#12802: test containment of ideals in class MPolynomialIdeal
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Reporter: mariah | Owner: AlexGhitza
Type: enhancement | Status: needs_info
Priority: minor | Milestone: sage-5.1
Component: commutative algebra | Resolution:
Keywords: sd40.5, groebner bases, ideals | Work issues: cache
handling
Report Upstream: N/A | Reviewers: Andrey
Novoseltsev, Simon King
Authors: John Perry | Merged in:
Dependencies: | Stopgaps:
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Comment (by john_perry):
Replying to [comment:35 SimonKing]:
> > > Perhaps one could make ideals non-hashable?
> >
> > I'm okay with that, too. Are ideals mutable? If so, the answer is
easy.
>
> I don't think they are mutable.
I don't think so, either. I don't see any way to add or subtract
generators from the ideal. Well, is there a conceivable use for the hash
of an ideal? For example, would someone need a set of ideals for
something? I'm pretty sure this is a possibility.
(Incidentally, when I wrote, "If so, the answer is easy," I meant, "If
'''not''', the answer is easy.")
> No. The hash is only computed when it is needed (hence, when the ideal
is put into a set or dictionary). The following toy example should
illustrate what is called when:
In that case, and if we can agree that someone might want to hash ideals,
I suggest we using the degrevlex Groebner basis for the hash, and include
a warning in the documentation that using an ideal with anything that
requires a hash could slow things down seriously. That way, people have
been warned. If this slows down some Sage functions that rely on
dictionaries, we could rewrite them to avoid that, as you are doing with
#12977.
Personally, I would rather have no hash than an incorrect one, even for
immutable objects. That said, it could be a valid long-term project to
find a hash for ideals.
> I promised to provide you with a ticket number for multiple
realisations: #7980.
Thanks. I'll look at it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12802#comment:36>
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