#16749: Speedup resultant of multivariate polynomials
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Reporter: mmarco | Owner:
Type: | Status: new
enhancement | Milestone: sage-6.3
Priority: major | Keywords: resultant, discriminant,
Component: algebra | polynomial, multivariate
Merged in: | Authors: Miguel Marco
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Up to now we rely on singular to compute resultants of multivariate
polynomials. There are faster ways.
Even computing the determinant of the sylvester matrix is usually (much)
faster.
First i have implemented a trick for bivariate polynomials over the
rationals (it could in principle work over any field with enough elements,
but it is not clear that it is faster there). The trick consists on
specialicing for several values of the surviving variable, compute the
(univariate) resultant for them, and then reconstruct by lagrange
interpolation.
It would also be worth to perform some benchmarks, and deduce a heuristic
for the cases where the current method is beaten by the sylvester matrix
determinant.
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Ticket URL: <http://trac.sagemath.org/ticket/16749>
Sage <http://www.sagemath.org>
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