Reasoning about Geometric Problems using an Elimination Method

The present work relates to a paper by (1991) in which he explained the reasoning about a set of selected, geometry-related problems by using the algebraic methods of characteristic sets (Ritt 1950; Wu 1984a, b), Gröbner bases (Buchberger 1985) and cylindrical algebraic decomposition (Collins 1975). Its main purpose is to demonstrate how to deal with the same set of geometric problems by using another algebraic method which is based on some elimination procedures proposed by (1993). We use the same formulations of the problems (with slight modifications when necessary) and the same set of illustrative examples given previously (Wang 1991). It is shown that for most of the examples our new method takes less computing time than the methods of characteristic sets and Gröbner bases do.