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Polynomials Author Victor V. Prasolov
ISBN-10 9783642039805
Release 2009-09-23
Pages 302
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Covers its topic in greater depth than the typical standard books on polynomial algebra


Polynomials Author
ISBN-10 9783642040122
Release 2009
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Polynomials has been writing in one form or another for most of life. You can find so many inspiration from Polynomials also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Polynomials book for free.

Polynomials and Polynomial Inequalities

Polynomials and Polynomial Inequalities Author Peter Borwein
ISBN-10 0387945091
Release 1995-09-27
Pages 480
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This book examines polynomials as they arise in analysis, focusing on polynomials and rational functions of a single variable. Coverage includes Chebyshev and Descartes systems, denseness and inequalities satisfied by polynomials and rational functions.

Algorithms and Computation

Algorithms and Computation Author Peter Eades
ISBN-10 9783540456780
Release 2003-06-30
Pages 790
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Algorithms and Computation has been writing in one form or another for most of life. You can find so many inspiration from Algorithms and Computation also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Algorithms and Computation book for free.

Polynomial and Matrix Computations

Polynomial and Matrix Computations Author Dario Bini
ISBN-10 1461266866
Release 2012-09-27
Pages 416
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Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.

Effective Polynomial Computation

Effective Polynomial Computation Author Richard Zippel
ISBN-10 9781461531883
Release 2012-12-06
Pages 363
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Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

Mathematical Software ICMS 2006

Mathematical Software   ICMS 2006 Author Andres Iglesias
ISBN-10 9783540380863
Release 2006-08-31
Pages 452
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This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.

Solving Polynomial Equations

Solving Polynomial Equations Author Alicia Dickenstein
ISBN-10 9783540273578
Release 2006-01-27
Pages 426
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The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Computing and Combinatorics

Computing and Combinatorics Author Lusheng Wang
ISBN-10 9783540318064
Release 2005-09-07
Pages 1000
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Computing and Combinatorics has been writing in one form or another for most of life. You can find so many inspiration from Computing and Combinatorics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Computing and Combinatorics book for free.

Interior point Polynomial Algorithms in Convex Programming

Interior point Polynomial Algorithms in Convex Programming Author Yurii Nesterov
ISBN-10 1611970792
Release 1994
Pages 405
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Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.

Algorithms in Real Algebraic Geometry

Algorithms in Real Algebraic Geometry Author Saugata Basu
ISBN-10 9783540330981
Release 2006-07-06
Pages 662
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This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This second edition contains several recent results on discriminants of symmetric matrices and other relevant topics.

Computations in Algebraic Geometry with Macaulay 2

Computations in Algebraic Geometry with Macaulay 2 Author David Eisenbud
ISBN-10 9783662048511
Release 2013-03-14
Pages 329
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This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Polynomial Algorithms in Computer Algebra

Polynomial Algorithms in Computer Algebra Author Franz Winkler
ISBN-10 3211827595
Release 1996-08-02
Pages 270
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The book gives a thorough introduction to the mathematical underpinnings of computer algebra. The subjects treated range from arithmetic of integers and polynomials to fast factorization methods, Gröbner bases, and algorithms in algebraic geometry. The algebraic background for all the algorithms presented in the book is fully described, and most of the algorithms are investigated with respect to their computational complexity. Each chapter closes with a brief survey of the related literature.

Computer Algebra in Scientific Computing

Computer Algebra in Scientific Computing Author Vladimir P. Gerdt
ISBN-10 9783319240213
Release 2015-09-10
Pages 494
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This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.

Computational Methods in Commutative Algebra and Algebraic Geometry

Computational Methods in Commutative Algebra and Algebraic Geometry Author Wolmer Vasconcelos
ISBN-10 3540213112
Release 2004-05-18
Pages 408
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This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Computer Algebra and Symbolic Computation

Computer Algebra and Symbolic Computation Author Joel S. Cohen
ISBN-10 1568811586
Release 2002-07-19
Pages 323
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This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and construct expressions, we can implement many elementary operations from algebra, trigonometry, calculus, and differential equations. With a minimum of prerequisites this book is accessible to and useful for students of mathematics, computer science, and other technical fields. The book contains a CD with the full, searchable text and implementations of all algorithms in the Maple, Mathematica, and MuPad programming languages.

Some Tapas of Computer Algebra

Some Tapas of Computer Algebra Author Arjeh M. Cohen
ISBN-10 3540634800
Release 1998-12-15
Pages 352
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This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.