#15061: Pari can't handle all polynomial resultants
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Reporter: robharron | Owner:
Type: defect | Status:
Priority: major | needs_info
Component: algebra | Milestone: sage-6.2
Keywords: pari, resultant, sylvester | Resolution:
matrix | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by gagern):
Replying to [comment:10 pbruin]:
> That commit only changed the order of the superclasses; the inheritance
was there before.
Thanks, I missed that fact.
> I agree that it is strange for polynomials over arbitrary fields to
inherit from that class. An alternative would be to "manually" prescribe
this inheritance for polynomials over fields that support conversion to
Singular, but that doesn't sound very attractive.
I see how
[http://git.sagemath.org/sage.git/tree/src/sage/rings/polynomial/polynomial_ring.py?id=6.2.rc1#n1467
the constructor of `PolynomialRing_field`] checks for singular support and
sets the `_has_singular` property accordingly. We could use that place to
change `element_class` in a suitable way. But if we wanted to handle this
using different classes, we'd add one more point to the already dense
network of generic vs. special, domain vs. field, sparse vs. dense. Not
sure I like that either.
> Another alternative would be to move `resultant()` to a more generic
polynomial class that first tries to use Singular and uses a generic
Python implementation in case that fails.
Sounds good. As a first step, we could change
[http://git.sagemath.org/sage.git/tree/src/sage/rings/polynomial/polynomial_singular_interface.py?id=6.2.rc1#n372
`Polynomial_singular_repr`] to check `self.parent()._has_singular` and
call `super` if that isn't set. We could then make sure that
[http://git.sagemath.org/sage.git/tree/src/sage/rings/polynomial/polynomial_element.pyx?id=6.2.rc1#n4798
`Polynomial.resultant`] falls back to `sylvester_matrix` if PARI doesn't
work. Although I don't know yet for which rings PARI *will* work. Messy
business…
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Ticket URL: <http://trac.sagemath.org/ticket/15061#comment:11>
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