What is computer algebra?

Three characteristics of computer algebra

• Computer algebra is concerned with computing in algebraic structure.
  
• The results of computer algebra algorithms are exact and not subject to approximation errors.
  
• In general the inputs to algorithms are expressions or formulas and one also expects expressions or formulas as the result.

Some applications areas of computer algebra

• Geometric theorem proving
  
• Analysis of algebraic varieties
  
• Modeling in science and technology
  
• The " Piano movers problem " in robotics
  

The limitations of computer algebra

• There are problems for which the computation of an exact symbolic solution is prohibitively expensive.
  
• There are some problems for which no exact symbolic solution is known.
  
• There are problems for which one can rigiously prove that no exact symbolic solution exists.
  

Computer algebra systems

• AXIOM
• Maple
  • Waterloo Maple Inc.
  • The Symbolic Computation Group
  • Maple index page
• Mathematica
• MACSYMA
• MuPAD
  • MuPAD homepage(mirror site in Japan)
  • MuPAD archives (mirror site in Japan)
• REDUCE
• Risa/Asir
  • Risa/Asir manual
  • Risa/Asir archives

Reference

• D.E. KNUTH
  The The Art of Computer Programming, Volume 2, Seminumerical Algorithms
  Reading, Mass. : Addison-Wesley,1997.

• F.Winkler
  Polynomial algorithms in computer algebra
  New York : Springer-Verlag,1996.

• K.O. Geddes, S.R. Czapor and G. Labahn
  Algorithms for computer algebra
  Boston : Kluwer Academic,1992.

• M. Mignotte
  Mathematics for computer algebra
  New York ; Tokyo : Springer-Verlag ,1992.

• B.W.Char,K.O.Geddes, etc
  First leaves: a tutorial introduction to Maple V
  Springer-Verlag,1993.