#19038: Better hash on FPGroups
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Reporter: nbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.9
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by nbruin:
Old description:
> As is pointed out on #19016 the hash on FPGroup elements is currently
> based on the (non-canonical) representation, whereas the equality test is
> a more elaborate one borrowed from Gap. That means currently, there are
> elements that are equal but have different hashes
> {{{
> sage: G.<a,b>=FreeGroup()
> sage: Q=G.quotient([a*b])
> sage: U=Q(a)*Q(b)
> sage: V=Q(1)
> sage: U==V
> True
> sage: hash(U)==hash(V)
> False
> }}}
> When Gap does succeed in testing equality, it does so via a normal form
> of its elements. One way of equipping FPGroups with a well-behaved hash
> is by getting that normal form from gap and hash that.
New description:
As is pointed out on #19016 the hash on FPGroup elements is currently
based on the (non-canonical) representation, whereas the equality test is
a more elaborate one borrowed from Gap. That means currently, there are
elements that are equal but have different hashes
{{{
sage: G.<a,b>=FreeGroup()
sage: Q=G.quotient([a*b])
sage: U=Q(a)*Q(b)
sage: V=Q(1)
sage: U==V
True
sage: hash(U)==hash(V)
False
}}}
When Gap does succeed in testing equality, it does so via a normal form of
its elements. One way of equipping FPGroups with a well-behaved hash is by
getting that normal form from gap and hash that.
The main inspiration for how to do this would come from Gap's
[https://github.com/gap-system/gap/blob/master/lib/grpfp.gi#L236
MakeFpGroupCompMethod source]
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Ticket URL: <http://trac.sagemath.org/ticket/19038#comment:2>
Sage <http://www.sagemath.org>
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