The application of Homogenization to simultaneous equations

  • Bernard Silver
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 138)


We have been studying the problem of solving small systems of symbolic simultaneous equations, of the type found on A level Mathematics exam papers. We have found that Homogenization, described in [Bundy and Silver 81], can be extended to provide a fairly powerful method for solving these problems. The work described here has been implemented as an extension to PRESS, a computer program, written in PROLOG, [Clocksin and Mellish 81], for solving symbolic, transcendental, non-differential equations, described in [Bundy and Welham 81], and [Sterling et al

We also discuss the technique of Elimination, and suggest how this might be implemented.


Homogenization simultaneous equations meta level inference algebraic manipulation mathematical reasoning equation solving-rewrite rules 


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  1. [Bundy and Silver 81]
    Bundy, A. and Silver, B. Homogenization: Preparing Equations for Change of Unknown. In Schank, R., editor, IJCAI7. International Joint Conference on Artificial Intelligence, 1981. Longer version available from Edinburgh as DAI Research Paper No. 159.Google Scholar
  2. [Bundy and Welham 81]
    Bundy, A. and Welham, B. Using meta-level inference for selective application of multiple rewrite rules in algebraic manipulation. Artificial Intelligence 16(2), 1981.Google Scholar
  3. [Clocksin and Mellish 81]
    Clocksin, W.F. and Mellish, C.S. Programming in Prolog. Springer Verlag, 1981.Google Scholar
  4. [Conte and de Boor 72]
    Conte, S.D. and de Boor, C. Elementary Numerical Analysis. McGraw-Hill Kogakusha, 1972.Google Scholar
  5. [Sterling et al 82]
    Sterling, L., Bundy, A., Byrd, L., O'Keefe, R., and Silver, B. Solving Symbolic Equations with PRESS. Research Paper 171, Dept. of Artificial Intelligence, Edinburgh, 1982. To appear in EUROCAM 1982 Proceedings.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Bernard Silver
    • 1
  1. 1.Department of Artificial IntelligenceUniversity of EdinburghUK

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