Systems of three polynomials with two separated variables

Authors:
Mohamed Elkadi;André Galligo
Affiliations:
Université de Nice;Université de Nice
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

Citing 4
Cited 0

Generalized resultants over unirational algebraic varieties

Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Multivariate polynomials, duality, and structured matrices

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Bernstein-Bezoutian matrices

Theoretical Computer Science - Algebraic and numerical algorithm
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

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Abstract

Motivated by the computation of intersection loci in Computer Aided Geometric Design (CAGD), we introduce and study the elimination problem for systems of three bivariate polynomial equations with separated variables. Such systems are simple sparse bivariate ones but resemble to univariate systems of two equations both geometrically and algebraically. Interesting structures for generalized Sylvester and bezoutian matrices can be explicited. Then one can take advantage of these structures to represent the objects and speed up the computations. A corresponding notion of subresultant is presented and related to a Gröbner basis of the polynomial system.