Automated and readable simplification of trigonometric expressions

doi:10.1016/j.mcm.2006.04.002

Mathematical and Computer Modelling

Volume 44, Issues 11–12, December 2006, Pages 1169-1177

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Abstract

Automated simplification of trigonometric expressions is an important problem that hasn’t been completely solved by current computer algebra systems. This paper presents a number of unique prescriptions for the ordering of some trigonometric transformation rules, which have been derived by observing how human experts follow their intuitive rules. We have implemented the procedure in Lisp because of its suitability for formula manipulations and rule-based reasoning systems. Consequently, it can simplify many trigonometric expressions which are even difficult to do by hand, and it achieves much better results for many hard problems than any of Maple, Mathematica, and Maxima do.

Keywords

Simplification of trigonometric expressions

Combination rules

Rule lists

Pattern matching

Automated reasoning

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¹: Hongguang Fu is with the Automated Reasoning Lab., Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610041, China. Tel.: +86 028 85224289; fax: +86 028 85229357.