On computing the resultant of generic bivariate polynomials

G. Villard


Maple worsheets companion to ISSAC'18 paper (doi) on the bivariate resultant and extensions.


■ A special Sylvester matrix

Construction in Section 3 of special polynomials such that their Sylvester matrix leads to a generic degree behaviour: Sylvester.mw.gz


■ Computation of the structured representation of the inverse of the Sylvester matrix

Techniques for Toeplitz-like matrix used in Proposition 5.1.

Computation of the Sigma.L.U representation using maple system solving: sigmaLU.mw.gz

Using Beckermann and Labahn algorithm for order bases, hence reduction of the problem to half-gcd and matrix fraction reconstruction: sigmaLU-orderB.mw.gz


■ The resultant algorithm

The algorithm of Figure 1: resultant.mw.gz.


■ Gröbner basis of two bivariate polynomials

Bivariate Gröbner basis via univariate Hermite normal form computation, Section 7: groebner.mw.gz


■ Diamond polynomial product

Computation of the characteristic polynomial in a univariate quotient algebra, Section 7.

Construction of a special point for the result in the generic case and an example: diamond.mw.gz


Last modified on Jeu 12 jul 2018 14:05:22 CEST

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