README

There are four programs here, makegp, gprun, grrun and conrun.
They are all written in standard C.
To make them all simply type make.

1. makegp
This is just an interactive way of inputting a permutation group.
For example, type
makegp s8
 You get the prompt:
   Input npt, nperms, init. nb.
   (which means number of points, number of generating permutations,
   number of initial base points - usually 0).
 Type:
8 2 0
  You get the prompt:
    Now input perms in cyclic not'n. End each perm with a '.'.
  Type, for example
(1,2)(3,4)(5,6). (2,3,5,7,8).


This produces the file s8.inperm, which is used as input to the next
program. You may decide to create this file directly, and not bother with
makegp.
 
2. gprun
This computes a base and strong generating set.
Type
gprun s8
  s8.inperm is input and s8.outperm is output.

3. grrun
This computes a presentation on the strong generators. The relations of
the presentation are output to stdout. They are also output to
s8.output.rel in a strange format.
For example, type:
grrun s8
  You get the incomprehensible prompt:
    Input a,b,l1,l2.
    maxcos = a*lorb+b
    Exit lookahead after scanning l1 or eliminating l2 cosets.
  I recommend you input
1.5 50 30 1
  Then the relations are printed - for example - negative numebrs denote
  inverses of generators. Often many of these relations are redundant.

4. conrun
If you really want a presentation using your original generators (and not
with the additional strong generators) then use this program first to
compute the regular permutation representation. It should work for groups
up to order about 100000. For example:

conrun -h s8 outperm triv inperm

The regular generators are output to s8.inperm.nr
I suggest you then do

mv s8.inperm.nr s8reg.inperm

Then

gprun -b s8reg

(The -b option means a base is already known - do not use it except in this
situation.)

Then finally:

grrun s8reg

This produces a presentation with 14 relators - again many of these are
redundant - usually the earlier ones are redundant and the later ones
crucial. This example took about 60 seconds on my computer. Magma is much
quicker, and takes only a few seconds, mainly because the coset enumerator in
Magma is so much better.