کتابخانه

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 1
Contents......Page 9
Preface......Page 11
1.1 Computer Algebra Systems......Page 21
1.2 Mathematical Pseudo-Language (MPL)......Page 22
1.3 Automatic Simplification and Expression Structure......Page 25
1.4 General Polynomial Expressions......Page 31
1.5 Miscellaneous Operators......Page 32
2.1 The Integers......Page 37
2.2 Rational Number Arithmetic......Page 57
2.3 Fields......Page 64
3.1 The Goal of Automatic Simplification......Page 83
3.2 An Automatic Simplification Algorithm......Page 111
4.1 Elementary Concepts and Polynomial Division......Page 131
4.2 Greatest Common Divisors in F[x]......Page 146
4.3 Computations in Elementary Algebraic Number Fields......Page 166
4.4 Partial Fraction Expansion in F(x)......Page 186
5. Polynomial Decomposition......Page 199
5.1 Theoretical Background......Page 200
5.2 A Decomposition Algorithm......Page 208
6.1 Multivariate Polynomials and Integral Domains......Page 221
6.2 Polynomial Division and Expansion......Page 227
6.3 Greatest Common Divisors......Page 249
7.1 The Resultant Concept......Page 285
7.2 Polynomial Relations for Explicit Algebraic Numbers......Page 309
8.1 Multiple Division and Reduction......Page 317
8.2 Equivalence, Simplification, and Ideals......Page 338
8.3 A Simplification Algorithm......Page 354
9. Polynomial Factorization......Page 369
9.1 Square-Free Polynomials and Factorization......Page 370
9.2 Irreducible Factorization: The Classical Approach......Page 380
9.3 Factorization in Zp[x]......Page 390
9.4 Irreducible Factorization: A Modern Approach......Page 419
Bibliography......Page 451
Index......Page 461