ELIMINATION PROCEDURES FOR MECHANICAL THEOREM-PROVING IN GEOMETRY

In this paper, methods for the algebraic decision problem of mechanical theorem proving in elementary geometry are described on the basis of some elimination procedures for polynomial systems. The methods can determine whether or not a geometric theorem is generically true and whether it is true or false for each of the components including degenerate ones, with projection and irreducible decomposition. Theorems which have been proved using an implementation of the methods in Maple include the Simson Theorem, Butterfly Theorem, Secant Theorem, Feuerbach Theorem, Steiner Theorem, Steiner-Lehmus Theorem, Merely Theorem and Thebault-Taylor Theorem, of which some are taken as illustrative examples in the paper.