Computer Algebra and Symbolic Computation:

MathematicaT, MapleT, 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. Computer Algebra and Symbolic Computation: Mathematical Methods includes complexity analysis of algorithms and recent developments in the field. It is well suited for self-study and can be used as the basis for a graduate course. Maintaining the style set by Elementary Algorithms, the author explains mathematical methods as needed while introducing advanced methods to treat complex operations.

Preface	p. ix
Background Concepts	p. 1
Computer Algebra Systems	p. 1
Mathematical Pseudo-Language (MPL)	p. 2
Automatic Simplification and Expression Structure	p. 5
General Polynomial Expressions	p. 11
Miscellaneous Operators	p. 12
Integers, Rational Numbers, and Fields	p. 17
The Integers	p. 17
Rational Number Arithmetic	p. 37
Fields	p. 44
Automatic Simplification	p. 63
The Goal of Automatic Simplification	p. 63
An Automatic Simplification Algorithm	p. 91
Single Variable Polynomials	p. 111
Elementary Concepts and Polynomial Division	p. 111
Greatest Common Divisors in F[x]	p. 126
Computations in Elementary Algebraic Number Fields	p. 146
Partial Fraction Expansion in F(x)	p. 166
Polynomial Decomposition	p. 179
Theoretical Background	p. 180
A Decomposition Algorithm	p. 188
Multivariate Polynomials	p. 201
Multivariate Polynomials and Integral Domains	p. 201
Polynomial Division and Expansion	p. 207
Greatest Common Divisors	p. 229
The Resultant	p. 265
The Resultant Concept	p. 265
Polynomial Relations for Explicit Algebraic Numbers	p. 289
Polynomial Simplification with Side Relations	p. 297
Multiple Division and Reduction	p. 297
Equivalence, Simplification, and Ideals	p. 318
A Simplification Algorithm	p. 334
Polynomial Factorization	p. 349
Square-Free Polynomials and Factorization	p. 350
Irreducible Factorization: The Classical Approach	p. 360
Factorization in Z[subscript p x]	p. 370
Irreducible Factorization: A Modern Approach	p. 399
Bibliography	p. 431
Index	p. 441
Table of Contents provided by Syndetics. All Rights Reserved.

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Computer Algebra and Symbolic Computation: Mathematical Methods

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