REDUCE: Software for algebraic computation
REDUCE: Software for algebraic computation
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
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.)
Automatic Discovery of Theorems in Elementary Geometry
Journal of Automated Reasoning
Automated Geometric Reasoning: Dixon Resultants, Gröbner Bases, and Characteristic Sets
Selected Papers from the International Workshop on Automated Deduction in Geometry
Automatic Determination of Geometric Loci. 3D-Extension of Simson-Steiner Theorem
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Computing Locus Equations for Standard Dynamic Geometry Environments
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
First Steps on Using OpenMath to Add Proving Capabilities to Standard Dynamic Geometry Systems
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Adding remote computational capabilities to Dynamic Geometry Systems
Mathematics and Computers in Simulation
Connecting the 3D DGS Calques3D with the CAS Maple
Mathematics and Computers in Simulation
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
On the parametric representation of dynamic geometry constructions
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
Using free open source software for intelligent geometric computing
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
Automated discovery in elementary extrema problems
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Automatic deduction in (dynamic) geometry: Loci computation
Computational Geometry: Theory and Applications
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Both computer algebra systems (CASs) and dynamic geometry systems (DGSs) have reached a high level of development. Some CASs (like Maple or Derive) include specific and powerful packages devoted to Euclidean geometry, but CASs have incorporated neither mouse drawing capabilities nor dynamic capabilities. Meanwhile, the well-known DGSs do not provide algebraic facilities. Maple's and Derive's paramGeo packages and the DGS-CAS translator (all freely available from the authors) make it possible to draw a geometric configuration with the mouse (using The Geometer's Sketchpad 3 or 4) and to obtain the coordinates, equations, etc., of the drawn configuration in Maple's or Derive's syntax. To obtain complicated formulae, coordinates of points or equations of loci, to perform automatic theorem proving and to perform automatic discovery directly from sketches are examples of straightforward applications. Moreover, this strategy could be adapted to other CASs and DGSs. This work clearly has a didactic application in geometric problems exploration. Nevertheless, its main interest is to provide a convenient time-saving way to introduce data when dealing with rule and compass geometry, which has a wider scope than only educational purposes.