Readable Simplification Procedures for Trigonometric Expressions

abstract

The simplification of trigonometric expressions is very difficult problem in mathematics researching and education. In this paper, we proposes a synthetic algorithm to automatically produce the readable simplification process for trigonometric expressions. The meanings of simplification are defined firstly, one of important requirements is that if we input a trigonometric monomial like "sin(x+y-z)* sin(x+z-y)*sin(y+z-x)", the computer output must the same trigonometric monomial by the expansion and simplification procedures. In order to make the algorithm more efficient, firstly we establish a library for all trigonometric transformations, then we combine the fixed trigonometric transformation procedures and the searching database. The algorithm have been implemented by Allegro Lisp and the implementations for about 300 examples demonstrated the average CPU time is about 1 minute and can solve some problems unsolved by Maple.