Computer algebra : systems and algorithms for algebraic computation

Author(s)

Bibliographic Information

Computer algebra : systems and algorithms for algebraic computation

J. H. Davenport, Y. Siret, E. Tournier ; translated from the French by A. Davenport and J. H. Davenport

Academic Press, c1993

2nd ed

Other Title

Calcul formel

Available at  / 35 libraries

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Note

First published in 1988

Bibliography: p. 275-292

Includes index

Description and Table of Contents

Description

A book for students and researchers in theoretical computer science, mathematics, physics and engineering. Computer algebra is the name of the technology for manipulating mathematical formulae by computer. The rapid evolution of hardware and software makes it accessible to every scientist and engineer who uses mathematical methods. This book aims to provide an introduction to computer algebra, catering to both the interested beginner and the experienced pure mathematician and computer scientist. The new developments in the second edition give a good comprehensive review, and the book contains references to fundamental papers, and worked examples. In addition to being a general text on the subject, the book includes an appendix describing the use of one particular algebra system REDUCE.

Table of Contents

  • Part 1 How to use a computer algebra system
  • introduction
  • features of computer algebra systems
  • syntax of the associated languages
  • areas covered by existing systems
  • computer algebra by example
  • MACSYMA's possibilities in algebra
  • general possibilities
  • the division of the circle into 17 equal parts
  • availability of MACSYMA
  • other systems
  • AXIOM. Part 2 The problem of data representation
  • representations of data representation
  • representations of integers
  • representations of fractions, representations of polynomials
  • polynomials in several variables
  • representations of rational functions
  • representations of algebraic functions
  • representations of transcendentals
  • representations of matrices, representations of series. Part 3 Polynomial simplification
  • simplification of polynomial equations
  • simplification of real polynomial systems. Part 4 Advanced algorithms
  • modular methods
  • p-adic methods. Part 5 Formal integration and differential equations
  • introduction
  • integration of rational functions
  • the integration of more complicated functions
  • integration of logarithmic functions
  • integration of exponential functions, algebraic solutions of o.d.e.s.
  • asymptotic solutions of o.d.e.s.
  • appendix
  • algebraic background
  • annex
  • REDUCE - a computer algebra system
  • introduction
  • syntax of REDUCE
  • declarations
  • commands
  • built-in facilities
  • manipulation of expressions
  • substitution
  • matrix algebra
  • IRENA.

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