Elimination Methods In Polynomial Computer Algebra

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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.

Elimination Methods In Polynomial Computer Algebra

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Author : V Bykov
language : en
Publisher:
Release Date : 1998-10-31

Elimination Methods In Polynomial Computer Algebra written by V Bykov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-31 with categories.

Algorithms And Techniques In Computer Algebra

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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-15

Algorithms And Techniques In Computer Algebra written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-15 with Mathematics categories.

**Algorithms and Techniques in Computer Algebra** provides a comprehensive introduction to this rapidly developing field, covering the basic concepts, core algorithms, and practical applications of computer algebra. Suitable for both undergraduate and graduate students in computer science, mathematics, and engineering, this book is an essential resource for anyone looking to master the essential concepts and techniques of computer algebra. With in-depth explanations, illustrative examples, and comprehensive exercises, this book covers a wide range of topics, from the basic concepts of field theory and ring theory to advanced topics such as Gröbner bases and analytic integration. It also includes a chapter dedicated to recent developments and open problems in computer algebra, keeping readers abreast of the latest advancements in the field. One of the key strengths of **Algorithms and Techniques in Computer Algebra** is its focus on practical applications. It demonstrates how computer algebra can be used to solve real-world problems in various fields, including cryptography, coding theory, robotics, computer graphics, and artificial intelligence. This makes the book not only a valuable resource for students but also a practical guide for professionals seeking to apply computer algebra to their work. Whether you are a seasoned professional looking to expand your knowledge or a beginner seeking to understand the fundamentals of computer algebra, **Algorithms and Techniques in Computer Algebra** is the perfect resource for you. With its clear and concise explanations, illustrative examples, and comprehensive exercises, this book will help you master the essential concepts and techniques of this exciting field. If you like this book, write a review!

Computer Algebra Handbook

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

Computer Algebra Handbook written by Johannes Grabmeier 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.

Two ideas lie gleaming on the jeweler's velvet. The first is the calculus, the sec ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berlinski, The Advent of the Algorithm First there was the concept of integers, then there were symbols for integers: I, II, III, 1111, fttt (what might be called a sticks and stones representation); I, II, III, IV, V (Roman numerals); 1, 2, 3, 4, 5 (Arabic numerals), etc. Then there were other concepts with symbols for them and algorithms (sometimes) for ma nipulating the new symbols. Then came collections of mathematical knowledge (tables of mathematical computations, theorems of general results). Soon after algorithms came devices that provided assistancefor carryingout computations. Then mathematical knowledge was organized and structured into several related concepts (and symbols): logic, algebra, analysis, topology, algebraic geometry, number theory, combinatorics, etc. This organization and abstraction lead to new algorithms and new fields like universal algebra. But always our symbol systems reflected and influenced our thinking, our concepts, and our algorithms.

Polynomial Algorithms In Computer Algebra

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

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 2012-12-06 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.

Modern Computer Algebra

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Author : Joachim von zur Gathen
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-03

Modern Computer Algebra written by Joachim von zur Gathen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Computers categories.

Computer algebra systems are gaining importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority also make 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; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. For the new edition, errors have been corrected, the text has been smoothed and updated, and new sections on greatest common divisors and symbolic integration have been added.

Topics In Several Complex Variables

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Author : Zair Ibragimov
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-21

Topics In Several Complex Variables written by Zair Ibragimov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-21 with Mathematics categories.

This volume contains the proceedings of the Special Session on Several Complex Variables, which was held during the first USA-Uzbekistan Conference on Analysis and Mathematical Physics from May 20–23, 2014, at California State University, Fullerton. This volume covers a wide variety of topics in pluripotential theory, symplectic geometry and almost complex structures, integral formulas, holomorphic extension, and complex dynamics. In particular, the reader will find articles on Lagrangian submanifolds and rational convexity, multidimensional residues, S-parabolic Stein manifolds, Segre varieties, and the theory of quasianalytic functions.

Handbook Of Automated Reasoning

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Author : Alan J.A. Robinson
language : en
Publisher: Gulf Professional Publishing
Release Date : 2001-06-21

Handbook Of Automated Reasoning written by Alan J.A. Robinson and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-21 with Computers categories.

Handbook of Automated Reasoning.

Integrated Formal Methods

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Author : Erika Ábrahám
language : en
Publisher: Springer
Release Date : 2016-05-23

Integrated Formal Methods written by Erika Ábrahám and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-23 with Computers categories.

This book constitutes the refereed proceedings of the 12th International Conference on Integrated Formal Methods, IFM 2016, held in Reykjavik, Iceland, in June 2016. The 33 papers presented in this volume were carefully reviewed and selected from 99 submissions. They were organized in topical sections named: invited contributions; program verification; probabilistic systems; concurrency; safety and liveness; model learning; SAT and SMT solving; testing; theorem proving and constraint satisfaction; case studies.

Algorithms For Computer Algebra

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Author : Keith O. Geddes
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30

Algorithms For Computer Algebra written by Keith O. Geddes 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 2007-06-30 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.