Reasoning about Surfaces Using Differential Zero and Ideal Decomposition
Identifieur interne : 00A156 ( Main/Exploration ); précédent : 00A155; suivant : 00A157Reasoning about Surfaces Using Differential Zero and Ideal Decomposition
Auteurs : Philippe Aubry [France] ; Dongming Wang [France]Source :
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.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="it"><term>algèbre différentielle</term><term>automatic reasoning</term><term>differential algebra</term><term>differential geometry</term><term>décomposition triangulaire</term><term>géométrie différentielle</term><term>raisonnement automatique</term><term>triangular decomposition</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Aubry, Philippe" sort="Aubry, Philippe" uniqKey="Aubry P" first="Philippe" last="Aubry">Philippe Aubry</name></region><name sortKey="Wang, Dongming" sort="Wang, Dongming" uniqKey="Wang D" first="Dongming" last="Wang">Dongming Wang</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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