#14025: Comparison of elements of the quotient group of a FreeGroup
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Reporter: ppurka | Owner: joyner
Type: defect | Status: new
Priority: major | Milestone: sage-wishlist
Component: group theory | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #12339 | Stopgaps:
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Comment (by mmarco):
In general, that is an undecidable problem, so it is not surprising that
we don't get an answer.
In some cases there are some things that could be done, like trying to get
a normal form (by using rewriting systems, or automatic structures), or
symmetric representations (if the group is finite). But again, these
methods will only work for some groups, and in general we cannot know in
advance if they will work for a given group, so it is not advisable to
implement these methods as a general way to compare words. We will have to
live with the fact that finitely presented groups present this kind of
undecidable problems.
When/if we get kbmag to work under libgap, we could be able to compute
automatic structures for FP groups, which would work in this particular
example (but not in general).
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Ticket URL: <http://trac.sagemath.org/ticket/14025#comment:2>
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