Title: Computer algebra and symbolic computation: mathematical methods | Author(s): Joel S. Cohen | Publisher: CRC Press | Year: 2003 | Language: English | Pages: 470 | ISBN: 9781568811598, 1568811594 | Size: 3 MB | Extension: pdf Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polynomial factorization. It is well-suited for self-study and can be used as the basis for a graduate course. Table of contents : Mathematical Methods......Page 1Contents......Page 9Preface......Page 111.1 Computer Algebra Systems......Page 211.2 Mathematical Pseudo-Language (MPL)......Page 221.3 Automatic Simplification and Expression Structure......Page 251.4 General Polynomial Expressions......Page 311.5 Miscellaneous Operators......Page 322.1 The Integers......Page 372.2 Rational Number Arithmetic......Page 572.3 Fields......Page 643.1 The Goal of Automatic Simplification......Page 833.2 An Automatic Simplification Algorithm......Page 1114.1 Elementary Concepts and Polynomial Division......Page 1314.2 Greatest Common Divisors in F[x]......Page 1464.3 Computations in Elementary Algebraic Number Fields......Page 1664.4 Partial Fraction Expansion in F(x)......Page 1865. Polynomial Decomposition......Page 1995.1 Theoretical Background......Page 2005.2 A Decomposition Algorithm......Page 2086.1 Multivariate Polynomials and Integral Domains......Page 2216.2 Polynomial Division and Expansion......Page 2276.3 Greatest Common Divisors......Page 2497.1 The Resultant Concept......Page 2857.2 Polynomial Relations for Explicit Algebraic Numbers......Page 3098.1 Multiple Division and Reduction......Page 3178.2 Equivalence, Simplification, and Ideals......Page 3388.3 A Simplification Algorithm......Page 3549. Polynomial Factorization......Page 3699.1 Square-Free Polynomials and Factorization......Page 3709.2 Irreducible Factorization: The Classical Approach......Page 3809.3 Factorization in Zp[x]......Page 3909.4 Irreducible Factorization: A Modern Approach......Page 419Bibliography......Page 451Index......Page 461
Computer algebra and symbolic computation: mathematical methods
Title: Computer algebra and symbolic computation: mathematical methods | Author(s): Joel S. Cohen | Publisher: CRC Press | Year: 2003 | Language: English | Pages: 470 | ISBN: 9781568811598, 1568811594 | Size: 3 MB | Extension: pdf Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polynomial factorization. It is well-suited for self-study and can be used as the basis for a graduate course. Table of contents : Mathematical Methods......Page 1Contents......Page 9Preface......Page 111.1 Computer Algebra Systems......Page 211.2 Mathematical Pseudo-Language (MPL)......Page 221.3 Automatic Simplification and Expression Structure......Page 251.4 General Polynomial Expressions......Page 311.5 Miscellaneous Operators......Page 322.1 The Integers......Page 372.2 Rational Number Arithmetic......Page 572.3 Fields......Page 643.1 The Goal of Automatic Simplification......Page 833.2 An Automatic Simplification Algorithm......Page 1114.1 Elementary Concepts and Polynomial Division......Page 1314.2 Greatest Common Divisors in F[x]......Page 1464.3 Computations in Elementary Algebraic Number Fields......Page 1664.4 Partial Fraction Expansion in F(x)......Page 1865. Polynomial Decomposition......Page 1995.1 Theoretical Background......Page 2005.2 A Decomposition Algorithm......Page 2086.1 Multivariate Polynomials and Integral Domains......Page 2216.2 Polynomial Division and Expansion......Page 2276.3 Greatest Common Divisors......Page 2497.1 The Resultant Concept......Page 2857.2 Polynomial Relations for Explicit Algebraic Numbers......Page 3098.1 Multiple Division and Reduction......Page 3178.2 Equivalence, Simplification, and Ideals......Page 3388.3 A Simplification Algorithm......Page 3549. Polynomial Factorization......Page 3699.1 Square-Free Polynomials and Factorization......Page 3709.2 Irreducible Factorization: The Classical Approach......Page 3809.3 Factorization in Zp[x]......Page 3909.4 Irreducible Factorization: A Modern Approach......Page 419Bibliography......Page 451Index......Page 461