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.

Elimination Practice

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Author : Dongming Wang
language : en
Publisher: World Scientific
Release Date : 2004

Elimination Practice written by Dongming Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.

Polynomial Elimination at Work; The Epsilon Library; The CharSets Package; The TriSys and SiSys Modules; The GEOTHER Environment; Relevant Elimination Tools; Solving Polynomial Systems; Automated Theorem Proving and Discovering in Geometry; Symbolic Geometric Computation; Selected Problems in Computer Mathematics.

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.

Applied Algebra Algebraic Algorithms And Error Correcting Codes

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Author : Gérard Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 1995

Applied Algebra Algebraic Algorithms And Error Correcting Codes written by Gérard 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 1995 with Algebra categories.

This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gröbner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.

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.

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!

Quantifier Elimination And Cylindrical Algebraic Decomposition

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Author : Bob F. Caviness
language : en
Publisher: Springer
Release Date : 1998-04-16

Quantifier Elimination And Cylindrical Algebraic Decomposition written by Bob F. Caviness and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-16 with Computers categories.

George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. This volume is a state-of-the art collection of important papers on CAD and QE and on the related area of algorithmic aspects of real geometry. In addition to original contributions by S. Basu et al., L. González-Vega et al., G. Hagel, H. Hong and J.R. Sendra, J.R. Johnson, S. McCallum, D. Richardson, and V. Weispfenning and a survey by G.E. Collins outlining the twenty-year progress in CAD-based QE it brings together seminal publications from the area: A. Tarski: A Decision Method for Elementary Algebra and Geometry G.E. Collins: Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition M.J. Fischer and M.O. Rabin: Super-Exponential Complexity of Presburger Arithmetic D.S. Arnon et al.: Cylindrical Algebraic Decomposition I: The Basic Algorithm; II: An Adjacency Algorithm for the Plane H. Hong: An Improvement of the Projection Operator in Cyclindrical Algebraic Decomposition G.E. Collins and H. Hong: Partial Cylindrical Algebraic Decomposition for Quantifier Elimination H. Hong: Simple Solution Formula Construction in Cylindrical Algebraic Decomposition Based Quantifier Elimination J. Renegar: Recent Progress on the Complexity of the Decision Problem for the Reals

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.