Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond
Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond

Author: Teo Mora

Publisher: Cambridge University Press

Published: 2016-04-01

Total Pages: 833

ISBN-13: 1316381382

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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
Solving Polynomial Equation Systems

Author: Teo Mora

Publisher: Cambridge University Press

Published: 2003

Total Pages: 833

ISBN-13: 1107109639

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Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.

Intelligent Computer Mathematics
Intelligent Computer Mathematics

Author: Christoph Benzmüller

Publisher: Springer Nature

Published: 2020-07-17

Total Pages: 337

ISBN-13: 3030535185

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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.

Computer Algebra in Scientific Computing
Computer Algebra in Scientific Computing

Author: François Boulier

Publisher: Springer Nature

Published: 2023-08-23

Total Pages: 441

ISBN-13: 3031417240

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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.

An Invitation to Analytic Combinatorics
An Invitation to Analytic Combinatorics

Author: Stephen Melczer

Publisher: Springer Nature

Published: 2020-12-22

Total Pages: 418

ISBN-13: 3030670805

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This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.

Solving Polynomial Equation Systems
Solving Polynomial Equation Systems

Author: Teo Mora

Publisher:

Published: 2003

Total Pages: 439

ISBN-13: 9780511178887

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Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.

Computer Algebra Methods for Equivariant Dynamical Systems
Computer Algebra Methods for Equivariant Dynamical Systems

Author: Karin Gatermann

Publisher: Springer

Published: 2007-05-06

Total Pages: 163

ISBN-13: 3540465197

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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.

Computer Algebra and Symbolic Computation
Computer Algebra and Symbolic Computation

Author: Joel S. Cohen

Publisher: CRC Press

Published: 2002-07-19

Total Pages: 323

ISBN-13: 1439863695

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This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and

Algebraic Cryptanalysis
Algebraic Cryptanalysis

Author: Gregory Bard

Publisher: Springer Science & Business Media

Published: 2009-08-14

Total Pages: 372

ISBN-13: 0387887571

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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.