HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

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
Document type :
Conference papers
Complete list of metadata
https://hal.inria.fr/inria-00100607
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 2:48:05 PM
Last modification on : Friday, February 4, 2022 - 3:29:59 AM

Identifiers

  • HAL Id : inria-00100607, version 1

Collections

INRIA | CNRS | LORIA | UNIV-LORRAINE | INRIA2

Citation

Philippe Aubry, Dongming Wang. Reasoning about Surfaces Using Differential Zero and Ideal Decomposition. Third International Workshop on Automated Deduction in Geometry - ADG'2000, J. Richter-Gebert, D. Wang, 2000, Zurich, Switzerland, pp.154-174. ⟨inria-00100607⟩

Export

BibTeX TEI DC DCterms EndNote Datacite

Share

Metrics

Record views

50

 

Contact                    Legal Notice                    Personal Data