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Matrix Representations of Algebraic Varieties: Matrix-based implicit representations of algebraic curves and surfaces and applications (Omn.Univ.Europ.) - Softcover
Synopsis
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.
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About the Author
I am a lecturer in the Department of Mathematics, Hanoi National University of Education, Vietnam. My research interests are algebra computer and computational Geometry. I received a BS and an MS in Math from Hanoi National University of Education in 2001 and 2005, respectively, and a PhD in applied Math from the University of Nice, France in 2011.
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Matrix Representations of Algebraic Varieties: Matrix-based implicit representations of algebraic curves and surfaces and applications (Omn.Univ.Europ.)
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Matrix Representations of Algebraic Varieties
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Matrix Representations of Algebraic Varieties
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 108 pp. Englisch. Seller Inventory # 9786131598104
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Matrix Representations of Algebraic Varieties : Matrix-based implicit representations of algebraic curves and surfaces and applications
Published by
Éditions Universitaires Européennes, 2011
ISBN 10: 613159810X
ISBN 13: 9786131598104
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Seller Inventory # 9786131598104
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Matrix Representations of Algebraic Varieties
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Luu Ba ThangI am a lecturer in the Department of Mathematics, Hanoi National University of Education, Vietnam. My research interests are algebra computer and computational Geometry. I received a BS and an MS in Math from Hanoi Nation. Seller Inventory # 5801654
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Matrix Representations of Algebraic Varieties
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ISBN 10: 613159810X
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Taschenbuch. Condition: Neu. Neuware -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.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 108 pp. Englisch. Seller Inventory # 9786131598104
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Matrix Representations of Algebraic Varieties: Matrix-based implicit representations of algebraic curves and surfaces and applications (Omn.Univ.Europ.)
Published by
Editions universitaires europeennes, 2011
ISBN 10: 613159810X
ISBN 13: 9786131598104
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Matrix Representations of Algebraic Varieties: Matrix-based implicit representations of algebraic curves and surfaces and applications (Omn.Univ.Europ.)
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ISBN 10: 613159810X
ISBN 13: 9786131598104
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