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Solving Systems Of Polynomial Equations
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Book Synopsis Solving Systems of Polynomial Equations by : Bernd Sturmfels
Download or read book Solving Systems of Polynomial Equations written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 2002 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solving Systems of Polynomial Equations by : Bernd Sturmfels
Download or read book Solving Systems of Polynomial Equations written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 2002 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solving Polynomial Equations by : Alicia Dickenstein
Download or read book Solving Polynomial Equations written by Alicia Dickenstein and published by Springer Science & Business Media. This book was released on 2005-04-27 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerically Solving Polynomial Systems with Bertini by : Daniel J. Bates
Download or read book Numerically Solving Polynomial Systems with Bertini written by Daniel J. Bates and published by SIAM. This book was released on 2013-11-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems by : Alexander Morgan
Download or read book Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems written by Alexander Morgan and published by SIAM. This book was released on 2009-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerically Solving Polynomial Systems with Bertini by : Daniel J. Bates
Download or read book Numerically Solving Polynomial Systems with Bertini written by Daniel J. Bates and published by SIAM. This book was released on 2013-11-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applications of Computational Algebraic Geometry by : David A. Cox
Download or read book Applications of Computational Algebraic Geometry written by David A. Cox and published by American Mathematical Soc.. This book was released on 1998 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that "crunching equations" is now as easy as "crunching numbers" has had a profound impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusually elegant and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Gröbner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in this book assume no previous acquaintance with the material.
Book Synopsis Intermediate Algebra 2e by : Lynn Marecek
Download or read book Intermediate Algebra 2e written by Lynn Marecek and published by . This book was released on 2020-05-06 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Undergraduate Algebraic Geometry by : Miles Reid
Download or read book Undergraduate Algebraic Geometry written by Miles Reid and published by Cambridge University Press. This book was released on 1988-12-15 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.
Book Synopsis Solving Polynomial Equation Systems by : Teo Mora
Download or read book Solving Polynomial Equation Systems written by Teo Mora and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science by : Andrew J Sommese
Download or read book The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science written by Andrew J Sommese and published by World Scientific. This book was released on 2005-03-21 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solving Polynomial Equation Systems III: Volume 3, Algebraic Solving by : Teo Mora
Download or read book Solving Polynomial Equation Systems III: Volume 3, Algebraic Solving written by Teo Mora and published by Cambridge University Press. This book was released on 2015-08-07 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni–Kalkbrener Theorem, Stetter Algorithm, Cardinal–Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Book Synopsis Algorithms in Real Algebraic Geometry by : Saugata Basu
Download or read book Algorithms in Real Algebraic Geometry written by Saugata Basu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
Book Synopsis The Numerical Solution of Systems of Polynomials Arising in Engineering and Science by : Andrew John Sommese
Download or read book The Numerical Solution of Systems of Polynomials Arising in Engineering and Science written by Andrew John Sommese and published by World Scientific. This book was released on 2005 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solving Polynomial Equation Systems I by : Teo Mora
Download or read book Solving Polynomial Equation Systems I written by Teo Mora and published by Cambridge University Press. This book was released on 2003-03-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Polynomial Algebra by : Hans J. Stetter
Download or read book Numerical Polynomial Algebra written by Hans J. Stetter and published by SIAM. This book was released on 2004-05-01 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive treatment of numerical polynomial algebra, an area which so far has received little attention.
Book Synopsis Computations in Algebraic Geometry with Macaulay 2 by : David Eisenbud
Download or read book Computations in Algebraic Geometry with Macaulay 2 written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2001-09-25 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.
