#1819: move crypto.mq.MPolynomialSystem somewhere else
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Reporter: malb | Owner: malb
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.6.2
Component: commutative algebra | Keywords:
Author: Martin Albrecht | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by malb):
Replying to [comment:16 vbraun]:
> I don't see that anywhere in the `MPolynomialIdeal` class. Correct me if
I'm wrong,
> but the chosen generators and their order is immutable.
Yep.
> Even when computing a Groebner basis, the generators are not replaced by
this much
> more useful basis.
But the GB is cached and used for "interesting" operations.
> On the other hand, there are methods like `basis_is_groebner()` which
are obviously
> basis-dependent.
This was the compromise reached to (a) keep the notion that ideals are
different objects than their generators and to (b) still allow to query
some information about the basis. We should have separated stuff back then
perhaps. In any case, it was this method's name which sparked the debate
we're having between William and myself.
> It seems to me that Sage implements ideals very much as an immutable
sequence of
> polynomials with some methods attached.
I'd say: it attempts to present a view on ideals which abstracts away
chosen bases but with varying success.
> The individual methods do, of course, need Groebner bases but they never
change the > underlying sequence of polynomials.
But e.g. `intersection()` and `reduce()` actually use the GB and not the
provided basis, they are methods on the ideal and not on the generating
set. Some other methods are less clear such as `basis_is_groebner()` and
`interreduced_basis()`. These could perhaps be moved to
`PolynomialSequence`.
> I am aware that the ideals implicitly contain the term order, though I
found that a somewhat mixed blessing in #10708.
I wouldn't say this is because of the containment of term orderings but
because of lack of care dealing with them?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1819#comment:17>
Sage <http://www.sagemath.org>
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