gap-forum@samson.math.rwth-aachen.de
Just a couple of comments in regards to my question last week about the
direct calculation of characters. First: many thanks to Thomas Breuer
for a great answer; now I am tempted to bother the forum with more
questions :-) . Second I have just finished installing gap3.2 on a
DEC Ultrix workstation and on a PC. It looks fantastic! it took just a
few minutes on the PC to do the calculations below for the characters
of <2,3,4> and <2,3,5> -- it took the DEC 3100 a bit longer to do the same.
a := AbstractGenerator("a"); b := AbstractGenerator("b"); c := AbstractGenerator("c"); z := AbstractGenerator("z"); g4 := Group(a,b,c,z); g5 := Group(a,b,c,z); g4.relators := [a^2*z^-1,b^3*z^-1,c^4*z^-1,a*b*c*z^-1,z^2]; g5.relators := [a^2*z^-1,b^3*z^-1,c^5*z^-1,a*b*c*z^-1,z^2]; group4:=OperationCosetsFpGroup(g4,Subgroup(g4,[IdWord])); group5:=OperationCosetsFpGroup(g5,Subgroup(g5,[IdWord])); chr4 := CharTable(group4); chr5 := CharTable(group5);DisplayCharTable(chr4);
2 4 2 1 3 4 3 1 3 3 1 . 1 . 1 . 1 .1a 4a 6a 8a 2a 8b 3a 4b 2P 1a 2a 3a 4b 1a 4b 3a 2a 3P 1a 4a 2a 8b 2a 8a 1a 4b 5P 1a 4a 6a 8b 2a 8a 3a 4b 7P 1a 4a 6a 8a 2a 8b 3a 4bX.1 1 1 1 1 1 1 1 1 X.2 1 -1 1 -1 1 -1 1 1 X.3 2 . -1 . 2 . -1 2 X.4 2 . 1 A -2 -A -1 . X.5 2 . 1 -A -2 A -1 . X.6 3 -1 . 1 3 1 . -1 X.7 3 1 . -1 3 -1 . -1 X.8 4 . -1 . -4 . 1 . A = -E(8)+E(8)^3 = -ER(2) = -r2 DisplayCharTable(chr5);2 3 2 1 1 3 1 1 1 1 3 1 . 1 . 1 . 1 . . 5 1 . . 1 1 1 . 1 11a 4a 6a 10a 2a 5a 3a 5b 10b 2P 1a 2a 3a 5b 1a 5b 3a 5a 5a 3P 1a 4a 2a 10b 2a 5b 1a 5a 10a 5P 1a 4a 6a 2a 2a 1a 3a 1a 2a 7P 1a 4a 6a 10b 2a 5b 3a 5a 10aX.1 1 1 1 1 1 1 1 1 1 X.2 2 . 1 A -2 -A -1 -*A *A X.3 2 . 1 *A -2 -*A -1 -A A X.4 3 -1 . A 3 A . *A *A X.5 3 -1 . *A 3 *A . A A X.6 4 . 1 -1 4 -1 1 -1 -1 X.7 4 . -1 1 -4 -1 1 -1 1 X.8 5 1 -1 . 5 . -1 . . X.9 6 . . -1 -6 1 . 1 -1 A = -E(5)^2-E(5)^3 = (1+ER(5))/2 = 1+b5
Thanks to all the developers for a great tool.
Jacob Hirbawi
JcbHrb@CERF.net