Automated Deduction in Geometry

Colloque avec actes et comité de lecture. internationale.International audienceGEOTHER provides an environment for handling and proving theorems in geometry automatically. In this environment, geometric theorems are represented by means of predicate specifications. Several functions are implemented that allow one to translate the specification of a geometric theorem into English and Chinese statements, into algebraic expressions, and into logic formulas automatically. Geometric diagrams can also be drawn automatically from the predicate specification, and the drawn diagrams may be modified and animated with mouse click and dragging. Five algebraic provers based on Wu's method of characteristic sets, the Gröbner basis method, and other triangularization techniques are available for proving such theorems in elementary (and differential) geometry. Geometric meanings of the produced algebraic nondegeneracy conditions can be interpreted automatically, in most cases. PostScript and HTML files can be generated, also automatically, to document the manipulation and machine proof of the theorem. This paper presents these capabilities of GEOTHER, addresses some implementation issues, and reports on the performance of GEOTHER's algebraic provers