Computers in Nonassociative Rings and Algebras PDF Download

Author: Robert E. Beck
Publisher: Academic Press
ISBN: 1483267954
Category : Mathematics
Languages : en
Pages : 309

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Book Description
Computers in Nonassociative Rings and Algebras provides information pertinent to the computational aspects of nonassociative rings and algebras. This book describes the algorithmic approaches for solving problems using a computer. Organized into 10 chapters, this book begins with an overview of the concept of a symmetrized power of a group representation. This text then presents data structures and other computational methods that may be useful in the field of computational algebra. Other chapters consider several mathematical ideas, including identity processing in nonassociative algebras, structure theory of Lie algebra, and representation theory. This book presents as well an historical survey of the use of computers in Lie algebra theory, with specific reference to computing the coupling and recoupling coefficients for the irreducible representations of simple Lie algebras. The final chapter deals with how representations of semi-simple Lie algebras can be symmetrized in a straightforward manner. This book is a valuable resource for mathematicians.

Author: Klaus Denecke
Publisher: CRC Press
ISBN: 1482285835
Category : Mathematics
Languages : en
Pages : 396

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Book Description
Over the past 20 years, the emergence of clone theory, hyperequational theory, commutator theory and tame congruence theory has led to a growth of universal algebra both in richness and in applications, especially in computer science. Yet most of the classic books on the subject are long out of print and, to date, no other book has integrated these theories with the long-established work that supports them. Universal Algebra and Applications in Theoretical Computer Science introduces the basic concepts of universal algebra and surveys some of the newer developments in the field. The first half of the book provides a solid grounding in the core material. A leisurely pace, careful exposition, numerous examples, and exercises combine to form an introduction to the subject ideal for beginning graduate students or researchers from other areas. The second half of the book focuses on applications in theoretical computer science and advanced topics, including Mal'cev conditions, tame congruence theory, clones, and commutators. The impact of the advances in universal algebra on computer science is just beginning to be realized, and the field will undoubtedly continue to grow and mature. Universal Algebra and Applications in Theoretical Computer Science forms an outstanding text and offers a unique opportunity to build the foundation needed for further developments in its theory and in its computer science applications.

Author: Lev Sabinin
Publisher: CRC Press
ISBN: 1420003453
Category : Mathematics
Languages : en
Pages : 553

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Book Description
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.

Author: Freddy Van Oystaeyen
Publisher: CRC Press
ISBN: 9780824703677
Category : Mathematics
Languages : en
Pages : 470

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Book Description
This work is based on a set of lectures and invited papers presented at a meeting in Murcia, Spain, organized by the European Commission's Training and Mobility of Researchers (TMR) Programme. It contains information on the structure of representation theory of groups and algebras and on general ring theoretic methods related to the theory.

Author: J.L. Bueso
Publisher: Springer Science & Business Media
ISBN: 9401702853
Category : Computers
Languages : en
Pages : 307

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Book Description
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: Santos González
Publisher: Springer Science & Business Media
ISBN: 9401109907
Category : Mathematics
Languages : en
Pages : 429

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Book Description
This volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12--17, 1993. The conference brought together specialists from all over the world who work in this interesting and active field, which is currently enjoying much attention. All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection will point the way for further research for many years to come. The volume is of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics.

Author: Johannes Grabmeier
Publisher: Springer Science & Business Media
ISBN: 3642558267
Category : Computers
Languages : en
Pages : 656

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Book Description
This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Author: Wolfgang Wechler
Publisher: Springer Science & Business Media
ISBN: 3642767710
Category : Computers
Languages : en
Pages : 345

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Book Description
A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers.

Author: Alexander A. Mikhalev
Publisher: CRC Press
ISBN: 9780849389603
Category : Mathematics
Languages : en
Pages : 276

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Book Description
Combinatorial Aspects of Lie Superalgebras emphasizes the algorithmic and computational aspects of the combinatorial techniques of Lie superalgebras. It is written primarily for mathematicians and scientists who do not have a background in the field of infinite dimensional Lie superalgebras, but who realize the potential uses of the results. Consequently, the discussions provided on the applications of Lie superalgebras theory are clear and comprehensive and, throughout the text, primary attention is given to algorithms and examples. The examples illustrate theoretical results, and the algorithms, which can be used for symbolic calculations with Lie superalgebras, are based on basic and generally applicable rules and theorems. Combinatorial Aspects of Lie Superalgebras contains comprehensive literature citations and provides an excellent reference on the techniques and results of combinatorial theory of Lie superalgebras. Programs that have been developed by the authors for computation are included on a diskette at the back of the book, and complete directions for use are provided.

Author: Arjeh M. Cohen
Publisher: Springer Science & Business Media
ISBN: 3662038919
Category : Computers
Languages : en
Pages : 365

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Book Description
This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.