Matrix representations of algebraic varieties

Matrix-based implicit representations of algebraic curves and surfaces and applications

Thang Luu Ba - Collection Omn.univ.europ.

108 pages, parution le 20/10/2011

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Résumé

In this book, we introduce and study a new implicit representation of rational curves of arbitrary dimensions and propose an implicit representation of rational hypersurfaces. Then, we illustrate the advantages of this matrix representation by addressing several important problems of Computer Aided Geometric Design (CAGD): The curve/curve, curve/surface and surface/surface intersection problems, the point-on-curve and inversion problems, the computation of singularities of rational curves. We also develop some symbolic/numeric algorithms to manipulate these new representations for example: the algorithm for extracting the regular part of a non square pencil of univariate polynomial matrices and bivariate polynomial matrices. In the appendix of this book we present an implementation of these methods in the computer algebra systems Mathemagix and Maple. In the last chapter, we describe an algorithm which, given a set of univariate polynomials $f_1,...,f_s$ returns a set of polynomials $u_1,...,u_s$ with prescribed degree-bounds such that the degree of $\gcd(f_1+u_1,...,f_s+u_s)$ is bounded below by a given degree assuming some genericity hypothesis.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Editions universitaires européennes
Auteur(s)	Thang Luu Ba
Collection	Omn.univ.europ.
Parution	20/10/2011
Nb. de pages	108
Format	15 x 22
Couverture	Broché
Poids	177g
EAN13	9786131598104