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
Total Download : 7800163
Total Read : 9252283
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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
Total Download : 9434815
Total Read : 8170290
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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.

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
Total Download : 8760586
Total Read : 2442128
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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
Total Download : 6983922
Total Read : 7226367
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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.

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
Total Download : 1845334
Total Read : 4155271
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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.

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
Total Download : 1210323
Total Read : 2974456
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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.

Mathematics for Computer Algebra

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Author by : Maurice Mignotte
Languange Used : English, France, Spanish, Italia and chinese
Page : 346
Isbn : 1461391717
Identifier : 9781461391715
Release : 2012-12-06
Publisher by : Springer Science & Business Media
Category : Computers
Total Download : 5646525
Total Read : 8116580
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Description : Read Now Mathematics For Computer Algebra by Maurice Mignotte and you can download with pub, pdf, txt, doc, and more file format with free account. this book corresponds to a mathematical course given in 1986/87 at the university louis pasteur, strasbourg. this work is primarily intended for graduate students. the following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementary facts in combinatorics (maybe only newton's binomial formula), some theorems of analysis at the level of high schools, and some elementary algebra (basic results about groups, rings, fields and linear algebra). an important place is given to exercises. these exercises are only rarely direct applications of the course. more often, they constitute complements to the text. mostly, hints or references are given so that the reader should be able to find solutions. chapters one and two deal with elementary results of number theory, for example : the euclidean algorithm, the chinese remainder theorem and fermat's little theorem. these results are useful by themselves, but they also constitute a concrete introduction to some notions in abstract algebra (for example, euclidean rings, principal rings ... ). algorithms are given for arithmetical operations with long integers. the rest of the book, chapters 3 through 7, deals with polynomials. we give general results on polynomials over arbitrary rings. then polynomials with complex coefficients are studied in chapter 4, including many estimates on the complex roots of polynomials. some of these estimates are very useful in the subsequent chapters.

Rational Algebraic Curves A Computer Algebra Approach

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Author by : J. Rafael Sendra
Languange Used : English, France, Spanish, Italia and chinese
Page : 270
Isbn : 3540737251
Identifier : 9783540737254
Release : 2007-12-10
Publisher by : Springer Science & Business Media
Category : Mathematics
Total Download : 8324187
Total Read : 7474579
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Description : Read Now Rational Algebraic Curves by J. Rafael Sendra and you can download with pub, pdf, txt, doc, and more file format with free account. the central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. this amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. the book discusses various optimality criteria for rational parametrizations of algebraic curves.

Structured Matrices and Polynomials Unified Superfast Algorithms

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Author by : Victor Y. Pan
Languange Used : English, France, Spanish, Italia and chinese
Page : 278
Isbn : 1461201292
Identifier : 9781461201298
Release : 2012-12-06
Publisher by : Springer Science & Business Media
Category : Mathematics
Total Download : 1703214
Total Read : 2350127
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Description : Read Now Structured Matrices And Polynomials by Victor Y. Pan and you can download with pub, pdf, txt, doc, and more file format with free account. this user-friendly, engaging textbook makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. the book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.

Algebra: Polynomials, Galois Theory and Applications

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Author by : Frédéric Butin
Languange Used : English, France, Spanish, Italia and chinese
Page : 288
Isbn : 0486810151
Identifier : 9780486810157
Release : 2017-02-15
Publisher by : Courier Dover Publications
Category : Mathematics
Total Download : 6540717
Total Read : 4961714
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Description : Read Now Algebra Polynomials Galois Theory And Applications by Frédéric Butin and you can download with pub, pdf, txt, doc, and more file format with free account. suitable for advanced undergraduates and graduate students in mathematics and computer science, this precise, self-contained treatment of galois theory features detailed proofs and complete solutions to exercises. originally published in french as algèbre — polynômes, théorie de galois et applications informatiques, this 2017 dover aurora edition marks the volume's first english-language publication. the three-part treatment begins by providing the essential introduction to galois theory. the second part is devoted to the algebraic, normal, and separable galois extensions that constitute the center of the theory and examines abelian, cyclic, cyclotomic, and radical extensions. this section enables readers to acquire a comprehensive understanding of the galois group of a polynomial. the third part deals with applications of galois theory, including excellent discussions of several important real-world applications of these ideas, including cryptography and error-control coding theory. symbolic computation via the maple computer algebra system is incorporated throughout the text (though other software of symbolic computation could be used as well), along with a large number of very interesting exercises with full solutions.

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
Total Download : 2627147
Total Read : 1220044
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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.

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
Total Download : 2710832
Total Read : 4782168
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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.