#16316: cached_function and cached_method for unhashable elements
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Reporter: saraedum | Owner:
Type: enhancement | Status: positive_review
Priority: minor | Milestone: sage-6.3
Component: misc | Resolution:
Keywords: | Merged in:
Authors: Julian Rueth | Reviewers: Peter Bruin, Travis
Report Upstream: N/A | Scrimshaw
Branch: | Work issues:
u/saraedum/ticket/16316 | Commit:
Dependencies: #16251 | 83944fabe78c5561f0cc5b0845d5e8bdb30098c2
| Stopgaps:
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Comment (by pbruin):
Replying to [comment:38 tscrim]:
> Replying to [comment:34 pbruin]:
> > Hmm, I see. But if we store the parent itself, then I think we have to
make sure that all unhashable elements belong to parents satisfying unique
representation. Otherwise, calling a cached function on an element whose
parent is equal but not identical to the parent of an element that was
used before could return a cached result that lives in this equal-but-not-
identical parent.
>
> No, this isn't a problem because equal parents have equal hashes.
That is exactly what causes the problem. Consider the following example
with a hypothetical parent class `MyParent` that has unhashable elements
but does not have unique representation:
{{{
sage: @cached_function
sage: def f(x):
....: """
....: Return `x^2 + 1` in the parent of `x`.
....: """
....: return x^2 + 1
....:
sage: P = MyParent()
sage: Q = MyParent() # Q is equal but not identical to P
sage: f(P(0)).parent() is P
True
sage: f(Q(0)).parent() is Q
False # since the parents are equal, f(q) returns the cached f(p)
sage: f(P(0)) is f(Q(0))
True
}}}
This already happens before this patch with parent ''P'' and ''Q'' where
there exists a coercion map compatible with hashing (e.g. '''Z''' and
'''Q'''):
{{{
sage: @cached_function
....: def f(x):
....: return x^2 + 1
....:
sage: f(ZZ(0)).parent()
Integer Ring
sage: f(QQ(0)).parent()
Integer Ring
sage: f(ZZ(0)) is f(QQ(0))
True
}}}
However, I think we should avoid this situation whenever possible.
--
Ticket URL: <http://trac.sagemath.org/ticket/16316#comment:40>
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