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Computer Algebra — Historical Development, Characterization, and Prospects

In: Computer Algebra Handbook

Author

Listed:
  • Wolfram Koepf
  • Erich Kaltofen
  • Volker Weispfenning
  • Johannes Grabmeier
  • B. Heinrich Matzat

Abstract

Historically, the terms algebra and algorithm originate from the same source: the book Kitab al muhtasar fi hisab al-gabr w’aluqabalah by the Persian scientist Abu Ja’far Mohammed ibn Musa al-Khorezmi (cf. [Zemanek 1981] or [Ifrah 1991]) — compiled at the academy of science in Bagdad in the ninth century — uses al-gabr and muqabalah to describe symbolic transformations and term reductions respectively, which are performed to solve algebraic equations. Algorithmic manipulation of symbolic algebraic expressions remained to be the major task of algebra about until the end of the nineteenth century. At the beginning of the twentieth century, this method was amended and shadowed by developments in abstract algebra. There, the main interest is focussed on formal investigations of algebraic structures derived from axioms. This structural algebraic method has taken over considerable parts of mathematics nowadays.

Suggested Citation

  • Wolfram Koepf & Erich Kaltofen & Volker Weispfenning & Johannes Grabmeier & B. Heinrich Matzat, 2003. "Computer Algebra — Historical Development, Characterization, and Prospects," Springer Books, in: Johannes Grabmeier & Erich Kaltofen & Volker Weispfenning (ed.), Computer Algebra Handbook, chapter 1, pages 1-9, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55826-9_1
    DOI: 10.1007/978-3-642-55826-9_1
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