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 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 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 Gr bner Bases written by Thomas Becker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gr bner Bases Coding and Cryptography written by Massimiliano Sala and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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 An Introduction to Gr bner Bases written by Ralf Fröberg and published by John Wiley & Sons. This book was released on 1997-10-07 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Grobner Bases written by William Wells Adams and published by American Mathematical Soc.. This book was released on 1994 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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 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 Gr bner Bases and the Computation of Group Cohomology written by David J. Green and published by Springer Science & Business Media. This book was released on 2003-11-18 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gr bner Deformations of Hypergeometric Differential Equations written by Mutsumi Saito and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Gröbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Gröbner bases from the point of view of geometric deformations. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric PDE's introduced by Gelfand, Kapranov, and Zelevinsky. A number of original research results are contained in the book, and many open problems are raised for future research in this rapidly growing area of computational mathematics.
Download or read book Boolean Gr bner Bases written by Michael Brickenstein and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Using Algebraic Geometry written by David A. Cox and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Download or read book Gr bner Bases in Symbolic Analysis written by Markus Rosenkranz and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Grobner Bases and Applications written by Burchberger Winkler and published by . This book was released on 2014-05-14 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive account of theory and applications of Grobner bases, co-edited by the subject's inventor.
Download or read book Mathematical Aspects of Scientific Software written by J.R. Rice and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since scientific software is the fuel that drives today's computers to solve a vast range of problems, huge efforts are being put into the development of new software, systems and algorithms for scientific problem solving. This book explores how scientific software impacts the structure of mathematics, how it creates new subfields, and how new classes of mathematical problems arise. The focus is on five topics where the impact is currently being felt and where important new challenges exist, namely: the new subfield of parallel and geometric computations, the emergence of symbolic computation systems into "general" use, the potential emergence of new, high-level mathematical systems, and the crucial question of how to measure the performance of mathematical problem solving tools.
