gap> START_TEST("AddToIgs.tst");
# This example was sent to us by Heiko Dietrich. It formerly was very slow to
# compute and suffered from exponent size explosion.
# See also <
https://github.com/gap-packages/polycyclic/issues/17>.
gap> ftl := FromTheLeftCollector( 26 );
<<from the left collector with 26 generators>>
gap> SetRelativeOrder( ftl, 1, 5 );
gap> SetPower( ftl, 1, [ 2, 1, 3, 1, 4, 1, 5, 1, 6, 1 ] );
gap> SetRelativeOrder( ftl, 2, 5 );
gap> SetPower( ftl, 2, [] );
gap> SetRelativeOrder( ftl, 3, 5 );
gap> SetPower( ftl, 3, [] );
gap> SetRelativeOrder( ftl, 4, 5 );
gap> SetPower( ftl, 4, [] );
gap> SetRelativeOrder( ftl, 5, 5 );
gap> SetPower( ftl, 5, [] );
gap> SetRelativeOrder( ftl, 6, 5 );
gap> SetPower( ftl, 6, [] );
gap> SetConjugate( ftl, 2, 1, [ 6, 1 ] );
gap> SetConjugate( ftl, 3, 1, [ 2, 1 ] );
gap> SetConjugate( ftl, 4, 1, [ 3, 1 ] );
gap> SetConjugate( ftl, 5, 1, [ 4, 1 ] );
gap> SetConjugate( ftl, 6, 1, [ 5, 1 ] );
gap> SetConjugate( ftl, 7, 1, [ 26, -1 ] );
gap> SetConjugate( ftl, 7, 6, [ 22, -1 ] );
gap> SetConjugate( ftl, 8, 1, [ 7, 1 ] );
gap> SetConjugate( ftl, 8, 2, [ 23, -1 ] );
gap> SetConjugate( ftl, 9, 1, [ 8, 1 ] );
gap> SetConjugate( ftl, 9, 3, [ 24, -1 ] );
gap> SetConjugate( ftl, 10, 1, [ 9, 1 ] );
gap> SetConjugate( ftl, 10, 4, [ 25, -1 ] );
gap> SetConjugate( ftl, 11, 1, [ 10, 1 ] );
gap> SetConjugate( ftl, 11, 5, [ 26, -1 ] );
gap> SetConjugate( ftl, 12, 1, [ 11, 1, 26, -1 ] );
gap> SetConjugate( ftl, 12, 6, [ 7, 1, 22, -1 ] );
gap> SetConjugate( ftl, 13, 1, [ 12, 1 ] );
gap> SetConjugate( ftl, 13, 2, [ 8, 1, 23, -1 ] );
gap> SetConjugate( ftl, 14, 1, [ 13, 1 ] );
gap> SetConjugate( ftl, 14, 3, [ 9, 1, 24, -1 ] );
gap> SetConjugate( ftl, 15, 1, [ 14, 1 ] );
gap> SetConjugate( ftl, 15, 4, [ 10, 1, 25, -1 ] );
gap> SetConjugate( ftl, 16, 1, [ 15, 1 ] );
gap> SetConjugate( ftl, 16, 5, [ 11, 1, 26, -1 ] );
gap> SetConjugate( ftl, 17, 1, [ 16, 1, 26, -1 ] );
gap> SetConjugate( ftl, 17, 6, [ 12, 1, 22, -1 ] );
gap> SetConjugate( ftl, 18, 1, [ 17, 1 ] );
gap> SetConjugate( ftl, 18, 2, [ 13, 1, 23, -1 ] );
gap> SetConjugate( ftl, 19, 1, [ 18, 1 ] );
gap> SetConjugate( ftl, 19, 3, [ 14, 1, 24, -1 ] );
gap> SetConjugate( ftl, 20, 1, [ 19, 1 ] );
gap> SetConjugate( ftl, 20, 4, [ 15, 1, 25, -1 ] );
gap> SetConjugate( ftl, 21, 1, [ 20, 1 ] );
gap> SetConjugate( ftl, 21, 5, [ 16, 1, 26, -1 ] );
gap> SetConjugate( ftl, 22, 1, [ 21, 1, 26, -1 ] );
gap> SetConjugate( ftl, 22, 6, [ 17, 1, 22, -1 ] );
gap> SetConjugate( ftl, 23, 1, [ 22, 1 ] );
gap> SetConjugate( ftl, 23, 2, [ 18, 1, 23, -1 ] );
gap> SetConjugate( ftl, 24, 1, [ 23, 1 ] );
gap> SetConjugate( ftl, 24, 3, [ 19, 1, 24, -1 ] );
gap> SetConjugate( ftl, 25, 1, [ 24, 1 ] );
gap> SetConjugate( ftl, 25, 4, [ 20, 1, 25, -1 ] );
gap> SetConjugate( ftl, 26, 1, [ 25, 1 ] );
gap> SetConjugate( ftl, 26, 5, [ 21, 1, 26, -1 ] );
gap> SetConjugate( ftl, -7, 1, [ 26, 1 ] );
gap> SetConjugate( ftl, -7, 6, [ 22, 1 ] );
gap> SetConjugate( ftl, -8, 1, [ 7, -1 ] );
gap> SetConjugate( ftl, -8, 2, [ 23, 1 ] );
gap> SetConjugate( ftl, -9, 1, [ 8, -1 ] );
gap> SetConjugate( ftl, -9, 3, [ 24, 1 ] );
gap> SetConjugate( ftl, -10, 1, [ 9, -1 ] );
gap> SetConjugate( ftl, -10, 4, [ 25, 1 ] );
gap> SetConjugate( ftl, -11, 1, [ 10, -1 ] );
gap> SetConjugate( ftl, -11, 5, [ 26, 1 ] );
gap> SetConjugate( ftl, -12, 1, [ 11, -1, 26, 1 ] );
gap> SetConjugate( ftl, -12, 6, [ 7, -1, 22, 1 ] );
gap> SetConjugate( ftl, -13, 1, [ 12, -1 ] );
gap> SetConjugate( ftl, -13, 2, [ 8, -1, 23, 1 ] );
gap> SetConjugate( ftl, -14, 1, [ 13, -1 ] );
gap> SetConjugate( ftl, -14, 3, [ 9, -1, 24, 1 ] );
gap> SetConjugate( ftl, -15, 1, [ 14, -1 ] );
gap> SetConjugate( ftl, -15, 4, [ 10, -1, 25, 1 ] );
gap> SetConjugate( ftl, -16, 1, [ 15, -1 ] );
gap> SetConjugate( ftl, -16, 5, [ 11, -1, 26, 1 ] );
gap> SetConjugate( ftl, -17, 1, [ 16, -1, 26, 1 ] );
gap> SetConjugate( ftl, -17, 6, [ 12, -1, 22, 1 ] );
gap> SetConjugate( ftl, -18, 1, [ 17, -1 ] );
gap> SetConjugate( ftl, -18, 2, [ 13, -1, 23, 1 ] );
gap> SetConjugate( ftl, -19, 1, [ 18, -1 ] );
gap> SetConjugate( ftl, -19, 3, [ 14, -1, 24, 1 ] );
gap> SetConjugate( ftl, -20, 1, [ 19, -1 ] );
gap> SetConjugate( ftl, -20, 4, [ 15, -1, 25, 1 ] );
gap> SetConjugate( ftl, -21, 1, [ 20, -1 ] );
gap> SetConjugate( ftl, -21, 5, [ 16, -1, 26, 1 ] );
gap> SetConjugate( ftl, -22, 1, [ 21, -1, 26, 1 ] );
gap> SetConjugate( ftl, -22, 6, [ 17, -1, 22, 1 ] );
gap> SetConjugate( ftl, -23, 1, [ 22, -1 ] );
gap> SetConjugate( ftl, -23, 2, [ 18, -1, 23, 1 ] );
gap> SetConjugate( ftl, -24, 1, [ 23, -1 ] );
gap> SetConjugate( ftl, -24, 3, [ 19, -1, 24, 1 ] );
gap> SetConjugate( ftl, -25, 1, [ 24, -1 ] );
gap> SetConjugate( ftl, -25, 4, [ 20, -1, 25, 1 ] );
gap> SetConjugate( ftl, -26, 1, [ 25, -1 ] );
gap> SetConjugate( ftl, -26, 5, [ 21, -1, 26, 1 ] );
#
gap> g := PcpGroupByCollector(ftl);
Pcp-group with orders [ 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0 ]
gap> gen:=[ g.1, g.1^4*g.2^4*g.3^4*g.4^4*g.6*g.7*g.25^-1*g.26^2 ];;
gap> U := Subgroup(g,gen);
Pcp-group with orders [ 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0 ]
gap> Igs(gen);
[ g1, g2*g3*g4*g5*g6, g3*g4*g5^3*g23^-1*g24^3*g25^2*g26,
g4*g5^2*g24^-1*g25^2*g26^-1, g5*g6^4*g22*g23^-1*g24^2*g26^-2,
g6*g22*g23^2*g24*g25^3*g26^-2, g7*g22^-4, g8*g23^-4, g9*g24, g10*g25,
g11*g26^-4, g12*g22^-3, g13*g23^-3, g14*g24^2, g15*g25^-3, g16*g26^-3,
g17*g22^-2, g18*g23^-2, g19*g24^-2, g20*g25^3, g21*g26^3, g22^5, g23^5,
g24^5, g25^5, g26^5 ]
#
# Fix a bug in AddToIgs
# See
https://github.com/gap-packages/polycyclic/issues/66
#
gap> G := PcGroupToPcpGroup( SmallGroup( 36, 9 ) );;
gap> gensG := [ G.1, G.4 ];;
gap> G = Subgroup( G, gensG );
true
# second example for issue #66
gap> G := ExamplesOfSomePcpGroups( 10 );;
gap> S := Subgroup( G, [ G.1, G.2, G.4 ] );;
gap> Igs(S);
[ g1, g2, g3^3, g4 ]
gap> G.3^3 in S;
true
gap> G.2^-1*G.4*G.2*G.4^-2;
g3^3
#
# third example for issue #66
#
gap> H := SmallGroup( 36, 9 );;
gap> gensH := [ H.1, H.4 ];;
gap> H = Subgroup( H, gensH );
true
gap> iso := IsomorphismPcpGroup( H );;
gap> G := Range( iso );;
gap> gensG := List( gensH, h -> h^iso );;
gap> S := Subgroup( G, gensG );;
gap> Igs( S );
[ g1, g2, g3*g4^2, g4 ]
gap> G = S;
true
# another example, this time from issue #56
gap> A:=AbelianPcpGroup([3,2,12]);;
gap> m:=MinimalGeneratingSet(A);;
gap> Length(m);
2
gap> List(AddToIgs([],m), Depth);
[ 1, 2, 3 ]
#
gap> STOP_TEST( "AddToIgs.tst", 1);
