# solving polynomial equation systems iv volume 4 buchberger theory and beyond

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## Solving Polynomial Equation Systems Iv Volume 4 Buchberger Theory And Beyond

**Author :**Teo Mora

**ISBN :**9781316381380

**Genre :**Mathematics

**File Size :**42. 73 MB

**Format :**PDF

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In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.

## Solving Polynomial Equation Systems Algebraic Solving

**Author :**Teo Mora

**ISBN :**LCCN:2001043132

**Genre :**Equations

**File Size :**81. 51 MB

**Format :**PDF, Mobi

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## Solving Polynomial Equation Systems I

**Author :**Teo Mora

**ISBN :**0511072953

**Genre :**Electronic books

**File Size :**84. 37 MB

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Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.

## A B

**Author :**Marko Petkovsek

**ISBN :**1568810636

**Genre :**Mathematics

**File Size :**23. 91 MB

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This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics. From the table of contents: * Proof Machines * Tightening the Target * The Hypergeometric Database * The Five Basic Algorithms: Sister Celine's Method, Gosper&'s Algorithm, Zeilberger's Algorithm, The WZ Phenomenon, Algorithm Hyper * Epilogue: An Operator Algebra Viewpoint * The WWW Sites and the Software (Maple and Mathematica) Each chapter contains an introduction to the subject and ends with a set of exercises.

## An Introduction To Grobner Bases

**Author :**William W. Adams and Philippe Loustaunau

**ISBN :**0821872168

**Genre :**

**File Size :**48. 53 MB

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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.

## Computational Commutative Algebra 1

**Author :**Martin Kreuzer

**ISBN :**9783540677338

**Genre :**Computers

**File Size :**59. 70 MB

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This accessible introduction to Grobner bases and their applications helps bridge the gap between theoretical computer algebra and actual computation. It includes 44 tutorials and 165 exercises as well as other numerous amusements.

## Algebraic And Geometric Ideas In The Theory Of Discrete Optimization

**Author :**Jesús A. De Loera

**ISBN :**9781611972436

**Genre :**Mathematics

**File Size :**38. 35 MB

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In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.