gap> Read("/home/math6/wdj/gap/games/grpdata.g");
gap> Read("/home/math6/wdj/gap/new/AbStab.g");
The record 'descriptions' contains brief descriptions of the functions
in this file.
Functions of importance: MakeAbStabChain, FactorPermGroupElement, Shrink
gap> descriptions;
rec(
  MakeAbChainShort := 
   "MakeAbChainShort( G )\n An attempt to shorten the generators of the stabil\
izer subgroups",
  Shrink := 
   "Shrink( G, elm )\n Shrinks the length of the word that represents elm in G\
.",
  map := "map( G, a )\n Maps the abstract word a to an element of G",
  FactorPermGroupElement := 
   "FactorPermGroupElement( G, elm )\n Returns an abstract word that represent\
s elm in the generators of G",
  MakeAbStabChain := 
   "MakeAbStabChain( G <,l > )\n Creates a chain of stabilizer subgroups for G\
, with preference given to the\n ordering of the points listed in l",
  FirstStabilizer := 
   "FirstStabilizer( G <,l > )\n Returns the stabilizer in G of the first move\
d point in l",
  NewMinGenSet := "NewMinGenSet( X )\n An attempt at a faster MinGenSet",
  MinGenSet := 
   "MinGenSet( X )\n Returns a group generated by X (either a group or a set o\
f generators) that\n has a subset of X (or X.generators) as generators, with p\
reference to\n the ordering of X",
  WordInStrongGens := 
   "WordInStrongGens(G,x)\n Writes x in terms of strong generators of G",
  WordModStabilizer := 
   "WordModStabilizer(G,x)\n Returns [s, a], where s is in a stabilizer subgro\
up of G, a is a word and\n x = map(G,a) * y",
  GenTable := 
   "GenTable( G <,base> <,wantInverse> )\n Creates a table of elements that ge\
nerate a stabilizing subgroup of G",
  LeftSchreier := 
   "LeftSchreier( G <,base> <,wantInverse> )\n Creates the left Schreier trans\
versal in G of a stabilizer subgroup",
  MakeShortStab := 
   "MakeShortStab( G <,base> <,wantInverse> )\n The same as MakeStab, but it t\
ries to make the transversal elements shorter",
  MakeStab := 
   "MakeStab( G <,base> <,wantInverse> )\n Creates the first portion of the ch\
ain",
  AddSpot := 
   "AddSpot( list, position, thing )\n Binds 'list[position]' and adds 'thing'\
 to the list 'list[postition]'",
  AddAbstractGens := 
   "AddAbstractGens( G )\n Creates the list G.abstractGenerators corresponding\
 to G.generators.",
  Shrink_arg := "Shrink_arg( list )\n Converts [arg] to arg",
  execute := "execute( f, list )\n Does f(arg), where list = [arg]" )
gap> descriptions;
rec(
  MakeAbChainShort := 
   "MakeAbChainShort( G )\n An attempt to shorten the generators of the stabil\
izer subgroups",
  Shrink := 
   "Shrink( G, elm )\n Shrinks the length of the word that represents elm in G\
.",
  map := "map( G, a )\n Maps the abstract word a to an element of G",
  FactorPermGroupElement := 
   "FactorPermGroupElement( G, elm )\n Returns an abstract word that represent\
s elm in the generators of G",
  MakeAbStabChain := 
   "MakeAbStabChain( G <,l > )\n Creates a chain of stabilizer subgroups for G\
, with preference given to the\n ordering of the points listed in l",
  FirstStabilizer := 
   "FirstStabilizer( G <,l > )\n Returns the stabilizer in G of the first move\
d point in l",
  NewMinGenSet := "NewMinGenSet( X )\n An attempt at a faster MinGenSet",
  MinGenSet := 
   "MinGenSet( X )\n Returns a group generated by X (either a group or a set o\
f generators) that\n has a subset of X (or X.generators) as generators, with p\
reference to\n the ordering of X",
  WordInStrongGens := 
   "WordInStrongGens(G,x)\n Writes x in terms of strong generators of G",
  WordModStabilizer := 
   "WordModStabilizer(G,x)\n Returns [s, a], where s is in a stabilizer subgro\
up of G, a is a word and\n x = map(G,a) * y",
  GenTable := 
   "GenTable( G <,base> <,wantInverse> )\n Creates a table of elements that ge\
nerate a stabilizing subgroup of G",
  LeftSchreier := 
   "LeftSchreier( G <,base> <,wantInverse> )\n Creates the left Schreier trans\
versal in G of a stabilizer subgroup",
  MakeShortStab := 
   "MakeShortStab( G <,base> <,wantInverse> )\n The same as MakeStab, but it t\
ries to make the transversal elements shorter",
  MakeStab := 
   "MakeStab( G <,base> <,wantInverse> )\n Creates the first portion of the ch\
ain",
  AddSpot := 
   "AddSpot( list, position, thing )\n Binds 'list[position]' and adds 'thing'\
 to the list 'list[postition]'",
  AddAbstractGens := 
   "AddAbstractGens( G )\n Creates the list G.abstractGenerators corresponding\
 to G.generators.",
  Shrink_arg := "Shrink_arg( list )\n Converts [arg] to arg",
  execute := "execute( f, list )\n Does f(arg), where list = [arg]" )
gap> G:=MinGenSet(f1,f2,f3,f4,r1,r2,r3,r4);
Error, Function: number of args must be 1
gap> gen:=Set([f1,f2,f3,f4,r1,r2,r3,r4]);
[ (25,26,27,28,29,30,31,32), (17,18,19,20,21,22,23,24), 
  ( 9,10,11,12,13,14,15,16), ( 4,31)( 5,30)( 6,29)( 7,28)(12,23)(13,22)(14,21)
    (15,20), ( 3,30)( 4,29)( 5,28)( 6,27)(11,22)(12,21)(13,20)(14,19), 
  ( 2,29)( 3,28)( 4,27)( 5,26)(10,21)(11,22)(12,23)(13,24), (1,2,3,4,5,6,7,8),
  ( 1,28)( 2,27)( 3,26)( 4,25)( 9,20)(10,19)(11,18)(12,17) ]
gap> G:=MinGenSet(gen);
Group( (25,26,27,28,29,30,31,32), (17,18,19,20,21,22,23,24), ( 9,10,11,12,13,
 14,15,16), ( 4,31)( 5,30)( 6,29)( 7,28)(12,23)(13,22)(14,21)(15,20), ( 3,30)
( 4,29)( 5,28)( 6,27)(11,22)(12,21)(13,20)(14,19), ( 2,29)( 3,28)( 4,27)
( 5,26)(10,21)(11,22)(12,23)(13,24), (1,2,3,4,5,6,7,8) )
gap> Size(G);
437763136697395052544000000
gap> f1;
( 1,28)( 2,27)( 3,26)( 4,25)( 9,20)(10,19)(11,18)(12,17)
gap> 2_cycle:=(1,2);
(1,2)
gap> 2_cycle in G;
true
gap> 2cycle:=Shrink(G,2_cycle);
g1^-2*g5^-1*g1*g4^-1*g1*g4^-1*g1^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-3*g5^-1*g1^-1*g\
5^-1*g7*g5^-1*g1^2*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7*g5^-1*\
g1^-1*g5^-1*g7^-1*g5^-1*g1^-4*g5^-1*g7*g5^-1*g1*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^\
-2*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7^4*g5^-1*g1\
*g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^2*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^3*g\
5^-1*g1*g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1

gap> FactorPermGroupElement(G,f2);
g6
gap> FactorPermGroupElement(G,f3);
g5
gap> FactorPermGroupElement(G,f4);
g4
gap> FactorPermGroupElement(G,r1);
g7
gap> FactorPermGroupElement(G,r2);
g3
gap> FactorPermGroupElement(G,r3);
g2
gap> FactorPermGroupElement(G,r4);
g1
gap> 2cyclea:=Shrink(G,2cycle);
g1^-2*g5^-1*g1*g4^-1*g1*g4^-1*g1^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-3*g5^-1*g1^-1*g\
5^-1*g7*g5^-1*g1^2*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7*g5^-1*\
g1^-1*g5^-1*g7^-1*g5^-1*g1^-4*g5^-1*g7*g5^-1*g1*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^\
-2*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1*g1^2*g5^-1*g7^4*g5^-1*g1\
*g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7*g5^-1*g1^2*g5^-1*g7^-1*g5^-1*g1*g5^-1*g7^3*g\
5^-1*g1*g5^-1*g7^-3*g5^-1*g1^-1*g5^-1*g7^2*g5^-1*g1^-1*g5^-1*g7^-1*g5^-1
gap> quit;



cycle2:=[r4^(-2),f3,r4,f4,r4,f4,r4^(-1),
r1^2,f3,r4^(-1),f3,r1^(-3),f3,r4^(-1),
f3,r1,f3,r4^2,f3,r1,f3,r4^(-1),
f3,r1^(-1),f3,r4^2,f3,r1,
f3,r4^(-1),f3,r1^(-1),f3,r4^(-4),f3,r1,
f3,r4,f3,r1^(-1),f3,r4,f3,
r1^(-2),f3,r4^(-1),f3,r1,f3,r4^(-1),f3,r1^(-1),
f3,r4^2,f3,r1^4,f3,r4,f3,
r1^(-3),f3,r4^(-1),f3,r1,f3,r4^2,
f3,r1^(-1),f3,r4,f3,r1^3,f3,r4,
f3,r1^(-3),f3,r4^(-1),f3,
r1^2,f3,r4^(-1),f3,r1^(-1),f3];