Reasoning about Surfaces Using Differential Zero and Ideal Decomposition

Philippe Aubry 1 Dongming Wang 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This paper presents methods for zero and ideal decomposition of partial differential polynomial systems and the application of these methods and their implementations to deal with problems from the local theory of surfaces. We show how to prove known geometric theorems and to derive unknown relations automatically. In particular, an algebraic relation between the first and the second fundamental coefficients in a very compact form has been derived, which is more general and has smaller degree than a relation discovered previously by Z.~Li. Moreover, we provide symmetric expressions for Li's relation and clarify his statement. Some examples of theorem proving and computational difficulties encountered in our experiments are also discussed.
keyword : triangular decomposition automatic reasoning differential algebra differential geometry algèbre différentielle géométrie différentielle décomposition triangulaire raisonnement automatique
Type de document :
Communication dans un congrès
J. Richter-Gebert, D. Wang. Third International Workshop on Automated Deduction in Geometry - ADG'2000, 2000, Zurich, Switzerland, Springer-Verlag, 2061, pp.154-174, 2000, Lecture Notes in Artificial Intelligence
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https://hal.inria.fr/inria-00100607
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 14:48:05
Dernière modification le : jeudi 11 janvier 2018 - 06:20:00

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  • HAL Id : inria-00100607, version 1

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Philippe Aubry, Dongming Wang. Reasoning about Surfaces Using Differential Zero and Ideal Decomposition. J. Richter-Gebert, D. Wang. Third International Workshop on Automated Deduction in Geometry - ADG'2000, 2000, Zurich, Switzerland, Springer-Verlag, 2061, pp.154-174, 2000, Lecture Notes in Artificial Intelligence. 〈inria-00100607〉

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