Gröbner Bases

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An Introduction to Grobner Bases

William W. Adams and Philippe Loustaunau
An Introduction to Grobner Bases Book PDF

Author : William W. Adams and Philippe Loustaunau
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 46,9 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.

Gröbner Bases and Applications

Bruno Buchberger,Franz Winkler
Gr bner Bases and Applications Book PDF

Author : Bruno Buchberger,Franz Winkler
Publisher : Cambridge University Press
Page : 566 pages
File Size : 52,7 Mb
Release : 1998-02-26
Category : Mathematics
ISBN : 0521632986

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Gröbner Bases and Applications by Bruno Buchberger,Franz Winkler Pdf

Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.

An Introduction to Gröbner Bases

Ralf Fröberg
An Introduction to Gr bner Bases Book PDF

Author : Ralf Fröberg
Publisher : John Wiley & Sons
Page : 198 pages
File Size : 52,5 Mb
Release : 1997-10-07
Category : Mathematics
ISBN : 0471974420

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An Introduction to Gröbner Bases by Ralf Fröberg Pdf

Grobner-Basen werden von Mathematikern und Informatikern zunehmend fur eine breite Palette von Anwendungen genutzt, in denen die algorithmische algebraische Geometrie eine Rolle spielt. Hier werden Grobner-Basen von einem konstruktiven, wenig abstrakten Standpunkt aus behandelt, wobei nur geringe Vorkenntnisse in linearer Algebra und komplexen Zahlen vorausgesetzt werden; zahlreiche Beispiele helfen bei der Durchdringung des Stoffes. Mit einer Ubersicht uber aktuell erhaltliche relevante Softwarepakete.

Gröbner Bases in Control Theory and Signal Processing

Hyungju Park,Georg Regensburger
Gr bner Bases in Control Theory and Signal Processing Book PDF

Author : Hyungju Park,Georg Regensburger
Publisher : Walter de Gruyter
Page : 264 pages
File Size : 47,8 Mb
Release : 2007
Category : Mathematics
ISBN : 3110193337

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Gröbner Bases in Control Theory and Signal Processing by Hyungju Park,Georg Regensburger Pdf

This volume contains survey articles and original research papers, presenting the state of the art on applications of Grobner bases and related methods in control theory and signal processing. The topics covered include: Grobner bases in multidimensional systems, the Quillen-Suslin theorem and systems theory, statistical signal processing, parametric problems in control theory, stability of multidimensional input/output systems, wavelets and filter design, synthesis of multidimensional control systems, time-varying linear systems. The contributions are based on talks delivered at the Special Semester on Grobner Bases and Related Methods hosted by the Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences in Linz, Austria, in May 2006.

Grobner Bases in Ring Theory

Huishi Li
Grobner Bases in Ring Theory Book PDF

Author : Huishi Li
Publisher : World Scientific
Page : 295 pages
File Size : 43,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814365147

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Grobner Bases in Ring Theory by Huishi Li Pdf

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

Algorithmic Algebraic Combinatorics and Gröbner Bases

Mikhail Klin,Gareth A. Jones,Aleksandar Jurisic,Mikhail Muzychuk,Ilia Ponomarenko
Algorithmic Algebraic Combinatorics and Gr bner Bases Book PDF

Author : Mikhail Klin,Gareth A. Jones,Aleksandar Jurisic,Mikhail Muzychuk,Ilia Ponomarenko
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 53,8 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.

Gröbner Bases and Convex Polytopes

Bernd Sturmfels
Gr bner Bases and Convex Polytopes Book PDF

Author : Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 46,8 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.

Gröbner Bases

Thomas Becker,Volker Weispfenning
Gr bner Bases Book PDF

Author : Thomas Becker,Volker Weispfenning
Publisher : Springer Science & Business Media
Page : 587 pages
File Size : 55,8 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.

Gröbner Bases, Coding, and Cryptography

Massimiliano Sala,Teo Mora,Ludovic Perret,Shojiro Sakata,Carlo Traverso
Gr bner Bases Coding and Cryptography Book PDF

Author : Massimiliano Sala,Teo Mora,Ludovic Perret,Shojiro Sakata,Carlo Traverso
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 44,9 Mb
Release : 2009-05-28
Category : Mathematics
ISBN : 9783540938064

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Gröbner Bases, Coding, and Cryptography by Massimiliano Sala,Teo Mora,Ludovic Perret,Shojiro Sakata,Carlo Traverso Pdf

Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations. This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.

Gröbner Bases and the Computation of Group Cohomology

David J. Green
Gr bner Bases and the Computation of Group Cohomology Book PDF

Author : David J. Green
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 45,5 Mb
Release : 2003-11-18
Category : Mathematics
ISBN : 3540203397

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Gröbner Bases and the Computation of Group Cohomology by David J. Green Pdf

This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.

Noncommutative Gröbner Bases and Filtered-Graded Transfer

Huishi Li
Noncommutative Gr bner Bases and Filtered Graded Transfer Book PDF

Author : Huishi Li
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 48,9 Mb
Release : 2002-10-23
Category : Computers
ISBN : 3540441964

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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.

Gröbner Bases in Symbolic Analysis

Markus Rosenkranz,Dongming Wang
Gr bner Bases in Symbolic Analysis Book PDF

Author : Markus Rosenkranz,Dongming Wang
Publisher : Walter de Gruyter
Page : 362 pages
File Size : 41,8 Mb
Release : 2007
Category : Mathematics
ISBN : 311019323X

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Gröbner Bases in Symbolic Analysis by Markus Rosenkranz,Dongming Wang Pdf

This volume contains survey articles and original research papers, presenting the state of the art on applying the symbolic approach of Gröbner bases and related methods to differential and difference equations. The contributions are based on talks delivered at the Special Semester on Gröbner Bases and Related Methods hosted by the Johann Radon Institute of Computational and Applied Mathematics, Linz, Austria, in May 2006.

Boolean Gröbner Bases

Michael Brickenstein
Boolean Gr bner Bases Book PDF

Author : Michael Brickenstein
Publisher : Logos Verlag Berlin GmbH
Page : 158 pages
File Size : 50,6 Mb
Release : 2010
Category : Computers
ISBN : 9783832525972

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Boolean Gröbner Bases by Michael Brickenstein Pdf

There exist very few concepts in computational algebra which are as central to theory and applications as Grobner bases. This thesis describes theory, algorithms and applications for the special case of Boolean polynomials. These parts form the mathematical foundations of the PolyBoRi framework (developed by the author together with Alexander Dreyer). The PolyBoRi framework has applications spread over a large number of domains ranging from formal verification, computational biology to cryptanalysis and many more. It is emerged to a worldwide audience by the Sage computational algebra system.

Grobner Bases in Commutative Algebra

Viviana Ene,JŸrgen Herzog
Grobner Bases in Commutative Algebra Book PDF

Author : Viviana Ene,JŸrgen Herzog
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 52,6 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.

An Introduction to Gröbner Bases

William W. Adams,Philippe Loustaunau
An Introduction to Gr bner Bases Book PDF

Author : William W. Adams,Philippe Loustaunau
Publisher : American Mathematical Society
Page : 289 pages
File Size : 54,6 Mb
Release : 2022-04-25
Category : Mathematics
ISBN : 9781470469818

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An Introduction to Gröbner Bases by William W. Adams,Philippe Loustaunau Pdf

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.