On the application of Buchberger's algorithm to automated geometry theorem proving
Journal of Symbolic Computation
Using Gröbner bases to reason about geometry problems
Journal of Symbolic Computation
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
Computational Origami Construction as Constraint Solving and Rewriting
Electronic Notes in Theoretical Computer Science (ENTCS)
Geometry Constructions Language
Journal of Automated Reasoning
Towards an electronic geometry textbook
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Automatic verification of regular constructions in dynamic geometry systems
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Automated discovery in elementary extrema problems
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
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This paper proposes a geometric-object-oriented language for symbolic geometric computation, reasoning, and visualization. In this language, geometric objects are constructed with indefinite parametric data. Modifications and basic operations on these objects are enabled. Degeneracy and uncertainty are handled effectively by means of imposing conditions and assumptions and geometric statements are formulated by declaring relations among different objects. A system implemented on the basis of this language will allow the user to perform geometric computation and reasoning rigorously and to prove geometric theorems and generate geometric diagrams and interactive documents automatically. We present the overall design of the language, explain the capabilities, features, main components of the proposed system, provide specifications for some of its functors, report our experiments with a preliminary implementation of the system, and discuss some encountered difficulties and research problems.