#19016: A more naive sage.structure.element.__hash__
-------------------------+-------------------------------------------------
Reporter: | Owner:
ncohen | Status: needs_work
Type: | Milestone: sage-duplicate/invalid/wontfix
defect | Resolution:
Priority: | Merged in:
blocker | Reviewers:
Component: misc | Work issues:
Keywords: | Commit:
Authors: | 754dc5794a1a7004c8844cf7cfb64220957c36a5
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
u/ncohen/19016 |
Dependencies: |
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Old description:
> As reported on sage-devel [1], the default hash function implemented in
> `Element` makes it very likely that `hash` and `==` will not agree. With
> this branch, the hash is constant and set to 0, making it less likely.
> Incidentally, it fixes the following bug:
> {{{
> sage: G = groups.presentation.Cyclic(4)
> sage: G.cayley_graph().vertices()
> [1, a, a^2, a^-2, a^3, a^-1]
> }}}
>
> Nathann
>
> [1] https://groups.google.com/d/topic/sage-devel/6rXKkF87Gtc/discussion
New description:
As reported on sage-devel [1], the default hash function implemented in
`Element` (as `return hash(str(self)))`) causes a lot of troubles
- it breaks the {{{equality => same hash}}} assumption for finitely
presented groups
{{{
sage: G = groups.presentation.Cyclic(4)
sage: G.cayley_graph().vertices()
[1, a, a^2, a^-2, a^3, a^-1]
}}}
and symbolic expressions
{{{
sage: f=sin(x)^2
sage: g=1-cos(x)^2
sage: bool(f == g)
True
sage: hash(f) == hash(g)
False
}}}
and possibly many others
- it is highly incompatible with the `rename` feature (see also #8119)
{{{
sage: from sage.structure.element import Element
sage: class E(Element):
....: def __init__(self):
....: Element.__init__(self, Parent())
sage: e = E()
sage: hash(e)
-4965357552728411610
sage: e.rename('hey')
sage: hash(e)
-6429308858210906323
}}}
and similarly, hashing should not be available on any mutable object.
- it might be very bad for performance: see #18215 and #18239 for examples
There are several possibilities that are currently being discussed:
- make it return `0` by default (original proposition of the ticket)
- make it raise a `TypeError` by default (as it the case for `SageObject`,
see #18246)
- let it as it is but raise a Warning
[1] https://groups.google.com/d/topic/sage-devel/6rXKkF87Gtc/discussion
--
Comment (by nbruin):
Shoot. Is there a better way of reverting changes on trac? I ended up
cutting and pasting from the change log diff.
--
Ticket URL: <http://trac.sagemath.org/ticket/19016#comment:33>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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