#19594: Implement the cactus group
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: group theory | Resolution:
Keywords: cactus | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/groups/cactus_group-19594 | 7eb2a1278ea0ca08375f87e0f82081218a2ea1ec
Dependencies: | Stopgaps:
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Comment (by dimpase):
here is a direct check of the relations:
{{{
gap> s12:=(1,2); s13:=(1,3); s14:=(1,4); s23:=(2,3); s24:=(2,4);
s34:=(3,4);
(1,2)
(1,3)
(1,4)
(2,3)
(2,4)
(3,4)
gap> [s12^2, s13^2, s14^2, s23^2, s24^2, s34^2, s13*s12*s13^-1*s23^-1,
s13*s23*s13^-1*s12^-1, s14*s12*s14^-1*s34^-1, s14*s13*s14^-1*s24^-1,
s14*s23*s14^-1*s23^-1, s14*s24*s14^-1*s13^-1, s14*s34*s14^-1*s12^-1,
s24*s23*s24^-1*s34^-1, s24*s34*s24^-1*s23^-1, s34*s12*s34^-1*s12^-1 ];
[ (), (), (), (), (), (), (), (), (2,3,4), (2,4,3), (), (1,2,3), (1,3,2),
(), (), () ]
gap>
}}}
e.g. `s14*s12*s14^-1*s34^-1` evaluates to (2,3,4) in Sym(4)...
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Ticket URL: <http://trac.sagemath.org/ticket/19594#comment:20>
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