Modular non-alternating sums




The files here contain complete systems in the sense that for each weight we have all sums for all depths. Calculus however is modulus the prime number 2147479273 and products of lower weight objects have been omitted. Note however that sums that can be obtained trivially by a duality transformation were never part of the calculation. Also the divergent sums are not in the tables as they can easily be obtained by inverse shuffle or stuffle relations.

There is one big problem: the way the elements are treated elements that are zero are not listed in the tables. This will be corrected in the future.

The .log files are the output of the actual runs. They are the `raw' data.

hex7.log.bz2 Weight 7 (636).
hex8.log.bz2 Weight 8 (747).
hex9.log.bz2 Weight 9 (1026).
hex10.log.bz2 Weight 10 (1387).
hex11.log.bz2 Weight 11 (3180).
hex12.log.bz2 Weight 12 (4423).
hex13.log.bz2 Weight 13 (14776).
hex14.log.bz2 Weight 14 (31171).
hex15.log.bz2 Weight 15 (72736).
hex16.log.bz2 Weight 16 (198302).
hex17.log.bz2 Weight 17 (573367).
hex18.log.bz2 Weight 18 (1312607).
hex19.log.bz2 Weight 19 (3871527).
hex20.log.bz2 Weight 20 (8893495).
hex21.log.bz2 Weight 21 (25098764).
hex22.log.bz2 Weight 22 (62575127).
hex23.log.bz2 Weight 23 (166672740).
hex24.log.bz2 Weight 24 (434658649).

The .prc table files are

mzv7m.prc.bz2 Weight 7 (241).
mzv8m.prc.bz2 Weight 8 (284).
mzv9m.prc.bz2 Weight 9 (592).
mzv10m.prc.bz2 Weight 10 (838).
mzv11m.prc.bz2 Weight 11 (2588).
mzv12m.prc.bz2 Weight 12 (3717).
mzv13m.prc.bz2 Weight 13 (13809).
mzv14m.prc.bz2 Weight 14 (29730).
mzv15m.prc.bz2 Weight 15 (70278).
mzv16m.prc.bz2 Weight 16 (194269).
mzv17m.prc.bz2 Weight 17 (568910).
mzv18m.prc.bz2 Weight 18 (1303104).
mzv19m.prc.bz2 Weight 19 (3858928).
mzv20m.prc.bz2 Weight 20 (8863840).
mzv21m.prc.bz2 Weight 21 (25054954).
mzv22m.prc.bz2 Weight 22 (62292685).
mzv23m.prc.bz2 Weight 23 (166201067).
mzv24ma.prc.bz2 Weight 24 (113). mzv24ma.h.bz2

The file for weight 24 was rather big. We have split it in two and it can either be run in two parts with mzv24ma and mzv24mb or as one part with mzv24m. The last may need a computer with more than 16 Gbytes of memory.

The binary .sav files are

mzv7m.sav.bz2 Weight 7 (321).
mzv8m.sav.bz2 Weight 8 (367).
mzv9m.sav.bz2 Weight 9 (685).
mzv10m.sav.bz2 Weight 10 (795).
mzv11m.sav.bz2 Weight 11 (2184).
mzv12m.sav.bz2 Weight 12 (2768).
mzv13m.sav.bz2 Weight 13 (10818).
mzv14m.sav.bz2 Weight 14 (22691).
mzv15m.sav.bz2 Weight 15 (57633).
mzv16m.sav.bz2 Weight 16 (164051).
mzv17m.sav.bz2 Weight 17 (502779).
mzv18m.sav.bz2 Weight 18 (1164663).
mzv19m.sav.bz2 Weight 19 (3436018).
mzv20m.sav.bz2 Weight 20 (7965625).
mzv21m.sav.bz2 Weight 21 (22458968).
mzv22m.sav.bz2 Weight 22 (56923377).
mzv23m.sav.bz2 Weight 23 (149778023).
mzv24m.sav.bz2 Weight 24 (370158408).

and the .tbl files are given below. Note that some of these files were rather costly to produce. The file for weight 24 contains more than 2000000 table elements.

mzv7m.tbl.bz2 Weight 7 (341).
mzv8m.tbl.bz2 Weight 8 (443).
mzv9m.tbl.bz2 Weight 9 (860).
mzv10m.tbl.bz2 Weight 10 (1360).
mzv11m.tbl.bz2 Weight 11 (3407).
mzv12m.tbl.bz2 Weight 12 (5387).
mzv13m.tbl.bz2 Weight 13 (17199).
mzv14m.tbl.bz2 Weight 14 (35474).
mzv15m.tbl.bz2 Weight 15 (83224).
mzv16m.tbl.bz2 Weight 16 (215121).
mzv17m.tbl.bz2 Weight 17 (603211).
mzv18m.tbl.bz2 Weight 18 (1381021).
mzv19m.tbl.bz2 Weight 19 (3883367).
mzv20m.tbl.bz2 Weight 20 (8868968).
mzv21m.tbl.bz2 Weight 21 (24353126).
mzv22m.tbl.bz2 Weight 22 (61334250).
mzv23m.tbl.bz2 Weight 23 (158641719).
mzv24m.tbl.bz2 Weight 24 (394353847).

The other files are:

hex.frm The main program that produced the .log files. (6131)
hex.h The library used by hex.frm. (7975)
tosav.frm Creates the .sav files from the expr files. (703).
maketbl.frm The program that produced the .tbl files from the htable files. (456)

The baseinput.h file contains also results from the limited runs. It is used as input for the newbasis program. In baseinput.h we have collected only those sums that are candidate elements for a push down basis. In newbasis.frm we make a guess for such a basis and see whether newbasis.prc can then indeed create a procedure for this change of basis. If this procedure is complete we have indeed the right number of independent objects.

We have used the bzip2 program to compress because of its greater compression rate. Example:

expr23.h 2058458913
expr23.h.gz 287469357
expr23.h.bz2 166275216

The disadvantage is that the compression takes much time, but that is a one-time investment.

When studying the large files, please keep in mind that most editors have problems with files of several Gbytes. This holds specially on 32-bits systems and systems that have a memory that is smaller than a few times the size of the file.