Computer Algebra And Polynomials

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Computer Algebra And Polynomials

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Author : Jaime Gutierrez
language : en
Publisher: Springer
Release Date : 2015-01-20

Computer Algebra And Polynomials written by Jaime Gutierrez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-20 with Computers categories.

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 : Franz Winkler
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-08-02

Polynomial Algorithms In Computer Algebra written by Franz Winkler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-02 with Mathematics categories.

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.

Mathematics For Computer Algebra

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Author : Maurice Mignotte
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mathematics For Computer Algebra written by Maurice Mignotte and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

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.

Some Tapas Of Computer Algebra

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Author : Arjeh M. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Some Tapas Of Computer Algebra written by Arjeh M. Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Computers categories.

In the years 1994, 1995, two EIDMA mini courses on Computer Algebra were given at the Eindhoven University of Technology by, apart from ourselves, various invited lecturers. (EIDMA is the Research School 'Euler Institute for Discrete Mathematics and its Applications'.) The idea of the courses was to acquaint young mathematicians with algorithms and software for mathemat ical research and to enable them to incorporate algorithms in their research. A collection of lecture notes was used at these courses. When discussing these courses in comparison with other kinds of courses one might give in a week's time, Joachim Neubüser referred to our courses as 'tapas'. This denomination underlined that the courses consisted of appe tizers for various parts of algorithmic algebra; indeed, we covered such spicy topics as the link between Gröbner bases and integer programming, and the detection of algebraic solutions to differential equations. As a collection, the not es turned out to have some appeal of their own, which is the main reason why the idea came up of transforming them into book form. We feIt however, that the book should be distinguishable from a standard text book on computer algebra in that it retains its appetizing flavour by presenting a variety of topics at an accessible level with a view to recent developments.

Computer Algebra And Symbolic Computation

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Author : Joel S. Cohen
language : en
Publisher: CRC Press
Release Date : 2003-01-03

Computer Algebra And Symbolic Computation written by Joel S. Cohen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-03 with Computers categories.

Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polyno

Numerical Polynomial Algebra

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Author : Hans J. Stetter
language : en
Publisher: SIAM
Release Date : 2004-05-01

Numerical Polynomial Algebra written by Hans J. Stetter and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-01 with Mathematics categories.

This book is the first comprehensive treatment of numerical polynomial algebra, an area which so far has received little attention.

Elimination Methods In Polynomial Computer Algebra

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Author : V. Bykov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Elimination Methods In Polynomial Computer Algebra written by V. Bykov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Computer Algebra

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Author : R. Albrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Computer Algebra written by R. Albrecht and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

this gap. In sixteen survey articles the most important theoretical results, algorithms and software methods of computer algebra are covered, together with systematic references to literature. In addition, some new results are presented. Thus the volume should be a valuable source for obtaining a first impression of computer algebra, as well as for preparing a computer algebra course or for complementary reading. The preparation of some papers contained in this volume has been supported by grants from the Austrian "Fonds zur Forderung der wissenschaftlichen For schung" (Project No. 3877), the Austrian Ministry of Science and Research (Department 12, Dr. S. Hollinger), the United States National Science Foundation (Grant MCS-8009357) and the Deutsche Forschungsgemeinschaft (Lo-23 1-2). The work on the volume was greatly facilitated by the opportunity for the editors to stay as visitors at the Department of Computer and Information Sciences, University of Delaware, at the General Electric Company Research and Development Center, Schenectady, N. Y. , and at the Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, N. Y. , respectively. Our thanks go to all these institutions. The patient and experienced guidance and collaboration of the Springer-Verlag Wien during all the stages of production are warmly appreciated. The editors of the Cooperative editor of Supplementum Computing B. Buchberger R. Albrecht G. Collins R. Loos Contents Loos, R. : Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 1 Buchberger, B. , Loos, R. : Algebraic Simplification . . . . . . . . . . 11 Neubiiser, J. : Computing with Groups and Their Character Tables. 45 Norman, A. C. : Integration in Finite Terms. . . . . . . . . . . . . .

Algorithms For Computer Algebra

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Author : Keith O. Geddes
language : en
Publisher: Springer
Release Date : 2013-03-24

Algorithms For Computer Algebra written by Keith O. Geddes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-24 with Computers categories.

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.

Computer Algebra In Scientific Computing

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Author : Vladimir P. Gerdt
language : en
Publisher: Springer
Release Date : 2014-09-01

Computer Algebra In Scientific Computing written by Vladimir P. Gerdt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with Computers categories.

This book constitutes the proceedings of the 16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014, held in Warsaw, Poland, in September 2014. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as Studies in polynomial algebra are represented by contributions devoted to factoring sparse bivariate polynomials using the priority queue, the construction of irreducible polynomials by using the Newton index, real polynomial root finding by means of matrix and polynomial iterations, application of the eigenvalue method with symmetry for solving polynomial systems arising in the vibration analysis of mechanical structures with symmetry properties, application of Gröbner systems for computing the (absolute) reduction number of polynomial ideals, the application of cylindrical algebraic decomposition for solving the quantifier elimination problems, certification of approximate roots of overdetermined and singular polynomial systems via the recovery of an exact rational univariate representation from approximate numerical data, new parallel algorithms for operations on univariate polynomials (multi-point evaluation, interpolation) based on subproduct tree techniques.