Mechanical geometry theorem proving
Mechanical geometry theorem proving
Applications of Gro¨bner bases in non-linear computational geometry
Mathematical aspects of scientific software
Wu's method and its application to perspective viewing
Geometric reasoning
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
Automatic Discovery of Theorems in Elementary Geometry
Journal of Automated Reasoning
A dynamic-symbolic interface for geometric theorem discovery
Computers & Education
A software tool for the investigation of plane loci
Mathematics and Computers in Simulation
An Introduction to Geometry Expert
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Automatic determination of envelopes and other derived curves within a graphic environment
Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
Automatic determination of algebraic surfaces as loci of points
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Geometry expressions: a constraint based interactive symbolic geometry system
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
A bridge between dynamic geometry and computer algebra
Mathematical and Computer Modelling: An International Journal
Connecting the 3D DGS Calques3D with the CAS Maple
Mathematics and Computers in Simulation
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A package for investigating problems about configuration theorems in 3D-geometry and performing mechanical theorem proving and discovery is presented. It includes the preparation of the problem, consisting of three processes: defining the geometric objects in the configuration; determining the hypothesis conditions through a point-on-object declaration method; and fixing the thesis conditions. After this preparation, methods based both on Groebner Bases and Wu's method can be applied to prove thesis conditions or to complete hypothesis conditions. Homogeneous coordinates are used in order to treat projective problems (although affine and Euclidean problems can also be treated). A Maple implementation of the method has been developed. It has been used to extend to 3D some classic 2D theorems.