1990 年 5 巻 3 号 p. 311-323
A new scheme for geometric reasoning based on the integration of algebraic and symbolic methods is presented. In our previous paper we described advantages of Wu's method as our algebraic approach for geometric reasoning. Although the algebraic approach based on Wu's method is very powerful in geometric reasoning, it has some computational difficulties in algebraic calculations. In order to solve these difficulties, the algebraic method must be augmented with symbolic reasoning for introducing semantics of geometric concepts to algebraic expressions. In this paper, we integrate algebraic and symbolic approaches and thereby realize a new scheme for geometric reasoning. This new scheme incorporates advantages of both algebraic and symbolic methods. In order to show the validity of this scheme, examples of locus problems in geometry are solved by the system which we implemented.
