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..03-May-2022-

READMEH A D03-May-20222.2 KiB7559

conpdc1.cH A D03-May-20228.5 KiB246199

conpdc2.cH A D03-May-20227.6 KiB211191

conpdcd.cH A D03-May-20222.8 KiB8670

gpd.cH A D03-May-20221.4 KiB4635

gpp.cH A D03-May-20226.7 KiB190157

grd.cH A D03-May-20221.4 KiB5139

grp.cH A D03-May-20229.5 KiB288255

makefileH A D03-May-2022311 1614

mg.cH A D03-May-20221.8 KiB5753

permfns.cH A D03-May-20224 KiB166110

README

1There are four programs here, makegp, gprun, grrun and conrun.
2They are all written in standard C.
3To make them all simply type make.
4
51. makegp
6This is just an interactive way of inputting a permutation group.
7For example, type
8makegp s8
9 You get the prompt:
10   Input npt, nperms, init. nb.
11   (which means number of points, number of generating permutations,
12   number of initial base points - usually 0).
13 Type:
148 2 0
15  You get the prompt:
16    Now input perms in cyclic not'n. End each perm with a '.'.
17  Type, for example
18(1,2)(3,4)(5,6). (2,3,5,7,8).
19
20
21This produces the file s8.inperm, which is used as input to the next
22program. You may decide to create this file directly, and not bother with
23makegp.
24
252. gprun
26This computes a base and strong generating set.
27Type
28gprun s8
29  s8.inperm is input and s8.outperm is output.
30
313. grrun
32This computes a presentation on the strong generators. The relations of
33the presentation are output to stdout. They are also output to
34s8.output.rel in a strange format.
35For example, type:
36grrun s8
37  You get the incomprehensible prompt:
38    Input a,b,l1,l2.
39    maxcos = a*lorb+b
40    Exit lookahead after scanning l1 or eliminating l2 cosets.
41  I recommend you input
421.5 50 30 1
43  Then the relations are printed - for example - negative numebrs denote
44  inverses of generators. Often many of these relations are redundant.
45
464. conrun
47If you really want a presentation using your original generators (and not
48with the additional strong generators) then use this program first to
49compute the regular permutation representation. It should work for groups
50up to order about 100000. For example:
51
52conrun -h s8 outperm triv inperm
53
54The regular generators are output to s8.inperm.nr
55I suggest you then do
56
57mv s8.inperm.nr s8reg.inperm
58
59Then
60
61gprun -b s8reg
62
63(The -b option means a base is already known - do not use it except in this
64situation.)
65
66Then finally:
67
68grrun s8reg
69
70This produces a presentation with 14 relators - again many of these are
71redundant - usually the earlier ones are redundant and the later ones
72crucial. This example took about 60 seconds on my computer. Magma is much
73quicker, and takes only a few seconds, mainly because the coset enumerator in
74Magma is so much better.
75