The Structure Of Polynomial Ideals And Grobner Bases

Author : T. Dube
Publisher : Forgotten Books
ISBN 13 : 9780365358367
Total Pages : 38 pages
Book Rating : 4.63/5 ( download)

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Download or read book The Structure of Polynomial Ideals and Grobner Bases (Classic Reprint) written by T. Dube and published by Forgotten Books. This book was released on 2019-02 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Structure of Polynomial Ideals and Grobner Bases It is also easy to verify that if F is a monomial basis for a monomial ideal I, then F is a Grbbner basis for I with respect to every admissible ordering. The following lemmas provide some useful properties of normal forms. 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.

Author : T. Dube
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.65/5 ( download)

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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:

Author : Thomas W Dube
Publisher : Legare Street Press
ISBN 13 : 9781019461075
Total Pages : 0 pages
Book Rating : 4.71/5 ( download)

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Download or read book The Structure of Polynomial Ideals and Grobner Bases written by Thomas W Dube and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this illuminating work on algebraic geometry, Thomas W. Dubé offers a fresh perspective on polynomial ideals and Gröbner bases. Drawing on the latest developments in the field, Dubé introduces a powerful new approach to solving algebraic systems of equations, with wide-ranging applications in science and engineering. A must-read for anyone interested in cutting-edge research in algebraic geometry. 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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Viviana Ene
Publisher : American Mathematical Soc.
ISBN 13 : 0821872877
Total Pages : 178 pages
Book Rating : 4.71/5 ( download)

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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.

Author : William W. Adams and Philippe Loustaunau
Publisher : American Mathematical Soc.
ISBN 13 : 9780821872161
Total Pages : 308 pages
Book Rating : 4.68/5 ( download)

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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.

Author : Bernd Sturmfels
Publisher : American Mathematical Soc.
ISBN 13 : 0821804871
Total Pages : 176 pages
Book Rating : 4.72/5 ( download)

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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.

Author : Jürgen Herzog
Publisher : Springer
ISBN 13 : 3319953494
Total Pages : 321 pages
Book Rating : 4.96/5 ( download)

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Download or read book Binomial Ideals written by Jürgen Herzog and published by Springer. This book was released on 2018-09-28 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with a set of exercises and a list of related topics and results that will complement and offer a better understanding of the material presented. Binomial Ideals is suitable for graduate students in courses on commutative algebra, algebraic combinatorics, and statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource.

Author : Thomas Becker
Publisher :
ISBN 13 :
Total Pages : 608 pages
Book Rating : 4.21/5 ( download)

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Download or read book Gröbner Bases written by Thomas Becker and published by . This book was released on 1993 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: An algorithmic approach to the study of algebra is revealed by this text, which explores Groebner bases, defined by Buchberger in 1965, and the Buchberger algorithm. Algorithms using Groebner bases are implemented in almost every major computer algebra software system.

Author : Huishi Li
Publisher : World Scientific
ISBN 13 : 9814365149
Total Pages : 295 pages
Book Rating : 4.47/5 ( download)

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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

Author : William W. Adams
Publisher : American Mathematical Society
ISBN 13 : 1470469812
Total Pages : 289 pages
Book Rating : 4.18/5 ( download)

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Download or read book An Introduction to Gröbner Bases written by William W. Adams and published by American Mathematical Society. This book was released on 2022-04-25 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very carefully crafted introduction to the theory and some of the applications of Gröbner 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, Gröbner 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 Gröbner bases and their applications. Adams and Loustaunau cover the following topics: the theory and construction of Gröbner bases for polynomials with coefficients in a field, applications of Gröbner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and Gröbner bases in modules, and the theory of Gröbner 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.