Computer Algebra And Polynomials

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Computer Algebra and Polynomials Applications of Algebra and Number Theory

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Author by : Jaime Gutierrez
Languange Used : English, France, Spanish, Italia and chinese
Page : 213
Isbn : 3319150812
Identifier : 9783319150819
Release : 2015-01-20
Publisher by : Springer
Category : Computers
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Description : Read Now Computer Algebra And Polynomials by Jaime Gutierrez and you can download with pub, pdf, txt, doc, and more file format with free account. algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. however, for a long time they were not considered that important in view of the lack of real-life applications. this has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. this book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. the operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. the papers presented were selected from the workshop on computer algebra and polynomials, which was held in linz at the johann radon institute for computational and applied mathematics (ricam) during november 25-29, 2013, at the occasion of the special semester on applications of algebra and number theory.

Polynomial Algorithms in Computer Algebra

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Author by : Franz Winkler
Languange Used : English, France, Spanish, Italia and chinese
Page : 270
Isbn : 3709165717
Identifier : 9783709165713
Release : 2012-12-06
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now Polynomial Algorithms In Computer Algebra by Franz Winkler and you can download with pub, pdf, txt, doc, and more file format with free account. for several years now i have been teaching courses in computer algebra at the universitat linz, the university of delaware, and the universidad de alcala de henares. in the summers of 1990 and 1992 i have organized and taught summer schools in computer algebra at the universitat linz. gradually a set of course notes has emerged from these activities. people have asked me for copies of the course notes, and different versions of them have been circulating for a few years. finally i decided that i should really take the time to write the material up in a coherent way and make a book out of it. here, now, is the result of this work. over the years many students have been helpful in improving the quality of the notes, and also several colleagues at linz and elsewhere have contributed to it. i want to thank them all for their effort, in particular i want to thank b. buchberger, who taught me the theory of grabner bases nearly two decades ago, b. f. caviness and b. d. saunders, who first stimulated my interest in various problems in computer algebra, g. e. collins, who showed me how to compute in algebraic domains, and j. r. sendra, with whom i started to apply computer algebra methods to problems in algebraic geometry. several colleagues have suggested improvements in earlier versions of this book. however, i want to make it clear that i am responsible for all remaining mistakes.

Numerical Polynomial Algebra

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Author by : Hans J. Stetter
Languange Used : English, France, Spanish, Italia and chinese
Page : 472
Isbn : 9780898717976
Identifier : 0898717973
Release : 2004
Publisher by : SIAM
Category : Numerical analysis
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Description : Read Now Numerical Polynomial Algebra by Hans J. Stetter and you can download with pub, pdf, txt, doc, and more file format with free account. in many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. this book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far. the author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. for the application scientist, numerical polynomial algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. in addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas.

Elimination Methods in Polynomial Computer Algebra

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Author by : V. Bykov
Languange Used : English, France, Spanish, Italia and chinese
Page : 244
Isbn : 9401153027
Identifier : 9789401153027
Release : 2012-12-06
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now Elimination Methods In Polynomial Computer Algebra by V. Bykov and you can download with pub, pdf, txt, doc, and more file format with free account. the subject of this book is connected with a new direction in mathematics, which has been actively developed over the last few years, namely the field of polynomial computer algebra, which lies at the intersection point of algebra, mathematical analysis and programming. there were several incentives to write the book. first of all, there has lately been a considerable interest in applied nonlinear problems characterized by multiple sta tionary states. practical needs have then in their turn led to the appearance of new theoretical results in the analysis of systems of nonlinear algebraic equations. and finally, the introduction of various computer packages for analytic manipulations has made it possible to use complicated elimination-theoretical algorithms in prac tical research. the structure of the book is accordingly represented by three main parts: mathematical results driven to constructive algorithms, computer algebra realizations of these algorithms, and applications. nonlinear systems of algebraic equations arise in diverse fields of science. in particular, for processes described by systems of differential equations with a poly nomial right hand side one is faced with the problem of determining the number (and location) of the stationary states in certain sets.

Algorithms for Computer Algebra

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Author by : Keith O. Geddes
Languange Used : English, France, Spanish, Italia and chinese
Page : 586
Isbn : 0585332479
Identifier : 9780585332475
Release : 2007-06-30
Publisher by : Springer Science & Business Media
Category : Computers
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Description : Read Now Algorithms For Computer Algebra by Keith O. Geddes and you can download with pub, pdf, txt, doc, and more file format with free account. algorithms for computer algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. the book first develops the foundational material from modern algebra that is required for subsequent topics. it then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. numerous examples are integrated into the text as an aid to understanding the mathematical development. the algorithms developed for each topic are presented in a pascal-like computer language. an extensive set of exercises is presented at the end of each chapter. algorithms for computer algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. the book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Solving Systems of Polynomial Equations

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Author by : Bernd Sturmfels
Languange Used : English, France, Spanish, Italia and chinese
Page : 152
Isbn : 0821832514
Identifier : 9780821832516
Release : 2002
Publisher by : American Mathematical Soc.
Category : Mathematics
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Description : Read Now Solving Systems Of Polynomial Equations by Bernd Sturmfels and you can download with pub, pdf, txt, doc, and more file format with free account. a classic problem in mathematics is solving systems of polynomial equations in several unknowns. today, polynomial models are ubiquitous and widely used across the sciences. they arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, and numerous other areas. this book furnishes a bridge across mathematical disciplines and exposes many facets of systems of polynomial equations. it covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.the set of solutions to a system of polynomial equations is an algebraic variety - the basic object of algebraic geometry. the algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. exciting recent developments in computer software for geometric calculations have revolutionized the field. formerly inaccessible problems are now tractable, providing fertile ground for experimentation and conjecture. the first half of the book gives a snapshot of the state of the art of the topic. familiar themes are covered in the first five chapters, including polynomials in one variable, grobner bases of zero-dimensional ideals, newton polytopes and bernstein's theorem, multidimensional resultants, and primary decomposition.the second half of the book explores polynomial equations from a variety of novel and unexpected angles. it introduces interdisciplinary connections, discusses highlights of current research, and outlines possible future algorithms. topics include computation of nash equilibria in game theory, semidefinite programming and the real nullstellensatz, the algebraic geometry of statistical models, the piecewise-linear geometry of valuations and amoebas, and the ehrenpreis-palamodov theorem on linear partial differential equations with constant coefficients.throughout the text, there are many hands-on examples and exercises, including short but complete sessions in mapler, matlabr, macaulay 2, singular, phcpack, cocoa, and sostools software. these examples will be particularly useful for readers with no background in algebraic geometry or commutative algebra. within minutes, readers can learn how to type in polynomial equations and actually see some meaningful results on their computer screens. prerequisites include basic abstract and computational algebra. the book is designed as a text for a graduate course in computational algebra.

Computer Algebra and Symbolic Computation Elementary Algorithms

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Author by : Joel S. Cohen
Languange Used : English, France, Spanish, Italia and chinese
Page : 323
Isbn : 9781568811581
Identifier : 1568811586
Release : 2002-07-19
Publisher by : A K Peters/CRC Press
Category : Mathematics
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Description : Read Now Computer Algebra And Symbolic Computation by Joel S. Cohen and you can download with pub, pdf, txt, doc, and more file format with free account. this book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. the viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and construct expressions, we can implement many elementary operations from algebra, trigonometry, calculus, and differential equations. with a minimum of prerequisites this book is accessible to and useful for students of mathematics, computer science, and other technical fields. the book contains a cd with the full, searchable text and implementations of all algorithms in the maple, mathematica, and mupad programming languages.

Algorithms for Computer Algebra

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Author by : Keith O. Geddes
Languange Used : English, France, Spanish, Italia and chinese
Page : 586
Isbn : 0585332479
Identifier : 9780585332475
Release : 2007-06-30
Publisher by : Springer Science & Business Media
Category : Computers
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Description : Read Now Algorithms For Computer Algebra by Keith O. Geddes and you can download with pub, pdf, txt, doc, and more file format with free account. algorithms for computer algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. the book first develops the foundational material from modern algebra that is required for subsequent topics. it then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. numerous examples are integrated into the text as an aid to understanding the mathematical development. the algorithms developed for each topic are presented in a pascal-like computer language. an extensive set of exercises is presented at the end of each chapter. algorithms for computer algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. the book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Effective Polynomial Computation

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Author by : Richard Zippel
Languange Used : English, France, Spanish, Italia and chinese
Page : 363
Isbn : 1461531888
Identifier : 9781461531883
Release : 2012-12-06
Publisher by : Springer Science & Business Media
Category : Computers
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Description : Read Now Effective Polynomial Computation by Richard Zippel and you can download with pub, pdf, txt, doc, and more file format with free account. effective polynomial computation is an introduction to the algorithms of computer algebra. it discusses the basic algorithms for manipulating polynomials including factoring polynomials. these algorithms are discussed from both a theoretical and practical perspective. those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. effective polynomial computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. these results are either used in later algorithms (e.g. the discussion of lattices and diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. euclidean algorithm and p-adic numbers). among the unique features of effective polynomial computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. in addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

Elements of Computer Algebra With Applications

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Author by : Alkiviadis G. Akritas
Languange Used : English, France, Spanish, Italia and chinese
Page : 448
Isbn :
Identifier : UOM:39015019611295
Release : 1989-03-30
Publisher by : Wiley-Interscience
Category : Mathematics
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Description : Read Now Elements Of Computer Algebra With Applications by Alkiviadis G. Akritas and you can download with pub, pdf, txt, doc, and more file format with free account. numerical modeling in science and engineering myron b. allen, george f. pinder, and ismael herrera emphasizing applications, this treatment combines three traditionally distinct disciplines—continuum mechanics, differential equations, and numerical analysis—to provide a unified treatment of numerical modeling of physical systems. covers basic equations of macroscopic systems, numerical methods, steady state systems, dissipative systems, nondissipative systems, and high order, nonlinear, and coupled systems. 1988 (0 471-80635-8) 418 pp. mathematical modeling and digital simulation for engineers and scientists second edition jon m. smith totally updated, this second edition reflects the many developments in simulation and computer modeling theory and practice that have occurred over the past decade. it includes a new section on the use of modern numerical methods for generating chaos and simulating random processes, a section on simulator verification, and provides applications of these methods for personal computers. readers will find a wealth of practical fault detection and isolation techniques for simulator verification, fast functions evaluation techniques, and nested parenthetical forms and chebyshev economization techniques. 1987 (0 471-08599-5) 430 pp. numerical analysis 1987 david f. griffiths and george alistair watson an invaluable guide to the direction of current research in many areas of numerical analysis, this volume will be of great interest to anyone involved in software design, curve and surface fitting, the numerical solution of ordinary, partial, and integro-differential equations, and the real-world application of numerical techniques. 1988 (0 470-21012-5) 300 pp.

Modern Computer Algebra

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Author by : Joachim von zur Gathen
Languange Used : English, France, Spanish, Italia and chinese
Page : 233
Isbn : 1107245257
Identifier : 9781107245259
Release : 2013-04-25
Publisher by : Cambridge University Press
Category : Computers
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Description : Read Now Modern Computer Algebra by Joachim von zur Gathen and you can download with pub, pdf, txt, doc, and more file format with free account. computer algebra systems are now ubiquitous in all areas of science and engineering. this highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). a great deal of historical information and illustration enlivens the text. in this third edition, errors have been corrected and much of the fast euclidean algorithm chapter has been renovated.

Computer Algebra in Quantum Field Theory Integration, Summation and Special Functions

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Author by : Carsten Schneider
Languange Used : English, France, Spanish, Italia and chinese
Page : 411
Isbn : 3709116163
Identifier : 9783709116166
Release : 2013-10-05
Publisher by : Springer Science & Business Media
Category : Science
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Description : Read Now Computer Algebra In Quantum Field Theory by Carsten Schneider and you can download with pub, pdf, txt, doc, and more file format with free account. the book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. it presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular feynman integrals, difference and differential equations in the format of survey articles. the presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.