#17427: x==y while hash(x)!=hash(y) with SchemeMorphism_point_projective_field
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Reporter: ncohen | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.5
Component: PLEASE CHANGE | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:5 bhutz]:
> Notice that the sage developers guide says the following about hash:
>
> '“The only required property is that objects which compare equal have
the same hash value.” This is an assumption made by the Python language,
which in Sage we simply cannot make!'
That's just because the use of non-injective coercion maps means that
equality testing in sage isn't transitive when allowing elements from
multiple parents:
{{{
sage: 1 == GF(5)(1)
True
sage: GF(5)(1) == 6
True
sage: 1 == 6
False
}}}
which indeed means that you shouldn't have a dictionary where you use both
integers and finite field elements as keys. But at least there's an easy
rule there: If you use sage objects as keys in a dict, make sure they all
have the same parent, or make sure that you really know what you're doing.
If you can't even have a hash that works properly between elements of the
same parent then you shouldn't make those elements hashable. The hash will
be useless and it's misleading to have. This happened to p-adics, where
`==` was chosen to be too permissive to be transitive (they were
considered equal if their associated disks had non-empty intersection),
and indeed they are slated to lose their hash (see #11895)
{{{
sage: 1+O(k(9)) == 1+O(k(3))
True
sage: 1+O(k(3)) == 4+O(k(9))
True
sage: 1+O(k(9)) == 4+O(k(9))
False
}}}
(note it's the same issue as with ZZ and finite fields, but now inside the
same parent)
As long as you're taking projective space over integral domains with a
constructible field of fractions, you can just normalize a non-zero
coordinate to 1 and hash that (provided the implementation of the field of
fractions has an appropriate hash (fields that are a finite extension of a
FoF of a PID should be OK, if implemented correctly, and Noether
Normalization gives us that basically all fields we'll meet in sage are of
that type)). Yes, hashing is hard :-).
If you want to take projective space over non-integral domains, I think
you'll have bigger problems elsewhere.
--
Ticket URL: <http://trac.sagemath.org/ticket/17427#comment:6>
Sage <http://www.sagemath.org>
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