Search results for: groebner-bases

Gr bner Bases

Author : Thomas Becker
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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.

An Introduction to Grobner Bases

Author : William W. Adams and Philippe Loustaunau
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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.

An Introduction to Gr bner Bases

Author : Ralf Fröberg
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As algebra becomes more widely used in a variety of applications and computers are developed to allow efficient calculations in the field, so there becomes a need for new techniques to further this area of research. Grï¿1⁄2bner Bases is one topic which has recently become a very popular and important area of modern algebra. This book provides a concrete introduction to commutative algebra through Grï¿1⁄2bner Bases. The inclusion of exercises, lists of further reading and related literature make this a practical approach to introducing Grï¿1⁄2bner Bases. The author presents new concepts and results of recent research in the area allowing students and researchers in technology, computer science and mathematics to gain a basic understanding of the technique. A first course in algebra is the only prior knowledge required for this introduction. Chapter titles include: * Monomial ldeas * Grï¿1⁄2bner Bases * Algebraic Sets * Solving Systems of Polynomial Equations * Applications of Grï¿1⁄2bner Bases * Homogeneous Algebra * Hilbert Series * Variations of Grï¿1⁄2bner Bases * Improvements to Buchberger's Algorithms * Software

Gr bner Bases in Control Theory and Signal Processing

Author : Hyungju Alan Park
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This volume contains survey and original articles presenting the state of the art on the application of Gröbner bases in control theory and signal processing. The contributions are based on talks delivered at the Special Semester on Gröbner Bases and Related Methods at the Johann Radon Institute of Computational and Applied Mathematics (RICAM), Linz, Austria, in May 2006.

Gr bner Bases and Applications

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

Gr bner Bases Coding and Cryptography

Author : Massimiliano Sala
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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.

Gr bner Bases and Convex Polytopes

Author : Bernd Sturmfels
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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.

Groebner Bases

Author : Boo Barkee
File Size : 71.15 MB
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Noncommutative Gr bner Bases and Filtered Graded Transfer

Author : Huishi Li
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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.

Groebner Bases

Author : Moss E. Sweedler
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Systematic Encoding Via Groebner Bases for a Class of Algebraic Geometric Goppa Codes

Author : Chris Heegard
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Grobner Basis Methods for Integer Programming

Author : Rekha Rachel Thomas
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Degrees of Groebner Bases of Integer Programs

Author : Serkan Hoşten
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Groebner Bases and Symmetries

Author : Daniel Felipe Avila Girardot
File Size : 90.66 MB
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Geometric Theorem Proving Using the Groebner Basis Algorithm

Author : Karla Friné Rivas
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The purpose fo this project is to study ideals in polynomial rings and affine varieties in order to establish a connection between these two different concepts. Doing so will lead to an in depth examination of Groebner bases. Once this has been defined, step will be outlined that will enable the application of the Groebner Basis Algorithm to geometric problems.

International mathematical news

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Mathematical Reviews

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Automated Deduction in Geometry

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Computer Aided Systems Theory

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Author : IEEE Signal Processing Society
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