Elimination Methods In Polynomial Computer Algebra

Author : V. Bykov
Publisher : Springer Science & Business Media
ISBN 13 : 9401153027
Total Pages : 254 pages
Book Rating : 4.27/5 ( download)

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Download or read book Elimination Methods in Polynomial Computer Algebra written by V. Bykov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : V Bykov
Publisher :
ISBN 13 : 9789401153034
Total Pages : 260 pages
Book Rating : 4.35/5 ( download)

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Download or read book Elimination Methods in Polynomial Computer Algebra written by V Bykov and published by . This book was released on 1998-10-31 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : D. Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3709162025
Total Pages : 257 pages
Book Rating : 4.26/5 ( download)

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Download or read book Elimination Methods written by D. Wang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.

Author : Dongming Wang
Publisher : World Scientific
ISBN 13 : 1783260785
Total Pages : 232 pages
Book Rating : 4.82/5 ( download)

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Download or read book Elimination Practice written by Dongming Wang and published by World Scientific. This book was released on 2004-02-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a software library included, this book provides an elementary introduction to polynomial elimination in practice. The library Epsilon, implemented in Maple and Java, contains more than 70 well-documented functions for symbolic elimination and decomposition with polynomial systems and geometric reasoning. The book presents the functionality, implementation, and performance of Epsilon and demonstrates the usefulness of the elimination tool by a number of selected applications, together with many examples and illustrations. The reader will find Epsilon an efficient tool, applicable to a wide range of problems in science, engineering, and industry, and this book an accessible exposition and a valuable reference for elimination theory, methods, and practice. Contents:Polynomial Elimination at WorkThe Epsilon LibraryThe CharSets PackageThe TriSys and SiSys ModulesThe GEOTHER EnvironmentRelevant Elimination ToolsSolving Polynomial SystemsAutomated Theorem Proving and Discovering in GeometrySymbolic Geometric ComputationSelected Problems in Computer Mathematics Readership: Researchers and graduate students in symbolic mathematical computation, geometric reasoning and modeling, as well as mathematical software engineers. Keywords:Symbolic Computation;Mathematical Software;Elimination Method;Polynomial System;Computer Algebra;Geometric Reasoning;Surface ModelingReviews:“This book is a treasure … it will be welcomed by all those who are active in the area of elimination methods and will also attract new people to the exciting field of elimination methods, which is one of the oldest and, at the same time, one of the most topical areas in mathematics with a high future potential in all other areas of mathematics as well as in a wide range of applications in science, engineering, economy, etc.”Bruno Buchberger Professor of Computer Mathematics Johannes Kepler University, Austria

Author : Franz Winkler
Publisher : Springer Science & Business Media
ISBN 13 : 9783211827598
Total Pages : 294 pages
Book Rating : 4.95/5 ( download)

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Download or read book Polynomial Algorithms in Computer Algebra written by Franz Winkler and published by Springer Science & Business Media. This book was released on 1996-08-02 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Vladimir P. Gerdt
Publisher : Springer
ISBN 13 : 3319105159
Total Pages : 515 pages
Book Rating : 4.54/5 ( download)

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Download or read book Computer Algebra in Scientific Computing written by Vladimir P. Gerdt and published by Springer. This book was released on 2014-09-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Vladimir P. Gerdt
Publisher : Springer
ISBN 13 : 364232973X
Total Pages : 374 pages
Book Rating : 4.39/5 ( download)

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Download or read book Computer Algebra in Scientific Computing written by Vladimir P. Gerdt and published by Springer. This book was released on 2012-08-30 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2012, held in Maribor, Slovenia, in September 2012. The 28 full papers presented were carefully reviewed and selected for inclusion in this book. One of the main themes of the CASC workshop series, namely polynomial algebra, is represented by contributions devoted to new algorithms for computing comprehensive Gröbner and involutive systems, parallelization of the Gröbner bases computation, the study of quasi-stable polynomial ideals, new algorithms to compute the Jacobson form of a matrix of Ore polynomials, a recursive Leverrier algorithm for inversion of dense matrices whose entries are monic polynomials, root isolation of zero-dimensional triangular polynomial systems, optimal computation of the third power of a long integer, investigation of the complexity of solving systems with few independent monomials, the study of ill-conditioned polynomial systems, a method for polynomial root-finding via eigen-solving and randomization, an algorithm for fast dense polynomial multiplication with Java using the new opaque typed method, and sparse polynomial powering using heaps.

Author : Bob F. Caviness
Publisher : Springer Science & Business Media
ISBN 13 : 3709194598
Total Pages : 455 pages
Book Rating : 4.91/5 ( download)

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Download or read book Quantifier Elimination and Cylindrical Algebraic Decomposition written by Bob F. Caviness and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. It contains papers from a symposium held in Linz in 1993, reprints of seminal papers from the area including Tarski’s landmark paper as well as a survey outlining the developments in CAD based QE that have taken place in the last twenty years.

Author : Jaime Gutierrez
Publisher : Springer
ISBN 13 : 3319150812
Total Pages : 222 pages
Book Rating : 4.19/5 ( download)

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Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez and published by Springer. This book was released on 2015-01-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Karin Gatermann
Publisher : Springer
ISBN 13 : 3540465197
Total Pages : 163 pages
Book Rating : 4.95/5 ( download)

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Download or read book Computer Algebra Methods for Equivariant Dynamical Systems written by Karin Gatermann and published by Springer. This book was released on 2007-05-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.