Download or read book The Structure of Polynomial Ideals and Grobner Bases Classic Reprint written by T. Dube and published by . This book was released on 2015-08-05 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Structure of Polynomial Ideals and Grobner Bases The use of Grobner Bases is becoming increasingly important in algebraic computational geometry. As a result, there has been much activity in the recent years concerning the complexity of Buchberger's algorithm, and the degree of polynomials which it may produce. Bayer's thesis in 1982 provided the direction for recent research, and several recent papers have combined to show that the complexity of computing a Grobner Basis for a given ideal is double exponential in the number of variables. This paper introduces a new partitioning of a polynomial ideal. Using this partitioning, the sharpened degree bound can be obtained using only combinatorial arguments, and without the need to change coordinate systems. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."

Download or read book The Structure of Polynomial Ideals and Grobner Bases written by Thomas W. Dube and published by Franklin Classics Trade Press. This book was released on 2018-11-11 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Download or read book The Structure of Polynomial Ideals and Grobner Bases written by T. Dube and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Structure of Polynomial Ideals and Grobner Bases Primary Source Edition written by Thomas W. Dube and published by Nabu Press. This book was released on 2013-10 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Download or read book Grobner Bases in Commutative Algebra written by Viviana Ene and published by American Mathematical Soc.. This book was released on 2011-12-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise yet comprehensive and self-contained introduction to Grobner basis theory and its applications to various current research topics in commutative algebra. It especially aims to help young researchers become acquainted with fundamental tools and techniques related to Grobner bases which are used in commutative algebra and to arouse their interest in exploring further topics such as toric rings, Koszul and Rees algebras, determinantal ideal theory, binomial edge ideals, and their applications to statistics. The book can be used for graduate courses and self-study. More than 100 problems will help the readers to better understand the main theoretical results and will inspire them to further investigate the topics studied in this book.

Download or read book Grobner Bases and Convex Polytopes written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 1996 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.

Download or read book Gr bner Bases and Applications written by Bruno Buchberger and published by Cambridge University Press. This book was released on 1998-02-26 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.

Download or read book Harmony of Gr bner Bases and the Modern Industrial Society written by Takayuki Hibi and published by World Scientific. This book was released on 2012 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of research papers and expository survey articles presented by the invited speakers of the conference on OC Harmony of GrAbner Bases and the Modern Industrial SocietyOCO. Topics include computational commutative algebra, algebraic statistics, algorithms of D-modules and combinatorics. This volume also provides current trends on GrAbner bases and will stimulate further development of many research areas surrounding GrAbner bases."

Download or read book Miscellaneous results on Gr bner Bases for polynomial ideals II written by and published by . This book was released on 1982 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Grobner Bases written by William W. Adams and Philippe Loustaunau and published by American Mathematical Soc.. This book was released on 1994-07-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very carefully crafted introduction to the theory and some of the applications of Grobner bases ... contains a wealth of illustrative examples and a wide variety of useful exercises, the discussion is everywhere well-motivated, and further developments and important issues are well sign-posted ... has many solid virtues and is an ideal text for beginners in the subject ... certainly an excellent text. --Bulletin of the London Mathematical Society As the primary tool for doing explicit computations in polynomial rings in many variables, Grobner bases are an important component of all computer algebra systems. They are also important in computational commutative algebra and algebraic geometry. This book provides a leisurely and fairly comprehensive introduction to Grobner bases and their applications. Adams and Loustaunau cover the following topics: the theory and construction of Grobner bases for polynomials with coefficients in a field, applications of Grobner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and Grobner bases in modules, and the theory of Grobner bases for polynomials with coefficients in rings. With over 120 worked-out examples and 200 exercises, this book is aimed at advanced undergraduate and graduate students. It would be suitable as a supplement to a course in commutative algebra or as a textbook for a course in computer algebra or computational commutative algebra. This book would also be appropriate for students of computer science and engineering who have some acquaintance with modern algebra.

Download or read book Grobner Bases in Ring Theory written by Huishi Li and published by World Scientific. This book was released on 2012 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Preliminaries. 1.1. Presenting algebras by relations. 1.2. S-graded algebras and modules. 1.3. [symbol]-filtered algebras and modules -- 2. The [symbol]-leading homogeneous algebra A[symbol]. 2.1. Recognizing A via G[symbol](A): part 1. 2.2. Recognizing A via G[symbol](A): part 2. 2.3. The [symbol-graded isomorphism A[symbol](A). 2.4. Recognizing A via A[symbol] -- 3. Grobner bases: conception and construction. 3.1. Monomial ordering and admissible system. 3.2. Division algorithm and Grobner basis. 3.3. Grobner bases and normal elements. 3.4. Grobner bases w.r.t. skew multiplicative K-bases. 3.5. Grobner bases in K[symbol] and KQ. 3.6. (De)homogenized Grobner bases. 3.7. dh-closed homogeneous Grobner bases -- 4. Grobner basis theory meets PBW theory. 4.1. [symbol]-standard basis [symbol]-PBW isomorphism. 4.2. Realizing [symbol]-PBW isomorphism by Grobner basis. 4.3. Classical PBW K-bases vs Grobner bases. 4.4. Solvable polynomial algebras revisited -- 5. Using A[symbol] in terms of Grobner bases. 5.1. The working strategy. 5.2. Ufnarovski graph. 5.3. Determination of Gelfand-Kirillov Dimension. 5.4. Recognizing Noetherianity. 5.5. Recognizing (semi- )primeness and PI-property. 5.6. Anick's resolution over monomial algebras. 5.7. Recognizing finiteness of global dimension. 5.8. Determination of Hilbert series -- 6. Recognizing (non- )homogeneous p-Koszulity via A[symbol]. 6.1. (Non- )homogeneous p-Koszul algebras. 6.2. Anick's resolution and homogeneous p-Koszulity. 6.3. Working in terms of Grobner bases -- 7. A study of Rees algebra by Grobner bases. 7.1. Defining [symbol] by [symbol]. 7.2. Defining [symbol] by [symbol]. 7.3. Recognizing structural properties of [symbol] via [symbol]. 7.4. An application to regular central extensions. 7.5. Algebras defined by dh-closed homogeneous Grobner bases -- 8. Looking for more Grobner bases. 8.1. Lifting (finite) Grobner bases from O[symbol]. 8.2. Lifting (finite) Grobner bases from a class of algebras. 8.3. New examples of Grobner basis theory. 8.4. Skew 2-nomial algebras. 8.5. Almost skew 2-nomial algebras

Download or read book Noncommutative Gr bner Bases and Filtered Graded Transfer written by Huishi Li and published by Springer. This book was released on 2004-10-19 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.

Download or read book Algebraic Combinatorial and Algorithmic Issues Related to the Theory of Gr bner Bases of Polynomial Ideals written by Stéphane Collart and published by . This book was released on 1995 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multidimensional Systems Theory written by N.K. Bose and published by Springer. This book was released on 1985-06-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problem from the right end It isn't that they can't see the solution. and begin with the answers. It is that they can't see the problem. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown The point of a Pin. The Hermit Clad in Crane Feathers in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addi tion to this there are such new emerging subdisciplines as "experimental mathematical", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes.

Download or read book Solving Polynomial Equation Systems II written by Teo Mora and published by Cambridge University Press. This book was released on 2003 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. The presentation is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in its algorithmization.

Download or read book Gr bner Bases in Ring Theory written by Huishi Li and published by World Scientific. This book was released on 2012 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph strives to introduce a solid foundation on the usage of Gr”bner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Gr”bner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Gr”bner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand?Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non-)homogeneous p-Koszulity, PBW-deformation, and regular central extension.With a self-contained and constructive Gr”bner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations).

Download or read book Algorithmic Algebraic Combinatorics and Gr bner Bases written by Mikhail Klin and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries. There is special emphasis on algorithmic aspects and the use of the theory of Gröbner bases.