The resultant and gcd work well over rational but not over real or complex!
R.<x,y> = PolynomialRing(RR,2)
a = x^2 + y
b = x - y^2
a.resultant(b)
a.gcd(b)
This does not work while with QQ, it works. Anyone has an idea?
If you define your polynomial ring as follows, it does work:
sage: P.<y> = PolynomialRing(RR)
sage: R.<x> = PolynomialRing(P)
sage: a = x^2 + y
sage: b = x - y^2
sage: a.resultant(b)
The problem is that for these kind of inexact rings the methods are not implemented.
For the resultant, you can compute the resultant with
a.sylvester_matrix(b,x).det()
But I cannot promise performance nor numeric stability.
The gcd is more tricky. For instance, if you take univariate polynomials over an inexact rings and perform Euclides method, you will end with a gcd 1 due to numerical errors. You are asking for an approximate gcd which is not easy to compute.
Asked: 2014-02-12 18:03:49 +0200
Seen: 723 times
Last updated: Feb 16 '14
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