#13103: Makes BooleanPolynomial more compatible with MPolynomial
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Reporter: Bouillaguet | Owner: malb
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-5.1
Component: commutative algebra | Resolution:
Keywords: polybori | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Charles Bouillaguet | Merged in:
Dependencies: | Stopgaps:
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Comment (by malb):
Replying to [comment:2 Bouillaguet]:
> The cause of the bug in "positive" dimension (without the field
equations) is that BooleanPolynomialIdeal.groebner_basis() computes a
groebner basis '''modulo the field equations''', but this is not a
Groebner basis in general.
> Obvious fix :
> a) Compute GB modulo field equations with
BooleanPolynomialIdeal.groebner_basis()
> b) cast to MPolynomial
> c) Add field equations
> d) use MPolynomial.variety()
>
> This is guaranteed to be correct, but is probably a bit sub-optimal.
Adding the field equations may destroy the Groebner basis, but my guess is
that running the buchberger algorithm again should do little work.
Actually, adding the field equations would not destroy the GB, as PolyBoRi
actually computes the GB with the field equations implicitly added. The
result + field equations is a GB wrt to GF(2)[x1,...xn].
> This is implemented by the second patch.
This strategy looks fine to me. IIRC there is some special code in
PolyBoRi to do this faster, but for now this simple approach fixes an
embarrassing bug.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13103#comment:4>
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