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Matrix Representations of Algebraic Varieties


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  • Product Description

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.

Product Specifications
SKU :COC93701
AuthorThang Luu Ba
Number of Pages112
Publishing Year2011-10-20T00:00:00.000
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandNot defined
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00