Algorithmic Methods In Non Commutative Algebra

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 : Wolmer Vasconcelos
Publisher : Springer Science & Business Media
ISBN 13 : 9783540213116
Total Pages : 432 pages
Book Rating : 4.12/5 ( download)

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Download or read book Computational Methods in Commutative Algebra and Algebraic Geometry written by Wolmer Vasconcelos and published by Springer Science & Business Media. This book was released on 2004-05-18 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Author : Gebhard Böckle
Publisher : Springer
ISBN 13 : 3319705660
Total Pages : 753 pages
Book Rating : 4.68/5 ( download)

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Download or read book Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory written by Gebhard Böckle and published by Springer. This book was released on 2018-03-22 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

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 : Wolmer Vasconcelos
Publisher : Springer
ISBN 13 : 9783642589515
Total Pages : 0 pages
Book Rating : 4.10/5 ( download)

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Download or read book Computational Methods in Commutative Algebra and Algebraic Geometry written by Wolmer Vasconcelos and published by Springer. This book was released on 2004-06-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Author : Gert-Martin Greuel
Publisher : Springer Science & Business Media
ISBN 13 : 3540735410
Total Pages : 703 pages
Book Rating : 4.10/5 ( download)

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Download or read book A Singular Introduction to Commutative Algebra written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2007-11-05 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

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 : 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 : 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 : William Fajardo
Publisher : Springer Nature
ISBN 13 : 3030533786
Total Pages : 584 pages
Book Rating : 4.86/5 ( download)

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Download or read book Skew PBW Extensions written by William Fajardo and published by Springer Nature. This book was released on 2020-12-11 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over skew PBW extensions from a matrix point of view. To make this theory constructive, the theory of Gröbner bases of left (right) ideals and modules for bijective skew PBW extensions is developed. For example, syzygies and the Ext and Tor modules over these rings are computed. Finally, applications to some key topics in the noncommutative algebraic geometry of quantum algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded Artin–Schelter regular algebras, and the noncommutative Zariski cancellation problem. The book is addressed to researchers in noncommutative algebra and algebraic geometry as well as to graduate students and advanced undergraduate students.