Chapter 20 - Geometric theorem provers and algebraic equation solvers

Abstract

This chapter provides a collection of geometric theorem provers and algebraic equation solvers that are pieces of mathematical software. The methods of mechanizing mathematics are realized by means of computer software for solving scientific and engineering problems through symbolic and hybrid computation. The early theorem provers, though efficient, were written in basic programming languages and on primitive computers. The mechanization of mathematics consists of three layers, which include theory and algorithms, software, and applications. The value and significance of algorithmic developments are rendered visible by means of their successful applications. The development of effective geometric theorem provers and polynomial equation solvers is focused in this chapter. GEOmetry THeorem provER (GEOTHER) is an environment implemented in Maple with drawing routines and interface written in C for manipulating and proving geometric theorems. GEOTHER can automatically assign coordinates to each point in some optimal manner and translate the predicate representation of the theorem into an English statement, into a first-order logical formula, or into algebraic expressions.