Titlebook: Automated Deduction in Geometry; Third International Jürgen Richter-Gebert,Dongming Wang Conference proceedings 2001 Springer-Verlag Berli

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Giant Planets of Our Solar Systemts are emphasized. More precisely, we use the Calculus of inductive constructions and the system Coq to specify geometric concepts and to study and interactively handle proofs for the first two groups of Hilbert’s axiomatics. It is the first step to a formalization well adapted to the definition of

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A Hybrid Method for Solving Geometric Constraint Problems,f quadratic complexity for constraint problems with loops. This algorithm is complete for constraint problems about simple polygons. The key of the algorithm is to combine the idea of graph based methods for geometric constraint solving and geometric transformations from rule-based methods.

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Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study,solve the Birkhoff Interpolation Problem. We recall and partly improve two algorithms to find at least one point in each connected component of a real algebraic set defined by a single equation or a system of polynomial equations, both based on the computation of the critical points of a distance fu

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Randomized Xero Testing of Radical Expressions and Elementary Geometry Theorem Proving,on. This extends the well-known Schwartz’s probabilistic test for the vanishing of polynomials. The probabilistic test forms the basis of a new theorem prover for conjectures about ruler & compass constructions. Our implementation uses the Core Library which can perform exact comparison for .. Some

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The Kinds of Truth of Geometry Theorems,ons that can be added to the hypotheses to give a valid theorem. We show that (in a certain sense) all possible subsidiary conditions are implied by those obtained from the basis; that what we call the . of the theorem may be derived from the basis; and that the side polynomials may be classified in

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