#16316: cached_function and cached_method for unhashable elements
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Reporter: saraedum | Owner:
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-6.3
Component: misc | Resolution:
Keywords: | Merged in:
Authors: Julian Rueth | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/saraedum/ticket/16316 | a65ac8524294fde91e021c39b9f227277ec33d23
Dependencies: #16251 | Stopgaps:
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Comment (by pbruin):
It seems that the problem really has to do with key comparison in
dictionaries, not with hashing or caching specifically. Given (1)
Python's use of `==` for key comparison and (2) Sage's lenient
implementation of `==` for elements, we basically cannot use Sage elements
as dictionary keys.
One would like a third comparison operator, say `equal`^1^, that regards
two objects as equal if and only if all their "mathematically relevant"
properties (e.g. value and precision for real or ''p''-adic numbers, but
not memory location) are the same. Our caching problems would then
disappear if keys were compared using `equal`. In this hypothetical case,
the correct property for hash functions would be `X equal Y` => `hash(X)
== hash(Y)`.
- Do I understand correctly that the purpose of `cache_key` can be viewed
as emulating the "missing" `equal` by assigning to each object `X` a
(hashable) object `cache_key(X)` satisfying the condition `cache_key(X) ==
cache_key(Y)` <=> `X equal Y` ?
- If so, does the implementation in this ticket satisfy this condition?
(I am mainly worried that the parent of an element `x` does not seem to be
encoded in `cache_key(x)`.)
^1^ I just looked up the different comparison functions (`=`, `eq`, `eql`,
`equal` and `equalp`) in Lisp and `equal` seems to be the closest to what
we would need, hence I am using that notation. However, Lisp uses `eql`
by default for hash tables.
--
Ticket URL: <http://trac.sagemath.org/ticket/16316#comment:8>
Sage <http://www.sagemath.org>
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