#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 | a3ab2d2076464e3451720832ef384186abcc1552
Dependencies: | Stopgaps:
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Comment (by tscrim):
Okay, so the cactus group corresponds to type A,,n,, and when `R` is the
full power set of the index set. I've added the representation described
in the DJS paper here. One related question that comes to mind is what
happens when `t=1`, do we get a (faithful) representation of the right-
angled Coxeter group which has the `t=1` bilinear form? We have a lot to
think on for this...
The end result of our discussion as I see it is that we don't have a good
way to construct normal forms of elements at present. So for the purposes
of this ticket, should we include this as-is with a warning stating that
elements may be equal even if `==` does not necessarily return `True`?
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Ticket URL: <http://trac.sagemath.org/ticket/19594#comment:30>
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