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Construction automatique de figures géometriques et programmation logique avec contraintes

Abstract : The theoretical contributions of this work include : 1) exact and normal representation of constructible numbers (arithmetic expressions with multiple nested square roots of rational numbers), 2) algorithm for equality, disequality and inequality for such real numbers and 3) results for checking if a given constraint is redundant with respect to a system of quadratic constraints. This work is embeded in an environment CLP(Géométrie) using the Constraint Logic Programming approach. The main experimental contribution concern a set of 512 theorems in geometry proposed by Chou. It is the reduction in the number of quadratic extensions needed for the representation of geometrical situation by a careful choice of constructions. The result of this reduction is that the vast majority of the 512 theorems proposed by Chou can be handled with exact representation without prohibitive cost, practically only rational numbers are necessary in most cases. The close linkage of this work with man-machine tutoring make the proposed approach an interesting tool for teaching geometry. Three applications are demonstrated in this area. The main one concern a declarative approach for the definition and the manipulation of geometrical figures.
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https://tel.archives-ouvertes.fr/tel-00004922
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Submitted on : Friday, February 20, 2004 - 11:19:14 AM
Last modification on : Wednesday, November 4, 2020 - 3:06:59 AM
Long-term archiving on: : Thursday, September 13, 2012 - 2:05:19 PM

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  • HAL Id : tel-00004922, version 1

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Denis Bouhineau. Construction automatique de figures géometriques et programmation logique avec contraintes. Autre [cs.OH]. Université Joseph-Fourier - Grenoble I, 1997. Français. ⟨tel-00004922⟩

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