Résultant déterminantiel et applications

Elimane Ba 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In the first part, we define algebraically the determinantal resultant of a morphism of fi nite free modules f which input matrix of polynomials homogeneous f_i,j. Using the Eagon-Northcott and Buchsbaum-Rim complexes associated with the morphism f we provide e ffective methods to calculate the determinantal resultant as its degree. In the case where the polynomial f_i,j are in two variables, we show that the determinantal resultant is given by the determinant of a matrix of coefficients f_i,j , which is a generalization of the Sylvester matrix of two polynomials. In the second part of the thesis, we study the Bezier curves and surfaces intersection problems avoiding the well-known unstable conversion between Bernstein basis and power basis. These problems have a special shape which is degenerate for the Macaulay resultant. We prove the existence of an anisotropic resultant for these degenerate systems and propose an algorithm to calculate it.
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Submitted on : Wednesday, December 14, 2011 - 1:51:30 PM
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Elimane Ba. Résultant déterminantiel et applications. Algèbre commutative [math.AC]. Université Nice Sophia Antipolis, 2011. Français. ⟨tel-00651722⟩

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