COMPUTER ALGEBRA, Algorithms, Systems and Applications

Richard Liska, Ladislav Drska, Jiri Limpouch, Milan Sinor, Michael Wester, Franz Winkler

June 2, 1997

 
• Contents
• Introduction
  • What are algebraic calculations?
  • Why do algebraic calculations?
  • History
• Algorithms for algebraic computation
  • Algebraic structures
  • Representation of algebraic structures
  • Arithmetic
  • Simplification
  • Greatest common divisor
  • Resultant
  • Solving polynomial equations
  • Differentiation
  • Summation
  • Integration
  • Ordinary differential equations
  • Polynomial factorization
  • Quantifier elimination
• Integrated mathematical systems
  • Computer algebra systems
  • Peculiarities of programming in computer algebra systems
  • Expression Swell
• Basic possibilities of integrated mathematical systems
  • Axiom
  • Derive
  • Macsyma
  • Maple
  • Mathematica
  • Reduce
• Applications of computer algebra
  • Classical application areas
  • Other application areas
  • Case study 1. - Perturbation methods
  • Case study 2. - General theory of relativity
  • Case study 3. - Collision integrals in plasma physics
  • Case study 4. - Numerical solving of partial differential equations
  • Survey articles on applications
• Another sources of study
  • Basic references
  • Other references
  • Journals
  • Electronic information sources
  • References for CAS Comparisons
  • Computer Algebra Conferences
  • Manuals
  • Distributors addresses
• About this document ...