#6581: Groebner basis not working over symbolic ring
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Reporter: rhinton | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: commutative algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by john_perry):
> Anyway, do you know offhand why one needs the characteristic, but not
the other?
Bingo. In lines 302--307 of `multi_polynomial_sequence.py` we encounter:
{{{
if k.characteristic() != 2:
return PolynomialSequence_generic(parts, ring,
immutable=immutable, cr=cr, cr_str=cr_str)
elif k.degree() == 1:
return PolynomialSequence_gf2(parts, ring, immutable=immutable,
cr=cr, cr_str=cr_str)
elif k.degree() > 1:
return PolynomialSequence_gf2e(parts, ring, immutable=immutable,
cr=cr, cr_str=cr_str)
}}}
I can make this work via judicious use of a `try`/`catch`. I found some
other instances where it tried to compute a Singular representation of
itself (the `reduce` function in `multi_polynomial_element`, for
instance). That has allowed me to compute several Gröbner bases
successfully, including one similar to the ideal you couldn't get to work:
{{{
sage: J = R2.ideal([(a^2+b^2)*x + y, x+y])
sage: J
Ideal (x + y, x + y) of Multivariate Polynomial Ring in x, y over Fraction
Field of
Quotient of Multivariate Polynomial Ring in a, b over Rational Field by
the ideal
(a^2 + b^2 - 1)
sage: J.groebner_basis()
verbose 0 (2854: multi_polynomial_ideal.py, groebner_basis) Warning:
falling back to
very slow toy implementation.
[x + y]
}}}
I think the patch is worth adding. However, I'm still not sure this is
what the original requester wanted. Should I open a new ticket?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6581#comment:15>
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