/60*ln2^6+Sinf*li5half-2*li6half-1/2*s6; Fill Stab6(1,1,1,-1,1,1) =1/6*z2*z3*ln2+1/16*z2*z3*Sinf+1/12*z2* ln2*Sinf^3+1/4*z2*ln2^2*Sinf^2+1/4*z2*ln2^3*Sinf+1/16*z2*ln2^4 +7/10*z2^2*ln2*Sinf+27/40*z2^2*ln2^2+1/40*z2^2*Sinf^2+111/280 *z2^3-1/2*z3*ln2*Sinf^2-z3*ln2^2*Sinf-5/9*z3*ln2^3-7/48*z3* Sinf^3-1/6*z3^2-2*z5*ln2-63/32*z5*Sinf-1/36*ln2^3*Sinf^3-1/ 16*ln2^4*Sinf^2-7/120*ln2^5*Sinf-1/60*ln2^6+Sinf*li5half-2* li6half-1/2*s6; Fill Stab6(1,1,1,0,-1,-1) =1/16*z2*z3*ln2-3/4*z2*z3*Sinf+1/4*z2* ln2*Sinf^3-1/8*z2*ln2^2*Sinf^2+1/12*z2*ln2^3*Sinf+5/48*z2*ln2^4 +31/20*z2^2*ln2*Sinf-1/16*z2^2*Sinf^2-1/16*z2^3-7/16*z3*ln2^2 *Sinf-7/24*z3*ln2^3-5/48*z3*Sinf^3+67/384*z3^2-27/32*z5*Sinf -1/2*ln2^2*li4half+1/48*ln2^4*Sinf^2-1/120*ln2^5*Sinf-7/360* ln2^6+Sinf*li5half+1/2*Sinf^2*li4half+li6half; Fill Stab6(1,1,1,0,-1,1) =7/16*z2*z3*ln2+1/8*z2*z3*Sinf+1/6*z2* ln2^3*Sinf+7/48*z2*ln2^4+1/2*z2*li4half-1/8*z2^2*ln2^2-3/80* z2^2*Sinf^2+15/112*z2^3-7/16*z3*ln2^2*Sinf-7/24*z3*ln2^3-5/48 *z3*Sinf^3-29/384*z3^2+31/32*z5*ln2+1/8*z5*Sinf-ln2*Sinf* li4half-2*ln2*li5half-ln2^2*li4half-1/30*ln2^5*Sinf-1/36* ln2^6-Sinf*li5half-2*li6half-1/2*s6; Fill Stab6(1,1,1,0,0,-1) =-7/8*z2*z3*ln2+1/8*z2*z3*Sinf+1/4*z2 *ln2^2*Sinf^2+1/3*z2*ln2^3*Sinf+1/12*z2*ln2^4-z2*li4half+1/4* z2^2*ln2^2+3/8*z2^2*Sinf^2+257/280*z2^3-7/8*z3*ln2*Sinf^2-7/8 *z3*ln2^2*Sinf-7/24*z3*ln2^3-1/8*z3*Sinf^3-3/8*z3^2-31/32*z5* ln2+33/32*z5*Sinf-2*ln2*Sinf*li4half-2*ln2*li5half-ln2^2* li4half-1/24*ln2^4*Sinf^2-1/15*ln2^5*Sinf-1/36*ln2^6-2*Sinf* li5half-Sinf^2*li4half-2*li6half+1/2*s6; Fill Stab6(1,1,1,0,0,1) =-1/2*z2*z3*Sinf-1/20*z2^2*Sinf^2-31/ 140*z2^3+1/6*z3*Sinf^3+5/6*z3^2+2*z5*Sinf; Fill Stab6(1,1,1,0,1,-1) =-11/8*z2*z3*ln2+1/8*z2*z3*Sinf-1/4* z2*ln2*Sinf^3+3/8*z2*ln2^2*Sinf^2+5/12*z2*ln2^3*Sinf+1/12*z2* ln2^4-3/2*z2*li4half-31/20*z2^2*ln2*Sinf+3/8*z2^2*ln2^2+3/5* z2^2*Sinf^2+61/35*z2^3-7/8*z3*ln2*Sinf^2-7/8*z3*ln2^2*Sinf-7/ 24*z3*ln2^3+1/24*z3*Sinf^3+1/12*z3^2+4*z5*Sinf-3*ln2*Sinf* li4half-4*ln2*li5half-3/2*ln2^2*li4half-1/16*ln2^4*Sinf^2-11/ 120*ln2^5*Sinf-13/360*ln2^6-4*Sinf*li5half-3/2*Sinf^2*li4half -5*li6half; Fill Stab6(1,1,1,0,1,1) =z2*z3*Sinf-3/5*z2^2*Sinf^2-61/35*z2^3 +1/3*z3*Sinf^3+2/3*z3^2+4*z5*Sinf; Fill Stab6(1,1,1,1,-1,-1) =1/6*z2*z3*ln2-13/48*z2*z3*Sinf+1/12* z2*ln2*Sinf^3+1/8*z2*ln2^2*Sinf^2+1/6*z2*ln2^3*Sinf+1/12*z2* ln2^4+1/48*z2*Sinf^4+1/2*z2*li4half+1/4*z2^2*ln2*Sinf+9/80* z2^2*ln2^2+1/8*z2^2*Sinf^2+9/80*z2^3+1/6*z3*ln2^2*Sinf+1/9*z3 *ln2^3-7/48*z3*Sinf^3-7/24*z3^2+1/48*ln2^2*Sinf^4+1/18*ln2^3* Sinf^3+1/12*ln2^4*Sinf^2+1/24*ln2^5*Sinf+1/120*ln2^6-Sinf* li5half+1/2*Sinf^2*li4half+li6half; Fill Stab6(1,1,1,1,-1,1) =1/3*z2*z3*ln2-5/48*z2*z3*Sinf-1/12*z2* ln2*Sinf^3-1/8*z2*ln2^2*Sinf^2+1/24*z2*ln2^4-1/48*z2*Sinf^4+1/ 2*z2*li4half-13/20*z2^2*ln2*Sinf-27/80*z2^2*ln2^2-13/40*z2^2* Sinf^2-303/560*z2^3+1/2*z3*ln2*Sinf^2+2/3*z3*ln2^2*Sinf+5/18* z3*ln2^3+1/48*z3*Sinf^3+1/24*z3^2+z5*ln2+z5*Sinf+1/48*ln2^2 *Sinf^4+1/18*ln2^3*Sinf^3+1/12*ln2^4*Sinf^2+1/24*ln2^5*Sinf+1/ 120*ln2^6-Sinf*li5half+1/2*Sinf^2*li4half+li6half; Fill Stab6(1,1,1,1,0,-1) =7/16*z2*z3*ln2-11/48*z2*z3*Sinf-1/8*z2 *ln2^2*Sinf^2-1/6*z2*ln2^3*Sinf-1/24*z2*ln2^4-1/48*z2*Sinf^4+ 1/2*z2*li4half-1/8*z2^2*ln2^2-13/40*z2^2*Sinf^2-303/560*z2^3+ 7/16*z3*ln2*Sinf^2+7/16*z3*ln2^2*Sinf+7/48*z3*ln2^3-1/48*z3* Sinf^3-1/24*z3^2-z5*Sinf+ln2*Sinf*li4half+ln2*li5half+1/2* ln2^2*li4half+1/48*ln2^4*Sinf^2+1/30*ln2^5*Sinf+1/72*ln2^6+ Sinf*li5half+1/2*Sinf^2*li4half+li6half; Fill Stab6(1,1,1,1,0,1) =-1/6*z2*z3*Sinf+1/24*z2*Sinf^4+9/20* z2^2*Sinf^2+183/280*z2^3-1/6*z3*Sinf^3-1/3*z3^2-z5*Sinf; Fill Stab6(1,1,1,1,1,-1) =-1/6*z2*z3*ln2-1/12*z2*ln2*Sinf^3-1/ 8*z2*ln2^2*Sinf^2-1/12*z2*ln2^3*Sinf-1/48*z2*ln2^4-9/40*z2^2* ln2*Sinf-9/80*z2^2*ln2^2-1/6*z3*ln2*Sinf^2-1/6*z3*ln2^2*Sinf- 1/18*z3*ln2^3-1/5*z5*ln2-1/120*ln2*Sinf^5-1/48*ln2^2*Sinf^4-1/ 36*ln2^3*Sinf^3-1/48*ln2^4*Sinf^2-1/120*ln2^5*Sinf-1/720*ln2^6; Fill Stab6(1,1,1,1,1,1) =1/6*z2*z3*Sinf+1/48*z2*Sinf^4+9/80*z2^2 *Sinf^2+61/560*z2^3+1/18*z3*Sinf^3+1/18*z3^2+1/5*z5*Sinf+1/ 720*Sinf^6; #endprocedure * *--#] table6 : *--#[ tables : * #procedure tables(size) * * Tables of harmonic series at infinity. * Note that the definition of these series is slightly different from * what are called Euler/Zagier sums. * Notation for the tables: * A zero index means that one should be added to the absolute value * of the next index. The argument is inf (infinity). * Example: S(0,-1,0,0,2,1) = S(R(-2,3,1),inf) * The various weights are in separate files. * This makes that FORM will not even touch the table7.prc file if * size < 7. That saves much time. * File by J. Vermaseren, 5-jun-1998 * #do itabs = 1,`size' #call table`itabs' #enddo #endprocedure * *--#] tables : *--#[ theta : * #procedure theta(i) * * Routine deals with combinations of theta, delta, deltap and * sum functions. These are defined for each j`i'. The parameter gives the * i for which we have to do this. If we have to do them all we have to * sum over i. i=0 is not summed over. * An parameter N signifies N (which is usually identical to j0, * but we can always assume that N >= 0). * * Note: theta(x) = 1, x >= 0, = 0, x < 0 * delta(x) = 1, x = 0, = 0, x != 0 * deltap(x)= 1, x != 0, = 0, x = 0 * * NOTE! We make at one point the assumption that thetap(x) = theta(x+1) * The statement that assumes this has been marked with ***** in front. * * At all points we assume that N >= 0 and j`i' >= 0!!!! * The statements * id den(ep) = acc(1/ep) are for a special application. * In normal use they should be harmless. * * Routine by J.Vermaseren, 17-jan-1998 * #if `i' == N repeat id theta(x1?,x2?,?a) = theta(x1+x2,?a); repeat id delta(x1?,x2?,?a) = delta(x1+x2,?a); repeat id deltap(x1?,x2?,?a) = deltap(x1+x2,?a); repeat id theta(x?)*theta(x?) = theta(x); repeat id delta(x?)*delta(x?) = delta(x); repeat id deltap(x?)*deltap(x?) = deltap(x); id delta(x?)*deltap(x?) = 0; SplitArg,(N),theta,delta,deltap; id theta(x?,N/2) = theta(2*x,N); id theta(x?,-N/2) = theta(2*x,-N); id theta(N/2) = theta(0,N); id theta(-N/2) = delta(N); id delta(N/2) = delta(N); id delta(-N/2) = delta(N); id delta(x?,N/2) = delta(2*x,N); id delta(x?,-N/2) = delta(2*x,-N); id deltap(N/2) = deltap(N); id deltap(-N/2) = deltap(N); id deltap(x?,N/2) = deltap(2*x,N); id deltap(x?,-N/2) = deltap(2*x,-N); id theta(x?neg_,-N) = 0; id delta(x?neg_,-N) = 0; id delta(x?pos_,N) = 0; id theta(x?neg_,-2*N) = 0; id delta(x?neg_,-2*N) = 0; id delta(x?pos_,2*N) = 0; id theta(0,-N) = delta(0,N); id theta(N) = theta(0,N); id theta(2*N) = theta(0,N); id theta(-N) = delta(0,N); id theta(-2*N) = delta(0,N); id delta(N) = delta(0,N); id deltap(N) = theta(-1,N); id delta(-N) = delta(0,N); id deltap(-N) = theta(-1,N); id delta(2*N) = delta(0,N); id deltap(2*N) = theta(-1,N); id delta(-2*N) = delta(0,N); id deltap(-2*N) = theta(-1,N); id delta(x?,-N) = delta(-x,N); id deltap(x?,-N) = deltap(-x,N); id delta(x?,-2*N) = delta(-x/2,N)*Even(x); id deltap(x?,-2*N) = deltap(-x/2,N); id delta(x?,2*N) = delta(x/2,N)*Even(x); id deltap(x?,2*N) = deltap(x/2,N); id deltap(x?,N) = delta_(x)*theta(-1,N) +acc1(theta_(x)-delta_(x))*theta(0,N) +acc1(1-theta_(x))*(theta(x-1,N)+theta(-x-1,-N)); id theta(x?neg_,-N) = 0; id acc1(x?) = x; id,once,delta(x?,N) = theta_(-x)*su(x)*replace_(N,-x); repeat id,once,theta(x1?,N)*theta(x2?,N) = +theta(x1,N)*theta_(x2-x1) +theta(x2,N)*(theta_(x1-x2)-delta_(x1-x2)) ; repeat id,once,theta(x1?,-N)*theta(x2?,-N) = +theta(x1,-N)*theta_(x2-x1) +theta(x2,-N)*(theta_(x1-x2)-delta_(x1-x2)) ; id theta(x?pos0_,-N) = sum_(jjj,0,x,delta(-jjj,N)); id,once,delta(x?,N) = theta_(-x)*su(x)*replace_(N,-x); id su(x?) = delta(x+N); #do ii = 1,`MAXWEIGHT' if ( match(sum`ii'(j`ii',x1?,x2?)) ); id sum`ii'(j`ii',x1?,x2?) = sum`ii'(j`ii',x1,x2,x2-x1); if ( match(sum`ii'(j`ii',x1?,x2?,x3?pos0_)) ); id theta`ii'(x1?,x2?) = theta_(x1+x2); id den`ii'(x1?,x2?) = den(x1+x2); id fac`ii'(x1?,x2?) = fac(x1+x2); id invfac`ii'(x1?,x2?) = invfac(x1+x2); id S`ii'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id bino`ii'(x1?,x2?,x3?) = fac(x1)*invfac(x2+x3)*invfac(x1-x2-x3); id sign`ii'(x?) = sign(x); repeat id sum`ii'(j`ii',x1?,x2?,x3?pos0_) = sum`ii'(j`ii',x1,x2-1,x3-1)+replace_(j`ii',x2); id sum`ii'(j`ii',x1?,x2?,x3?neg_) = 0; else; id sum`ii'(j`ii',x1?,x2?,x3?neg_) = 0; id sum`ii'(j`ii',x1?,x2?,x3?) = sum`ii'(j`ii',x1,x2); endif; else; id theta`ii'(x1?,x2?) = theta_(x1+x2); id delta`ii'(x1?,x2?) = delta_(x1+x2); id deltap`ii'(x1?,x2?) = deltap_(x1+x2); id den`ii'(x1?,x2?) = den(x1+x2); id fac`ii'(x1?,x2?) = fac(x1+x2); id invfac`ii'(x1?,x2?) = invfac(x1+x2); id S`ii'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id bino`ii'(x1?,x2?,x3?) = fac_(x1)*invfac_(x2+x3)*invfac_(x1-x2-x3); id sign`ii'(x?) = sign_(x); endif; #enddo id den(ep) = acc(1/ep); id delta(x1?,x2?) = delta(x1+x2); id deltap(x1?,x2?) = deltap(x1+x2); id theta(x1?,x2?) = theta(x1+x2); id delta(x?) = delta_(x); id delta_(x?) = delta(x); id deltap(x?) = deltap_(x); id deltap_(x?) = deltap(x); id theta(x?) = theta_(x); id theta_(x?) = theta(x); #else repeat id f?{theta,theta0,...,theta`i',delta,delta0,...,delta`i',deltap,deltap0,...,deltap`i'}(x1?,x2?,?a) = f(x1+x2,?a); id f?{theta0,...,theta`i'}(x?) = theta(x); id f?{delta0,...,delta`i'}(x?) = delta(x); id f?{deltap0,...,deltap`i'}(x?) = deltap(x); id theta_(x?) = theta(x); id delta_(x?) = delta(x); id deltap_(x?) = deltap(x); repeat id theta(x?)*theta(x?) = theta(x); repeat id delta(x?)*delta(x?) = delta(x); repeat id deltap(x?)*deltap(x?) = deltap(x); SplitArg,(j`i'),theta,delta,deltap; id delta(x?,j`i') = delta`i'(x,j`i'); id deltap(x?,j`i') = deltap`i'(x,j`i'); id theta(x?,j`i') = theta`i'(x,j`i'); id delta(x?,2*j`i') = delta`i'(x/2,j`i')*Even(x); id deltap(x?,2*j`i') = deltap`i'(x,2*j`i'); id theta(x?,2*j`i') = theta`i'(x/2,j`i'); id delta(x?,-j`i') = delta`i'(-x,j`i'); id deltap(x?,-j`i') = deltap`i'(-x,j`i'); id theta(x?,-j`i') = theta`i'(x,-j`i'); id delta(x?,-2*j`i') = delta`i'(-x/2,j`i')*Even(x); id deltap(x?,-2*j`i') = deltap`i'(-x,2*j`i'); id theta(x?,-2*j`i') = theta`i'(x/2,-j`i'); id delta(j`i') = delta`i'(0,j`i'); id deltap(j`i') = deltap`i'(0,j`i'); id theta(j`i') = theta`i'(0,j`i'); id delta(-j`i') = delta`i'(0,j`i'); id deltap(-j`i') = deltap`i'(0,j`i'); id theta(-j`i') = delta`i'(0,j`i'); id delta(2*j`i') = delta`i'(0,j`i'); id deltap(2*j`i') = deltap`i'(0,j`i'); id theta(2*j`i') = theta`i'(0,j`i'); id delta(-2*j`i') = delta`i'(0,j`i'); id deltap(-2*j`i') = deltap`i'(0,j`i'); id theta(-2*j`i') = delta`i'(0,j`i'); id delta`i'(x?pos_,j`i') = 0; id delta`i'(x?neg_,-j`i') = 0; id deltap`i'(x?pos_,j`i') = 1; id deltap`i'(x?pos_,2*j`i') = 1; id deltap`i'(x?neg_,-j`i') = 1; id theta`i'(x?pos0_,j`i') = 1; id theta`i'(x?neg_,-j`i') = 0; #if `i' == 0 * * No sum taking place. * #else id sum`i'(j`i',x1?,x2?)*delta`i'(x?,j`i') = replace_(j`i',-x)*theta(x2+x)*theta(-x-x1)*theta(x2-x1); * * Remaining delta`i' functions do not depend on j`i' any longer: * if ( count(sum`i',1) == 0 ); id theta`i'(x1?,x2?) = theta(x1+x2); id delta`i'(x1?,x2?) = delta(x1+x2); id deltap`i'(x1?,x2?) = deltap(x1+x2); else; ***** repeat id sum`i'(j`i',x1?,x2?)*deltap`i'(x?,j`i') = +sum`i'(j`i',x1,x2)*(theta`i'(x-1,j`i')+theta`i'(-x-1,-j`i')); repeat id sum`i'(j`i',x1?,x2?)*deltap`i'(x?,2*j`i') = +sum`i'(j`i',x1,x2)*(theta`i'(x/2-1/2,j`i')+theta`i'(-x/2-1/2,-j`i')); repeat id theta`i'(?a)*theta`i'(?a) = theta`i'(?a); endif; #endif * * Now we have eliminated the delta functions. * Next are the theta functions. We first try to combine them. * repeat id theta`i'(x1?,j`i')*theta`i'(x2?,j`i') = +theta`i'(x1,j`i')*theta(x2-x1) +theta`i'(x2,j`i')*(theta(x1-x2)-delta(x1-x2)) ; repeat id theta`i'(x1?,-j`i')*theta`i'(x2?,-j`i') = +theta`i'(x1,-j`i')*theta(x2-x1) +theta`i'(x2,-j`i')*(theta(x1-x2)-delta(x1-x2)) ; repeat id delta`i'(x?,j`i')*delta`i'(x?,j`i') = delta`i'(x,j`i'); #if `i' == 0 * #else if ( count(delta`i',1) > 0 ); id sum`i'(j`i',x1?,x2?)*delta`i'(x?,j`i') = replace_(j`i',-x)*theta(x2+x)*theta(-x-x1); endif; if ( count(sum`i',1) == 0 ); id theta`i'(x1?,x2?) = theta(x1+x2); id delta`i'(x1?,x2?) = delta(x1+x2); id deltap`i'(x1?,x2?) = deltap(x1+x2); endif; id sum`i'(j`i',x1?,x2?)*theta`i'(x?,j`i') = +sum`i'(j`i',x1,x2)*theta(x1+x) +sum`i'(j`i',-x,x2)*theta(x2+x)*(theta(-x1-x)-delta(x+x1)); id sum`i'(j`i',x1?,x2?)*theta`i'(x?,-j`i') = +sum`i'(j`i',x1,x2)*theta(x-x2) +sum`i'(j`i',x1,x)*theta(x-x1)*(theta(x2-x)-delta(x-x2)); #endif if ( match(sum`i'(j`i',x1?,x2?)) ); id sum`i'(j`i',x1?,x2?) = sum`i'(j`i',x1,x2,x2-x1); if ( match(sum`i'(j`i',x1?,x2?,x3?pos0_)) ); id delta`i'(x1?,x2?) = delta_(x1+x2); id deltap`i'(x1?,x2?) = deltap_(x1+x2); id theta`i'(x1?,x2?) = theta_(x1+x2); id den`i'(x1?,x2?) = den(x1+x2); id fac`i'(x1?,x2?) = fac(x1+x2); id invfac`i'(x1?,x2?) = invfac(x1+x2); id S`i'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id bino`i'(x1?,x2?,x3?) = fac(x1)*invfac(x2+x3)*invfac(x1-x2-x3); id sign`i'(x?) = sign(x); repeat id sum`i'(j`i',x1?,x2?,x3?pos0_) = sum`i'(j`i',x1,x2-1,x3-1)+replace_(j`i',x2); id sum`i'(j`i',x1?,x2?,x3?neg_) = 0; #do ii = `i'+1,`MAXWEIGHT' if ( match(sum`ii'(j`ii',x1?,x2?)) ); id sum`ii'(j`ii',x1?,x2?) = sum`ii'(j`ii',x1,x2,x2-x1); if ( match(sum`ii'(j`ii',x1?,x2?,x3?int_)) ); id theta`ii'(x1?,x2?) = theta_(x1+x2); id den`ii'(x1?,x2?) = den(x1+x2); id fac`ii'(x1?,x2?) = fac(x1+x2); id invfac`ii'(x1?,x2?) = invfac(x1+x2); id S`ii'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id bino`ii'(x1?,x2?,x3?) = fac(x1)*invfac(x2+x3)*invfac(x1-x2-x3); id sign`ii'(x?) = sign(x); repeat id sum`ii'(j`ii',x1?,x2?,x3?pos0_) = sum`ii'(j`ii',x1,x2-1,x3-1)+replace_(j`ii',x2); id sum`ii'(j`ii',x1?,x2?,x3?neg_) = 0; else; id sum`ii'(j`ii',x1?,x2?,x3?) = sum`ii'(j`ii',x1,x2); #enddo #do ii = `i'+1,`MAXWEIGHT' endif; endif; #enddo else; id sum`i'(j`i',x1?,x2?,x3?neg_) = 0; id sum`i'(j`i',x1?,x2?,x3?) = sum`i'(j`i',x1,x2); endif; id den(ep) = acc(1/ep); else; id theta`i'(x1?,x2?) = theta_(x1+x2); id delta`i'(x1?,x2?) = delta_(x1+x2); id deltap`i'(x1?,x2?) = deltap_(x1+x2); id den`i'(x1?,x2?) = den(x1+x2); id fac`i'(x1?,x2?) = fac(x1+x2); id invfac`i'(x1?,x2?) = invfac(x1+x2); id S`i'(R(?a),x1?,x2?) = S(R(?a),x1+x2); id bino`i'(x1?,x2?,x3?) = fac_(x1)*invfac_(x2+x3)*invfac_(x1-x2-x3); id sign`i'(x?) = sign_(x); endif; id den(ep) = acc(1/ep); id theta(x1?,x2?) = theta(x1+x2); id delta(x1?,x2?) = delta(x1+x2); id deltap(x1?,x2?) = deltap(x1+x2); id delta(x?) = delta_(x); id delta_(x?) = delta(x); id deltap(x?) = deltap_(x); id deltap_(x?) = deltap(x); id theta(x?) = theta_(x); id theta_(x?) = theta(x); #endif * #endprocedure * *--#] theta : *--#[ StoZ : * #procedure StoZ(S,Z) * repeat; id,once,`S'(R(?a,n1?),N?) = SSZZ(R(n1),R(?a),N); repeat; id,SSZZ(R(n1?,?a),R(?b,n2?),N?) = SSZZ(R(n2,n1,?a),R(?b),N) +SSZZ(R(n1*sig_(n2)+n2*sig_(n1),?a),R(?b),N); endrepeat; id SSZZ(R(?a),R,N?) = `Z'(R(?a),N); endrepeat; * #endprocedure * *--#] StoZ : *--#[ ZtoS : * #procedure ZtoS(Z,S) * repeat; id,once,`Z'(R(?a,n1?),N?) = SSZZ(R(n1),R(?a),N); repeat; id,SSZZ(R(n1?,?a),R(?b,n2?),N?) = SSZZ(R(n2,n1,?a),R(?b),N) -SSZZ(R(n1*sig_(n2)+n2*sig_(n1),?a),R(?b),N); endrepeat; id SSZZ(R(?a),R,N?) = `S'(R(?a),N); endrepeat; * #endprocedure * *--#] ZtoS : *--#] Procedures : *--#[ Programs : *--#[ Powsum : * * This program is used to derive the powsum tables in the nndecl part. * Here it is deactivated with the #ifdef. * If you need to extend the tables, please copy the code to a separate * file (for example sumprog.frm), give MAX its proper value and run it. * Finally convert the output into extra code for filling the tables in * the nndecl.h part of this file. * #ifdef `THISISSUMPROGFORPOWSUM' #- #define MAX "20" #include summer.h CF F; Format nospaces; Off Statistics; .global * * We use the relation * sum(j,1,n,n*(n+1)*...*(n+k)) = n*(n+1)*...*(n+k+1)/(k+2) * The one with the sign we do via the doubling formula * Program by Jos Vermaseren, 4-sep-2003 * #do i = 1,`MAX' G F`i'(n) = n^`i'; #enddo Multiply num(0,n); #do i = 0,`MAX' id num(x?,n)*n = num(x+1,n)-num(x,n)*x; .sort #enddo id num(i?,n?) = num(i+1,n)/(i+1); repeat id num(i?pos_,n?) = num1(n)*num(i-1,n+1); id num(0,n?) = 1; repeat id num1(x1?)*num1(x2?) = num1(x1*x2); id num1(x?) = x; Print +f; .store #do i = 1,`MAX' G G`i' = (1+sign_(n))/2*(2*2^`i'*F(`i',n/2)-F(`i',n)) +(1-sign_(n))/2*(2*2^`i'*F(`i',(n+1)/2)-F(`i',n+1)+(n+1)^`i'*sign_(n)); #enddo #do i = 1,`MAX' id F(`i',nn?) = F`i'(nn); #enddo id sign_(n)*sign_(n) = 1; B sign_; Print +f; .store #do i = 1,`MAX' G FF`i'(n) = F`i'(n); #enddo #do i = 1,`MAX' G GG`i'(n) = G`i'; #enddo Multiply replace_(n,n-1); id sign_(n-1) = -sign_(n); B sign_; Print +f; .end #endif * *--#] Powsum : *--#] Programs : #endif