Non Commutative Computer Algebra With Applications

Author : Oleksandr Motsak
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
Page : 168 pages
File Size : 45,5 Mb
Release : 2011
Category : Electronic
ISBN : 3838127528

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Non-commutative Computer Algebra with applications by Oleksandr Motsak Pdf

This book that represents the author's Ph.D. thesis is devoted to constructive module theory of polynomial graded commutative algebras over a field. It treats the theory of Grobner bases, standard bases (SB) and syzygies as well as algorithms and their implementations over graded commutative algebras, which naturally unify exterior and commutative polynomial algebras. They are graded non-commutative, associative unital algebras over fields and may contain zero-divisors. In this book we try to make the most use out of a-priori knowledge about their characteristic (super-commutative) structure in developing direct symbolic methods, algorithms and implementations, which are intrinsic to these algebras and practically efficient. We also tackle their central localizations by generalizing a variation of Mora algorithm. In this setting we prove a generalized Buchberger's criterion, which shows that syzygies of leading terms play the utmost important role in SB and syzygy computations. We develop a variation of the La Scala-Stillman free resolution algorithm. Benchmarks show that our new algorithms and implementation are efficient. We give some applications of the developed framework.

Author : Svetlana Cojocaru,Gerhard Pfister,Victor Ufnarovski
Publisher : IOS Press
Page : 336 pages
File Size : 41,6 Mb
Release : 2005
Category : Electronic books
ISBN : 9781586035051

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Computational Commutative and Non-commutative Algebraic Geometry by Svetlana Cojocaru,Gerhard Pfister,Victor Ufnarovski Pdf

Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 44,9 Mb
Release : 2008-07-15
Category : Mathematics
ISBN : 9783540677338

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Computational Commutative Algebra 1 by Martin Kreuzer,Lorenzo Robbiano Pdf

This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.

Author : Jim Byrnes,Gerald Ostheimer
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 53,9 Mb
Release : 2006-01-28
Category : Mathematics
ISBN : 9781402023071

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Computational Noncommutative Algebra and Applications by Jim Byrnes,Gerald Ostheimer Pdf

The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over a century. Geometric algebras, introduced and classified by Clifford in the late 19th century, have played a prominent role in this effort, as seen in the mathematical work of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in applications to physics in the work of Pauli, Dirac and others. One of the most important applications of geometric algebras to geometry is to the representation of groups of Euclidean and Minkowski rotations. This aspect and its direct relation to robotics and vision will be discussed in several chapters of this multi-authored textbook, which resulted from the ASI meeting. Moreover, group theory, beginning with the work of Burnside, Frobenius and Schur, has been influenced by even more general problems. As a result, general group actions have provided the setting for powerful methods within group theory and for the use of groups in applications to physics, chemistry, molecular biology, and signal processing. These aspects, too, will be covered in detail. With the rapidly growing importance of, and ever expanding conceptual and computational demands on signal and image processing in remote sensing, computer vision, medical image processing, and biological signal processing, and on neural and quantum computing, geometric algebras, and computational group harmonic analysis, the topics of the book have emerged as key tools. The list of authors includes many of the world's leading experts in the development of new algebraic modeling and signal representation methodologies, novel Fourier-based and geometrictransforms, and computational algorithms required for realizing the potential of these new application fields. The intention of this textbook is share their profound wisdom with the many future stars of pure and computational noncommutative algebra. A key feature of both the meeting and the book will be their presentation of problems and applications that will shape the twenty-first century computational technology base.

Author : J.L. Bueso,José Gómez-Torrecillas,A. Verschoren
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 40,9 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9789401702850

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Algorithmic Methods in Non-Commutative Algebra by J.L. Bueso,José Gómez-Torrecillas,A. Verschoren Pdf

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.

Author : Jean Berstel,Christophe Reutenauer
Publisher : Cambridge University Press
Page : 263 pages
File Size : 51,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780521190220

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Noncommutative Rational Series with Applications by Jean Berstel,Christophe Reutenauer Pdf

A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.

Author : Jean Berstel
Publisher : Unknown
Page : 248 pages
File Size : 54,6 Mb
Release : 2011
Category : Machine theory
ISBN : 1107267765

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Noncommutative Rational Series with Applications by Jean Berstel Pdf

"The algebraic theory of automata was created by Schützenberger and Chomsky over 50 years ago and there has since been a great deal of development. Classical work on the theory of noncommutative power series has been augmented more recently to areas such as representation theory, combinatorial mathematics and theoretical computer science. This book presents to an audience of graduate students and researchers a modern account of the subject and its applications. The algebraic approach allows the theory to be developed in a general form of wide applicability. For example, number theoretic results can now be more fully explored, in addition to applications in automata theory, codes and noncommutative algebra. Much material, for example, Schützenberger's theorem on polynomially bounded rational series, and results on semi simple algebras, appear here for the first time in book form. In sum, this is an excellent resource and reference for all those working in algebra, theoretical computer science and their areas of overlap"--

Author : Klaus G. Fischer
Publisher : Routledge
Page : 182 pages
File Size : 49,5 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9781351458986

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Computational Algebra by Klaus G. Fischer Pdf

Based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. Focuses on both the practical and theoretical aspects of computational algebra. Demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to study algebras of finite rank.

Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer
Page : 322 pages
File Size : 47,9 Mb
Release : 2008-07-15
Category : Mathematics
ISBN : 354067733X

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Computational Commutative Algebra 1 by Martin Kreuzer,Lorenzo Robbiano Pdf

This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.

Author : Jean Berstel,Professor Department de Mathematiques-Informatique Christophe Reutenauer
Publisher : Unknown
Page : 128 pages
File Size : 49,9 Mb
Release : 2014-02-19
Category : Electronic
ISBN : 1299707580

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Noncommutative Rational Series with Applications by Jean Berstel,Professor Department de Mathematiques-Informatique Christophe Reutenauer Pdf

A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.

Author : Ihsen Yengui
Publisher : World Scientific
Page : 283 pages
File Size : 46,9 Mb
Release : 2021-05-17
Category : Mathematics
ISBN : 9789811238260

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Computational Algebra: Course And Exercises With Solutions by Ihsen Yengui Pdf

This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.

Author : David Cox,John Little,DONAL OSHEA
Publisher : Springer Science & Business Media
Page : 523 pages
File Size : 44,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475721812

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Ideals, Varieties, and Algorithms by David Cox,John Little,DONAL OSHEA Pdf

Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.

Author : Huishi Li
Publisher : CRC Press
Page : 230 pages
File Size : 46,7 Mb
Release : 2021-11-08
Category : Mathematics
ISBN : 9781000471106

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Noncommutative Polynomial Algebras of Solvable Type and Their Modules by Huishi Li Pdf

Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. In doing so, this book covers: A constructive introduction to solvable polynomial algebras and Gröbner basis theory for left ideals of solvable polynomial algebras and submodules of free modules The new filtered-graded techniques combined with the determination of the existence of graded monomial orderings The elimination theory and methods (for left ideals and submodules of free modules) combining the Gröbner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of different kinds of elimination orderings The computational construction of finite free resolutions (including computation of syzygies, construction of different kinds of finite minimal free resolutions based on computation of different kinds of minimal generating sets), etc. This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.

Author : Giovanni Pistone,Eva Riccomagno,Henry P. Wynn
Publisher : CRC Press
Page : 180 pages
File Size : 45,9 Mb
Release : 2000-12-21
Category : Mathematics
ISBN : 9781420035766

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Algebraic Statistics by Giovanni Pistone,Eva Riccomagno,Henry P. Wynn Pdf

Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Grobner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case

Author : Andres Iglesias,Nobuki Takayama
Publisher : Springer
Page : 467 pages
File Size : 46,5 Mb
Release : 2006-08-31
Category : Computers
ISBN : 9783540380863

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Mathematical Software - ICMS 2006 by Andres Iglesias,Nobuki Takayama Pdf

This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.