gap> Read("c:/gap/games/circles/circle5.g");
The record 'descriptions' contains brief descriptions of the functions
in this file.
Functions of importance: MakeAbStabChain, FactorPermGroupElement, Shrink
gap> g;
( 6,16,13,26,23,19,15,12,21,18,30,27,14,20)(17,22)(24,29,28,25)
gap> G;
Group( ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12), ( 1,13,14,15,16,17, 7,18,19,20,
 21,22), ( 4,23,24,15,25,26,10,27,28,20,29,30) )
gap> w:=FactorPermGroupElement(G,g);
g1^-1*g3^-1*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2*g1^-2*g3^3*g1^2*g2^-1*g1^-2*g3*g1^2\
*g2*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2*g1^-2*g3^2*g1^2*g2^-1*g1^-2*g3*\
g1^2*g2*g1^-2*g3^-2*g1^2*g2^-1*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^3*g1^-2\
*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2*g1^-2*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-4*g1^-2*\
g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-2*g1^-2*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2*g1^-2*g\
3^-1*g1^2*g2^-1*g1^-2*g3^3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2*\
g1^-2*g3*g1^2*g2^-1*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^2*g1^-2*g3*g1^2*g2\
^-1*g1^-2*g3^-1*g1^2*g2^4*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3*\
g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2^-1*g1^-2*g3^3*g1^2*g2*g1\
^-2*g3^-1*g1^2*g2^-1*g1^-2*g3*g1^2*g2^2*g1^-2*g3^-1*g1^2*g2^2*g1^-2*g3*g1^2*g2\
^-1*g1^-2*g3^-1*g1^2*g2^-4*g1^-2*g3*g1^2*g2*g1^-2*g3^-3*g1^2*g2^-1*g1^-2*g3^2*\
g1^2*g2^-1*g1^-1
gap> G.abstractGenerators;
[ g1, g2, g3 ]
gap> G.generators;
[ ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12), ( 1,13,14,15,16,17, 7,18,19,20,21,22)
    , ( 4,23,24,15,25,26,10,27,28,20,29,30) ]
gap> MappedWord(w,G.abstractGenerators,G.generators);
( 6,16,13,26,23,19,15,12,21,18,30,27,14,20)(17,22)(24,29,28,25)
gap> g1:=r1;
( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12)
gap> g2:=r2;
( 1,13,14,15,16,17, 7,18,19,20,21,22)
gap> g3:=r3;
( 4,23,24,15,25,26,10,27,28,20,29,30)
gap> w;
g1^-1*g3^-1*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2*g1^-2*g3^3*g1^2*g2^-1*g1^-2*g3*g1^2\
*g2*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2*g1^-2*g3^2*g1^2*g2^-1*g1^-2*g3*\
g1^2*g2*g1^-2*g3^-2*g1^2*g2^-1*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^3*g1^-2\
*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2*g1^-2*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-4*g1^-2*\
g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-2*g1^-2*g3*g1^2*g2*g1^-2*g3^-1*g1^2*g2*g1^-2*g\
3^-1*g1^2*g2^-1*g1^-2*g3^3*g1^2*g2*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2*\
g1^-2*g3*g1^2*g2^-1*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^2*g1^-2*g3*g1^2*g2\
^-1*g1^-2*g3^-1*g1^2*g2^4*g1^-2*g3*g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3*\
g1^2*g2^-1*g1^-2*g3^-1*g1^2*g2^-1*g1^-2*g3^-2*g1^2*g2^-1*g1^-2*g3^3*g1^2*g2*g1\
^-2*g3^-1*g1^2*g2^-1*g1^-2*g3*g1^2*g2^2*g1^-2*g3^-1*g1^2*g2^2*g1^-2*g3*g1^2*g2\
^-1*g1^-2*g3^-1*g1^2*g2^-4*g1^-2*g3*g1^2*g2*g1^-2*g3^-3*g1^2*g2^-1*g1^-2*g3^2*\
g1^2*g2^-1*g1^-1
gap> FactorPermGroupElement(G,r1);
g1
gap> r1;
( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12)
gap> FactorPermGroupElement(G,r2);
g2
gap> r2;
( 1,13,14,15,16,17, 7,18,19,20,21,22)
gap> FactorPermGroupElement(G,r3);
g3
gap> r3;
( 4,23,24,15,25,26,10,27,28,20,29,30)
gap> w1:=Shrink(G,g);
g3^-1*g2^-1*g1^-1*g3^-2*g1*g2*g1^-1*g3^3*g1^2*g2^2*g1^-2*g3^-1*g1^2*g2*g1^-2*g\
3*g1^2*g2^-1*g1^-1*g3^-1*g2^-3*g3*g2*g1*g2*g1^-2*g3^-1*g1^2*g2^-6*g1^-1*g3^-6*\
g2^2*g3*g2*g3^2*g1*g2^-1*g1^-1
gap> MappedWord(w1,G.abstractGenerators,G.generators);
( 6,16,13,26,23,19,15,12,21,18,30,27,14,20)(17,22)(24,29,28,25)
gap> w2:=r3^-1*r2^-1*r1^-1*r3^-2*r1*r2*r1^-1*r3^3*r1^2*r2^2;
( 1, 2, 3, 4)( 5,23)( 6,19,21,29)( 7, 8, 9,10)(11,27)(12,14,16,25)
(13,15,17,18,20,22)
gap> w3:=r1^-2*r3^-1*r1^2*r2*r1^-2*r3*r1^2*r2^-1*r1^-1*r3^-1;
( 1,12,11,26,25,24,23, 4, 3, 2)( 5,30,29,28,27,10, 9, 8, 7, 6)(14,15)(19,20)
gap> w4:=r2^-3*r3*r2*r1*r2*r1^-2*r3^-1r1^2*r2^-6*r1^-1*r3^-6;
Syntax error: '^' is not associative
w4:=r2^-3*r3*r2*r1*r2*r1^-2*r3^-1r1^2*r2^-6*r1^-1*r3^-6;
                                   ^
gap> w4:=r2^-3*r3*r2*r1*r2*r1^-2*r3^-1*r1^2*r2^-6*r1^-1*r3^-6;
( 1,20,14)( 4, 5,26)( 6,13)( 7,15,19)(10,11,30)(12,18)(16,28,17,21,24,22)
(23,27)(25,29)
gap> w5:=r2^2*r3*r2*r3^2*r1*r2^-1*r1^-1;
( 1,26,28,20)( 4,14,16, 6,17,18)( 7,30,24,15)(10,19,21,12,22,13)(23,25,27,29)
gap> w2*w3*w4*w5;
( 6,16,13,26,23,19,15,12,21,18,30,27,14,20)(17,22)(24,29,28,25)
gap> quit;


r3^(-1),r2^(-1),r1^(-1),r3^(-2),r1,r2,r1^(-1),r3^3,r1^2,r2^2,
r1^(-2),r3^(-1),r1^2,r2,r1^(-2),r3,r1^2,r2^(-1),r1^(-1),r3^(-1),
r2^(-3),r3,r2,r1,r2,r1^(-2),r3^(-1),r1^2,r2^(-6),r1^(-1),r3^(-6),
r2^2,r3,r2,r3^2,r1,r2^(-1),r1^(-1)