#5146: [with patch; needs review] implement MPolynomial_ideal.variety() for
GF(p)
with p > than what Singular supports
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Reporter: malb | Owner: malb
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: commutative algebra | Keywords:
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Comment(by john_perry):
Implementing Lazard's algorithm to solve this required a few subalgorithms
as well. Rather than clutter {{{multi_polynomial_ideal.py}}}, I appended
the functions to {{{toy_buchberger.py}}}. That seemed a natural location,
since this is a toy implementation, and computing the variety of a zero-
dimensional ideal is not an unnatural follow-up to Buchberger's algorithm.
That said, if someone prefers that this be placed in
{{{multi_polynomial_ideal.py}}}, or even in a new file, I can work with
that.
The implementation provided is (unsurprisingly) unoptimized more or less,
not even requiring a lexicographic ordering. On the upside, you don't need
a lexicographic ordering. Check out the doctest on
{{{triangular_factorization}}}.
I added doctests for all the new functions in {{{toy_buchberger.py}}}, and
a new doctest which tests for the system listed above. The patch uploaded
passes all the doctests, at least on my machine.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5146#comment:3>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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