#12339: Free Groups
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Reporter: mmarco |
Owner: joyner
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-5.5
Component: group theory |
Resolution:
Keywords: free groups, finitely presented groups, braids | Work
issues:
Report Upstream: N/A |
Reviewers: Volker Braun
Authors: Miguel Marco | Merged
in:
Dependencies: #6391, #13687, #13588 |
Stopgaps:
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Comment (by dimpase):
Replying to [comment:65 jhpalmieri]:
> Thanks, Volker, your new patches fixed my problem. It sounds like you're
saying that there is no good way to have
> {{{
> sage: G.<e0> = FreeGroup()
> sage: relns_G = [e0^2]
> sage: H.<e0, e1> = FreeGroup()
> sage: relns_H = [e0^2, e1]
> sage: G2 = G / relns_G
> sage: H2 = H / relns_H
> sage: G2 == H2
> }}}
> return True? That's unfortunate. Should `__eq__` raise a
`NotImplementedError` instead, or is that too unpythonic?
it seems to be more subtle, as the group presentations are different.
GAP has [http://www.gap-system.org/Gap3/Manual3/C023S008.htm several]
different classes of objects for finitely presented groups, with some of
them having presentation explicit.
GAP can check for finite group isomorphism.
The concept of free group in Sage ought to be better defined, i.e.
currently it seems to be a group with an attached presentation. It would
be good to have this explicitly explained in documentation.
>
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12339#comment:66>
Sage <http://www.sagemath.org>
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