Solving Polynomial Equations

Author : Alicia Dickenstein
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 49,8 Mb
Release : 2005-04-27
Category : Computers
ISBN : 9783540243267

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Solving Polynomial Equations by Alicia Dickenstein Pdf

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 : Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 52,6 Mb
Release : 2002
Category : Equations
ISBN : 9780821832516

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Solving Systems of Polynomial Equations by Bernd Sturmfels Pdf

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 : Teo Mora
Publisher : Unknown
Page : 128 pages
File Size : 44,5 Mb
Release : 2015
Category : Electronic
ISBN : 1316314812

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Solving Polynomial Equation Systems by Teo Mora Pdf

Author : Lynn Marecek,MaryAnne Anthony-Smith,Andrea Honeycutt Mathis
Publisher : Unknown
Page : 128 pages
File Size : 40,6 Mb
Release : 2020-05-06
Category : Electronic
ISBN : 1951693841

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Intermediate Algebra 2e by Lynn Marecek,MaryAnne Anthony-Smith,Andrea Honeycutt Mathis Pdf

Author : William A. Hardy
Publisher : Trafford Publishing
Page : 252 pages
File Size : 40,6 Mb
Release : 2005
Category : Education
ISBN : 9781412044530

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Polynomial Resolution Theory by William A. Hardy Pdf

This book is the definitive work on polynomial solution theory. Starting with the simplest linear equations with complex coefficients, this book proceeds in a step by step logical manner to outline the method for solving equations of arbitrarily high degree. Polynomial Resolution Theory is an invaluable book because of its unique perspective on the age old problem of solving polynomial equations of arbitrarily high degree. First of all Hardy insists upon pursuing the subject by using general complex coefficients rather than restricting himself to real coefficients. Complex numbers are used in ordered pair (x,y) form rather than the more traditional x + iy (or x + jy) notation. As Hardy comments, "The Fundamental Theorem of Algebra makes the treatments of polynomials with complex coefficients mandatory. We must not allow applications to direct the way mathematics is presented, but must permit the mathematical results themselves determine how to present the subject. Although practical, real-world applications are important, they must not be allowed to dictate the way in which a subject is treated. Thus, although there are at present no practical applications which employ polynomials with complex coefficients, we must present this subject with complex rather than restrictive real coefficients." This book then proceeds to recast familiar results in a more consistent notation for later progress. Two methods of solution to the general cubic equation with complex coefficients are presented. Then Ferrari's solution to the general complex bicubic (fourth degree) polynomial equation is presented. After this Hardy seamlessly presents the first extension of Ferrari's work to resolving the general bicubic (sixth degree) equation with complex coefficients into two component cubic equations. Eight special cases of this equation which are solvable in closed form are developed with detailed examples. Next the resolution of the octal (eighth degree) polynomial equation is developed along with twelve special cases which are solvable in closed form. This book is appropriate for students at the advanced college algebra level who have an understanding of the basic arithmetic of the complex numbers and know how to use a calculator which handles complex numbers directly. Hardy continues to develop the theory of polynomial resolution to equations of degree forty-eight. An extensive set of appendices is useful for verifying derived results and for rigging various special case equations. This is the 3rd edition of Hardy's book.

Author : Teo Mora
Publisher : Cambridge University Press
Page : 452 pages
File Size : 47,8 Mb
Release : 2003-03-27
Category : Mathematics
ISBN : 0521811546

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Solving Polynomial Equation Systems I by Teo Mora Pdf

Computational algebra; computational number theory; commutative algebra; handbook; reference; algorithmic; modern.

Author : Teo Mora
Publisher : Unknown
Page : 439 pages
File Size : 46,9 Mb
Release : 2003
Category : Equations
ISBN : 0511178883

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Solving Polynomial Equation Systems by Teo Mora Pdf

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 : Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler
Publisher : SIAM
Page : 372 pages
File Size : 42,8 Mb
Release : 2013-11-08
Category : Science
ISBN : 9781611972696

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Numerically Solving Polynomial Systems with Bertini by Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler Pdf

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 : Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler
Publisher : SIAM
Page : 372 pages
File Size : 41,8 Mb
Release : 2013-11-08
Category : Science
ISBN : 9781611972702

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Numerically Solving Polynomial Systems with Bertini by Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler Pdf

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 : Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 47,6 Mb
Release : 2002
Category : Equations
ISBN : 9780821832516

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Solving Systems of Polynomial Equations by Bernd Sturmfels Pdf

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 : Alexander Morgan
Publisher : SIAM
Page : 331 pages
File Size : 51,8 Mb
Release : 2009-01-01
Category : Computers
ISBN : 9780898719031

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Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems by Alexander Morgan Pdf

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.

Author : Teo Mora
Publisher : Cambridge University Press
Page : 128 pages
File Size : 50,6 Mb
Release : 2016-04-01
Category : Mathematics
ISBN : 9781316381380

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Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond by Teo Mora Pdf

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.

Author : Teo Mora
Publisher : Unknown
Page : 0 pages
File Size : 46,8 Mb
Release : 2003
Category : Equations
ISBN : 0511306024

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Solving Polynomial Equation Systems I by Teo Mora Pdf

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 : Alicia Dickenstein,Ioannis Z. Emiris
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 45,5 Mb
Release : 2005-12-29
Category : Mathematics
ISBN : 9783540273578

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Solving Polynomial Equations by Alicia Dickenstein,Ioannis Z. Emiris Pdf

The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Author : John P. Boyd
Publisher : SIAM
Page : 462 pages
File Size : 42,6 Mb
Release : 2014-09-23
Category : Mathematics
ISBN : 9781611973525

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Solving Transcendental Equations by John P. Boyd Pdf

Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute--not always needed, but indispensible when it is. The author's goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations.