The Structure Of Polynomial Ideals And Grobner Bases

Author : T. Dube
Publisher : Forgotten Books
Page : 38 pages
File Size : 49,9 Mb
Release : 2019-02
Category : Mathematics
ISBN : 0365358363

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The Structure of Polynomial Ideals and Grobner Bases (Classic Reprint) by T. Dube Pdf

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 : Unknown
Page : 0 pages
File Size : 53,6 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:897684265

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The Structure of Polynomial Ideals and Grobner Bases by T. Dube Pdf

Author : Thomas W Dube
Publisher : Legare Street Press
Page : 0 pages
File Size : 51,5 Mb
Release : 2023-07-18
Category : Electronic
ISBN : 1019461071

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The Structure of Polynomial Ideals and Grobner Bases by Thomas W Dube Pdf

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,JŸrgen Herzog
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 49,6 Mb
Release : 2011-12-01
Category : Mathematics
ISBN : 9780821872871

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Grobner Bases in Commutative Algebra by Viviana Ene,JŸrgen Herzog Pdf

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.
Page : 308 pages
File Size : 40,9 Mb
Release : 1994-07-21
Category : Mathematics
ISBN : 0821872168

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An Introduction to Grobner Bases by William W. Adams and Philippe Loustaunau Pdf

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.
Page : 162 pages
File Size : 50,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804872

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Gröbner Bases and Convex Polytopes by Bernd Sturmfels Pdf

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers 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 Grobner 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 : Huishi Li
Publisher : Springer
Page : 202 pages
File Size : 53,5 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540457657

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Noncommutative Gröbner Bases and Filtered-Graded Transfer by Huishi Li Pdf

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.

Author : Huishi Li
Publisher : World Scientific
Page : 295 pages
File Size : 54,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814365130

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Gr”bner Bases in Ring Theory by Huishi Li Pdf

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).

Author : Thomas Becker,Volker Weispfenning,Heinz Kredel
Publisher : Unknown
Page : 608 pages
File Size : 51,7 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015029465021

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Gröbner Bases by Thomas Becker,Volker Weispfenning,Heinz Kredel Pdf

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 : Mikhail Klin,Gareth A. Jones,Aleksandar Jurisic,Mikhail Muzychuk,Ilia Ponomarenko
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 55,8 Mb
Release : 2009-12-24
Category : Mathematics
ISBN : 9783642019609

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Algorithmic Algebraic Combinatorics and Gröbner Bases by Mikhail Klin,Gareth A. Jones,Aleksandar Jurisic,Mikhail Muzychuk,Ilia Ponomarenko Pdf

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.

Author : Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama
Publisher : Springer Nature
Page : 375 pages
File Size : 45,5 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9783030264543

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Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers by Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama Pdf

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.

Author : Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Publisher : Springer
Page : 201 pages
File Size : 51,5 Mb
Release : 2013-08-24
Category : Mathematics
ISBN : 9783642387425

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Monomial Ideals, Computations and Applications by Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón Pdf

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

Author : Thomas Becker,Volker Weispfenning
Publisher : Springer Science & Business Media
Page : 587 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209133

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Gröbner Bases by Thomas Becker,Volker Weispfenning Pdf

The origins of the mathematics in this book date back more than two thou sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.

Author : Teo Mora
Publisher : Cambridge University Press
Page : 833 pages
File Size : 48,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9781107109636

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Solving Polynomial Equation Systems by Teo Mora Pdf

Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.

Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 46,7 Mb
Release : 2008-07-15
Category : Mathematics
ISBN : 9783540677338

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Computational Commutative Algebra 1 by Martin Kreuzer,Lorenzo Robbiano Pdf

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.