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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Matrix Representations of Algebraic Varieties

Matrix Representations of Algebraic Varieties

Luu Ba-T

Paperback

Series: Omn.Univ.Europ.

Literary CriticismGeneral Mathematics

ISBN10: 613159810X
ISBN13: 9786131598104
Publisher: Ed Universitaires Europeennes
Published: Feb 28 2018
Pages: 112
Weight: 0.39
Height: 0.27 Width: 5.98 Depth: 9.02
Language: French
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 hypothes

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