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International Conference on Artificial Intelligence and Symbolic Mathematical Computing

AISMC 1996: Artificial Intelligence and Symbolic Mathematical Computation pp 274–288Cite as

Solving geometrical constraint systems using CLP based on linear constraint solver

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1138))

Abstract

Euclidean geometrical configurations obtained with ruler, square and compass may be described as arithmetic constraint systems over rational numbers and consequently belong to the domain of CLP(R). Unfortunately, CLP based on linear constraint solvers which are efficient and can deal with geometrical constraints such as parallelism, perpendicularity, belonging to a line i.e. pseudo-linear constraints, cannot handle quadratic constraints introduced when using circles.

Two problems arise with quadratic constraints: the first problem is how to solve mixed constraint systems i.e. linear constraints combined with quadratic constraints; the second problem is how to represent the real numbers involved in the resolution of mixed constraints, so that correctness and completeness of linear constraint solvers are preserved.

In this paper we present a naive algorithm for mixed constraints based on a cooperation with a linear constraint solver. We define a representation for the real numbers, i.e. constructible numbers, occuring in Euclidean geometry. This representation preserves correctness and completeness of above algorithms. A survey over 512 theorems of Euclidean geometry shows that from both theoretical and experimental points of view, this representation is appropriate. This work is intended to be used to verify geometrical properties in Intelligent Tutoring System for geometry.

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Authors and Affiliations

  1. Laboratoire IMAG-LSR, BP 53 X, 38041, Grenoble Cedex 9, France

    Denis Bouhineau

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  1. Denis Bouhineau
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Jacques Calmet John A. Campbell Jochen Pfalzgraf

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© 1996 Springer-Verlag Berlin Heidelberg

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Bouhineau, D. (1996). Solving geometrical constraint systems using CLP based on linear constraint solver. In: Calmet, J., Campbell, J.A., Pfalzgraf, J. (eds) Artificial Intelligence and Symbolic Mathematical Computation. AISMC 1996. Lecture Notes in Computer Science, vol 1138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61732-9_63

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  • DOI: https://doi.org/10.1007/3-540-61732-9_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61732-7

  • Online ISBN: 978-3-540-70740-0

  • eBook Packages: Springer Book Archive

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