On the application of Buchberger's algorithm to automated geometry theorem proving
Journal of Symbolic Computation
REDUCE: Software for algebraic computation
REDUCE: Software for algebraic computation
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Applications of Gro¨bner bases in non-linear computational geometry
Mathematical aspects of scientific software
Careful algebraic translations of geometry theorems
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Wu's method and its application to perspective viewing
Geometric reasoning
Mathematica: a system for doing mathematics by computer (2nd ed.)
Mathematica: a system for doing mathematics by computer (2nd ed.)
AXIOM: the scientific computation system
AXIOM: the scientific computation system
Introduction to Maple (2nd ed.)
Introduction to Maple (2nd ed.)
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
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
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
A maple package for automatic theorem proving and discovery in 3D-geometry
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Geometry expressions: a constraint based interactive symbolic geometry system
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
3D extension of Steiner chains problem
Mathematical and Computer Modelling: An International Journal
A bridge between dynamic geometry and computer algebra
Mathematical and Computer Modelling: An International Journal
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Many (2D) Dynamic Geometry Systems (DGSs) are able to export numeric coordinates and equations with numeric coefficients to Computer Algebra Systems (CASs). Moreover, different approaches and systems that link (2D) DGSs with CASs, so that symbolic coordinates and equations with symbolic coefficients can be exported from the DGS to the CAS, already exist. Although the 3D DGS Calques3D can export numeric coordinates and equations with numeric coefficients to Maple and Mathematica, it cannot export symbolic coordinates and equations with symbolic coefficients. A connection between the 3D DGS Calques3D and the CAS Maple, that can handle symbolic coordinates and equations with symbolic coefficients, is presented here. Its main interest is to provide a convenient time-saving way to explore problems and directly obtain both algebraic and numeric data when dealing with a 3D extension of ''ruler and compass geometry''. This link has not only educational purposes but mathematical ones, like mechanical theorem proving in geometry, geometric discovery (hypotheses completion), geometric loci finding... As far as we know, there is no comparable ''symbolic'' link in the 3D case, except the prototype 3D-LD (restricted to determining algebraic surfaces as geometric loci).