Solving Systems Of Polynomial Equations
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Solving Systems Of Polynomial Equations
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Author : Bernd Sturmfels
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Solving Systems Of Polynomial Equations written by Bernd Sturmfels and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
Numerically Solving Polynomial Systems With Bertini
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Author : Daniel J. Bates
language : en
Publisher: SIAM
Release Date : 2013-11-08
Numerically Solving Polynomial Systems With Bertini written by Daniel J. Bates and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-08 with Science categories.
This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.
Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems
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Author : Alexander Morgan
language : en
Publisher: SIAM
Release Date : 2009-01-01
Solving Polynomial Systems Using Continuation For Engineering And Scientific Problems written by Alexander Morgan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Computers categories.
This book introduces the numerical technique of polynomial continuation, which is used to compute solutions to systems of polynomial equations. Originally published in 1987, it remains a useful starting point for the reader interested in learning how to solve practical problems without advanced mathematics. Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems is easy to understand, requiring only a knowledge of undergraduate-level calculus and simple computer programming. The book is also practical; it includes descriptions of various industrial-strength engineering applications and offers Fortran code for polynomial solvers on an associated Web page. It provides a resource for high-school and undergraduate mathematics projects. Audience: accessible to readers with limited mathematical backgrounds. It is appropriate for undergraduate mechanical engineering courses in which robotics and mechanisms applications are studied.
Solving Polynomial Equations
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Author : Alicia Dickenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-27
Solving Polynomial Equations written by Alicia Dickenstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-27 with Computers categories.
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Solving Polynomial Equation Systems
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Author : Teo Mora
language : en
Publisher:
Release Date : 2015
Solving Polynomial Equation Systems written by Teo Mora and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science
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Author : Andrew John Sommese
language : en
Publisher: World Scientific
Release Date : 2005
The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science written by Andrew John Sommese and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.
Solving Polynomial Equation Systems I
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Author : Teo Mora
language : en
Publisher: Cambridge University Press
Release Date : 2003-03-27
Solving Polynomial Equation Systems I written by Teo Mora and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-27 with Mathematics categories.
Computational algebra; computational number theory; commutative algebra; handbook; reference; algorithmic; modern.
General Theory Of Algebraic Equations
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Author : Etienne Bézout
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
General Theory Of Algebraic Equations written by Etienne Bézout and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.
This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.
Solving Polynomial Equation Systems Iv Volume 4 Buchberger Theory And Beyond
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Author : Teo Mora
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-01
Solving Polynomial Equation Systems Iv Volume 4 Buchberger Theory And Beyond written by Teo Mora and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-01 with Mathematics categories.
In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Solving Polynomial Equation Systems
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Author : Teo Mora
language : en
Publisher:
Release Date : 2003
Solving Polynomial Equation Systems written by Teo Mora and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Equations categories.
Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
