Non Commutative Computer Algebra With Applications

Author : Oleksandr Motsak
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
ISBN 13 : 9783838127521
Total Pages : 168 pages
Book Rating : 4.28/5 ( download)

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Download or read book Non-commutative Computer Algebra with applications written by Oleksandr Motsak and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2011 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Wolf Daniel Andres
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.54/5 ( download)

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Download or read book Noncommutative Computer Algebra with Applications in Algebraic Analysis written by Wolf Daniel Andres and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jean Berstel
Publisher : Cambridge University Press
ISBN 13 : 0521190223
Total Pages : 263 pages
Book Rating : 4.20/5 ( download)

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Download or read book Noncommutative Rational Series with Applications written by Jean Berstel and published by Cambridge University Press. This book was released on 2011 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern account of the subject and its applications. Excellent resource for those working in algebra and theoretical computer science.

Author : Svetlana Cojocaru
Publisher : IOS Press
ISBN 13 : 1586035053
Total Pages : 336 pages
Book Rating : 4.51/5 ( download)

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Download or read book Computational Commutative and Non-commutative Algebraic Geometry written by Svetlana Cojocaru and published by IOS Press. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Viktor Levandovskyy
Publisher :
ISBN 13 :
Total Pages : 249 pages
Book Rating : 4.23/5 ( download)

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Download or read book Non-commutative Computer Algebra for Polynomial Algebras written by Viktor Levandovskyy and published by . This book was released on 2005 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Martin Kreuzer
Publisher : Springer Science & Business Media
ISBN 13 : 3540706283
Total Pages : 326 pages
Book Rating : 4.81/5 ( download)

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Download or read book Computational Commutative Algebra 1 written by Martin Kreuzer and published by Springer Science & Business Media. This book was released on 2008-07-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 1402023073
Total Pages : 435 pages
Book Rating : 4.71/5 ( download)

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Download or read book Computational Noncommutative Algebra and Applications written by Jim Byrnes and published by Springer Science & Business Media. This book was released on 2006-01-28 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 9401702853
Total Pages : 307 pages
Book Rating : 4.50/5 ( download)

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Download or read book Algorithmic Methods in Non-Commutative Algebra written by J.L. Bueso and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : David Cox
Publisher : Springer Science & Business Media
ISBN 13 : 1475721811
Total Pages : 523 pages
Book Rating : 4.12/5 ( download)

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Download or read book Ideals, Varieties, and Algorithms written by David Cox and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Klaus G. Fischer
Publisher : Routledge
ISBN 13 : 1351458981
Total Pages : 182 pages
Book Rating : 4.86/5 ( download)

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Download or read book Computational Algebra written by Klaus G. Fischer and published by Routledge. This book was released on 2018-02-19 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.