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Author : Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 46,58 MB
Release : 2002
Category : Mathematics
ISBN : 0821832514
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.
Author : Alicia Dickenstein
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 32,7 MB
Release : 2005-04-27
Category : Computers
ISBN : 3540243267
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.
Author : Teo Mora
Publisher :
Page : pages
File Size : 23,99 MB
Release : 2015
Category :
ISBN : 9781316314814
Author : Daniel J. Bates
Publisher : SIAM
Page : 372 pages
File Size : 40,47 MB
Release : 2013-11-08
Category : Science
ISBN : 1611972698
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.
Author : Teo Mora
Publisher : Cambridge University Press
Page : 0 pages
File Size : 36,49 MB
Release : 2003-03-27
Category : Mathematics
ISBN : 9780521811545
With the advent of computers, theoretical studies and solution methods for polynomial equations have changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasizing computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show 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.
Author : Teo Mora
Publisher : Cambridge University Press
Page : 452 pages
File Size : 30,72 MB
Release : 2003-03-27
Category : Mathematics
ISBN : 9780521811545
Computational algebra; computational number theory; commutative algebra; handbook; reference; algorithmic; modern.
Author : Teo Mora
Publisher :
Page : 439 pages
File Size : 50,96 MB
Release : 2003
Category : Equations
ISBN : 9780511178887
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.
Author : Lynn Marecek
Publisher :
Page : pages
File Size : 19,86 MB
Release : 2020-05-06
Category :
ISBN : 9781951693848
Author : Daniel J. Bates
Publisher : SIAM
Page : 372 pages
File Size : 15,36 MB
Release : 2013-11-08
Category : Science
ISBN : 1611972701
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.
Author : Teo Mora
Publisher : Cambridge University Press
Page : 792 pages
File Size : 41,41 MB
Release : 2003
Category : Mathematics
ISBN : 9780521811569
This volume focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. The presentation is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in its algorithmization.