Algorithms For Computer Algebra Pdf Book
Author by: Franz WinklerLanguange: enPublisher by: Springer Science & Business MediaFormat Available: PDF, ePub, MobiTotal Read: 32Total Download: 953File Size: 53,5 MbDescription: 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. Caviness and B. Saunders, who first stimulated my interest in various problems in computer algebra, G. Collins, who showed me how to compute in algebraic domains, and J. 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. Author by: Keith O.
GeddesLanguange: enPublisher by: Springer Science & Business MediaFormat Available: PDF, ePub, MobiTotal Read: 35Total Download: 922File Size: 54,5 MbDescription: 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.
Author by: V. BykovLanguange: enPublisher by: Springer Science & Business MediaFormat Available: PDF, ePub, MobiTotal Read: 30Total Download: 213File Size: 46,7 MbDescription: 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. Author by: Richard ZippelLanguange: enPublisher by: Springer Science & Business MediaFormat Available: PDF, ePub, MobiTotal Read: 30Total Download: 274File Size: 47,6 MbDescription: 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. Author by: Jaime GutierrezLanguange: enPublisher by: SpringerFormat Available: PDF, ePub, MobiTotal Read: 91Total Download: 197File Size: 50,5 MbDescription: 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. Author by: Johannes GrabmeierLanguange: enPublisher by: Springer Science & Business MediaFormat Available: PDF, ePub, MobiTotal Read: 13Total Download: 555File Size: 55,8 MbDescription: This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
Author by: B. BuchbergerLanguange: enPublisher by: Springer Science & Business MediaFormat Available: PDF, ePub, MobiTotal Read: 28Total Download: 208File Size: 51,5 MbDescription: 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.
Computer Science Algorithms Book
3877), the Austrian Ministry of Science and Research (Department 12, Dr. 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. 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.
Algorithms For Computer Algebra Pdf Books
C.: Integration in Finite Terms. Author by: Joel S. CohenLanguange: enPublisher by: A K Peters, Ltd.Format Available: PDF, ePub, MobiTotal Read: 16Total Download: 166File Size: 43,8 MbDescription: This text: is well-suited for self-study and can be used as the basis for an advanced undergraduate or beginning graduate course; maintains the style set by Elementary Algorithms; introduces advanced methods to treat complex operations; presents implementations in such programs as Mathematica, Maple, and MuPAD; and includes a CD with the complete text, hyperlinks, and algorithms as well as additional reference files. For the student, Mathematical Methods is an essential companion to Elementary Algorithms, illustrating applications of basic ideas. For the professional, Mathematical Methods is a look at new applications of familiar concepts.