## 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