Solving Polynomial Equation Systems Iv Volume 4 Buchberger Theory And Beyond

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Solving Polynomial Equation Systems Iv Volume 4 Buchberger Theory And Beyond
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Author : Teo Mora
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-01
Solving Polynomial Equation Systems Iv Volume 4 Buchberger Theory And Beyond written by Teo Mora 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 2016-04-01 with Mathematics categories.
In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Solving Polynomial Equation Systems
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Author : Teo Mora
language : en
Publisher: Cambridge University Press
Release Date : 2003
Solving Polynomial Equation Systems written by Teo Mora 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 with Mathematics categories.
Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.
Computer Algebra In Scientific Computing
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Author : François Boulier
language : en
Publisher: Springer Nature
Release Date : 2023-08-23
Computer Algebra In Scientific Computing written by François Boulier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-23 with Computers categories.
This book constitutes the refereed proceedings of the 25th International Workshop on Computer Algebra in Scientific Computing, CASC 2023, which took place in Havana, Cuba, during August 28-September 1, 2023. The 22 full papers included in this book were carefully reviewed and selected from 29 submissions. They focus on the theory of symbolic computation and its implementation in computer algebra systems as well as all other areas of scientific computing with regard to their benefit from or use of computer algebra methods and software.
Intelligent Computer Mathematics
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Author : Christoph Benzmüller
language : en
Publisher: Springer Nature
Release Date : 2020-07-17
Intelligent Computer Mathematics written by Christoph Benzmüller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-17 with Computers categories.
This book constitutes the refereed proceedings of the 13th International Conference on Intelligent Computer Mathematics, CICM 2020, held in Bertinoro, Italy, in July 2020*. The 15 full papers, 1 invited paper and 2 abstracts of invited papers presented were carefully reviewed and selected from a total of 35 submissions. The papers focus on advances in automated theorem provers and formalization, computer algebra systems and their libraries, and applications of machine learning, among other topics. * The conference was held virtually due to the COVID-19 pandemic.
Solving Polynomial Equation Systems
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Author : Teo Mora
language : en
Publisher:
Release Date : 2016
Solving Polynomial Equation Systems written by Teo Mora and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with MATHEMATICS categories.
In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Numerical Polynomial Algebra
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Author : Hans J. Stetter
language : en
Publisher: SIAM
Release Date : 2004-01-01
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 2004-01-01 with Mathematics categories.
In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, Numerical Polynomial Algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas.
Solving Polynomial Equation Systems
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Author : Teo Mora
language : en
Publisher:
Release Date : 2016
Solving Polynomial Equation Systems written by Teo Mora and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Commutative algebra categories.
Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.
Algebraic Cryptanalysis
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Author : Gregory Bard
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-14
Algebraic Cryptanalysis written by Gregory Bard 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 2009-08-14 with Computers categories.
Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two covers finite field linear algebra; Part Three covers the solution of Polynomial Systems of Equations, with a survey of the methods used in practice, including SAT-solvers and the methods of Nicolas Courtois. Topics include: Analytic Combinatorics, and its application to cryptanalysis The equicomplexity of linear algebra operations Graph coloring Factoring integers via the quadratic sieve, with its applications to the cryptanalysis of RSA Algebraic Cryptanalysis is designed for advanced-level students in computer science and mathematics as a secondary text or reference book for self-guided study. This book is suitable for researchers in Applied Abstract Algebra or Algebraic Geometry who wish to find more applied topics or practitioners working for security and communications companies.
Ideals Varieties And Algorithms
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Author : David Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Ideals Varieties And Algorithms written by David Cox 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 2013-04-17 with Mathematics categories.
We wrote this book to introduce undergraduates to some interesting ideas in algebraic geometry and commutative algebra. Until recently, these topics involved a lot of abstract mathematics and were only taught in graduate school. But in the 1960's, Buchberger and Hironaka discovered new algorithms for manipulating systems of polynomial equations. Fueled by the development of computers fast enough to run these algorithms, the last two decades have seen a minor revolution in commutative algebra. The ability to compute efficiently with polynomial equations has made it possible to investigate complicated examples that would be impossible to do by hand, and has changed the practice of much research in algebraic geometry. This has also enhanced the importance of the subject for computer scientists and engineers, who have begun to use these techniques in a whole range of problems. It is our belief that the growing importance of these computational techniques warrants their introduction into the undergraduate (and graduate) mathematics curricu lum. Many undergraduates enjoy the concrete, almost nineteenth century, flavor that a computational emphasis brings to the subject. At the same time, one can do some substantial mathematics, including the Hilbert Basis Theorem, Elimination Theory and the Nullstellensatz. The mathematical prerequisites of the book are modest: the students should have had a course in linear algebra and a course where they learned how to do proofs. Examples of the latter sort of course include discrete math and abstract algebra.
Solving Polynomial Equations
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Author : Alicia Dickenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-29
Solving Polynomial Equations written by Alicia Dickenstein 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 2005-12-29 with Mathematics categories.
The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.