[GAP Forum] List all elements in a Weyl group using GAP.

[Jianrong Li]

Dear members of the Forum,

I use the following codes to list all elements in B3 Weyl group.

Are there some other methods which can obtain the list of elements in Weyl
group in GAP? Thank you very much.

Best wishes,
Jianrong.

F:=FreeGroup("a", "b", "c");
<free group on the generators [ a, b, c ]>
gap> B:=F/[ F.1^2, F.2^2, F.3^2, (F.1*F.2)^4, (F.2*F.3)^3, (F.3*F.1)^2 ];
<fp group on the generators [ a, b, c ]>
gap> Size(B);
48
gap> Elements(B);
[ <identity ...>, a*b*a*b*c*b*a*b, c, c*b, a*b*a*b, b*a*b*c*b*a*b*c,
  a*b*a*b*c*b*a*b*c, a*b*a*c*b*a*b*c, b*a*b*c, a*c, b, a*c*b*a*b,
  b*a*b*c*b*a*b, b*c, a*c*b*a, a*b*a*b*c*b, a*c*b*a*b*c, a*b*a*b*c*b*a,
  c*b*a*b*c, a, a*b*a*c*b*a, b*c*b*a*b*c, b*a, c*b*a*b, b*c*b, a*b*a,
  a*b*c*b*a*b*c, a*b*a*b*c, b*a*c*b*a*b, a*b*c*b*a*b, b*a*b*c*b*a,
  a*b*a*c*b*a*b, b*a*b*c*b, c*b*a, b*a*b, a*b*c*b, b*c*b*a, a*b, b*a*c*b*a,
  a*b*a*c*b, b*a*c*b*a*b*c, a*b*a*c, a*b*c, b*a*c, a*c*b, b*a*c*b,
a*b*c*b*a,
  b*c*b*a*b ]
gap>