#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 SimonKing):
Replying to [comment:32 john_perry]:
> The only part that surprises me is that items with the same hash are put
into a bucket. I had learned hashes differently.
Isn't that how hash tables work? Sorry, I am not a computer scientist, it
could easily be that I misunderstood the internals of dictionaries.
> I see; the hash has been broken a while. I can suggest a quick hash
function, actually: compute a Groebner basis of the ''homogenized'' ideal
'''up to degree''' ''d'' for some small value of ''d''. (Standard
homogenization, if there's any doubt.)
Wouldn't that, again, depend on the term order? And how should one choose
''d''? After all, if you compute a Gröbner basis out to degree ''d'' but
there are further elements in higher degree, then the ''complete'' Gröbner
basis will have a different hash.
Perhaps one could make ideals non-hashable? After all, what one needs in
applications (to my experience) is the tuple of generators of the ideal.
> This strikes me as a significantly different problem, albeit related,
deserving of its own ticket.
OK.
> > Anyway, ideals that are independent of a default term order could
probably be implemented using the "parents with multiple realisations"
that have recently been introduced (hence, Cc to Nicolas...). I wonder,
though, if that would be possible without a speed regression.
>
> Can you point me to a thread or ticket?
Sorry, have to catch a bus. I hope I don't forget to answer later. But
perhaps Nicolas beats me to it?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12802#comment:33>
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