The application of Homogenization to simultaneous equations
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.
KeywordsHomogenization simultaneous equations meta level inference algebraic manipulation mathematical reasoning equation solving-rewrite rules
Unable to display preview. Download preview PDF.
- [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
- [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
- [Clocksin and Mellish 81]Clocksin, W.F. and Mellish, C.S. Programming in Prolog. Springer Verlag, 1981.Google Scholar
- [Conte and de Boor 72]Conte, S.D. and de Boor, C. Elementary Numerical Analysis. McGraw-Hill Kogakusha, 1972.Google Scholar
- [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