Automated and readable simplification of trigonometric expressions

Authors:
Hongguang Fu;Xiuqin Zhong;Zhenbing Zeng
Affiliations:
Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610041, China;Chengdu Institute of Computer Applications, Chinese Academy of Sciences, Chengdu 610041, China;Software Engineering Institute, East China Normal University, Shanghai 200062, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

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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.