InforLorV4, Hal, Corpus, bibRecord, 003F92

Reasoning about Surfaces Using Differential Zero and Ideal Decomposition

Identifieur interne : 003F92 ( Hal/Corpus ); précédent : 003F91; suivant : 003F93

Reasoning about Surfaces Using Differential Zero and Ideal Decomposition

Auteurs : Philippe Aubry ; Dongming Wang

Source :

RBID : Hal:inria-00100607

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:

https://hal.inria.fr/inria-00100607

Links to Exploration step

Hal:inria-00100607

Le document en format XML

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<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>
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<hal api="V3"><titleStmt><title xml:lang="en">Reasoning about Surfaces Using Differential Zero and Ideal Decomposition</title>
<author role="aut"><persName><forename type="first">Philippe</forename>
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<idno type="halRefHtml">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</idno>
<idno type="halRef">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</idno>
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<notesStmt><note type="commentary">Colloque avec actes et comité de lecture. internationale.</note>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">Reasoning about Surfaces Using Differential Zero and Ideal Decomposition</title>
<author role="aut"><persName><forename type="first">Philippe</forename>
<surname>Aubry</surname>
</persName>
<email>Philippe.Aubry@lip6.fr</email>
<idno type="halAuthorId">100315</idno>
<orgName ref="#struct-364223"></orgName>
<affiliation ref="#struct-2364"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Dongming</forename>
<surname>Wang</surname>
</persName>
<idno type="halAuthorId">131871</idno>
<orgName ref="#struct-364223"></orgName>
<affiliation ref="#struct-2364"></affiliation>
</author>
</analytic>
<monogr><idno type="localRef">A01-R-311 || aubry01a</idno>
<meeting><title>Third International Workshop on Automated Deduction in Geometry - ADG'2000</title>
<date type="start">2000</date>
<settlement>Zurich, Switzerland</settlement>
</meeting>
<respStmt><resp>conferenceOrganizer</resp>
<name>J. Richter-Gebert, D. Wang</name>
</respStmt>
<editor>J. Richter-Gebert, D. Wang</editor>
<imprint><publisher>Springer-Verlag</publisher>
<biblScope unit="serie">Lecture Notes in Artificial Intelligence</biblScope>
<biblScope unit="volume">2061</biblScope>
<biblScope unit="pp">154-174</biblScope>
<date type="datePub">2000</date>
</imprint>
</monogr>
</biblStruct>
</sourceDesc>
<profileDesc><langUsage><language ident="en">English</language>
</langUsage>
<textClass><keywords scheme="author"><term xml:lang="it">triangular decomposition</term>
<term xml:lang="it">automatic reasoning</term>
<term xml:lang="it">differential algebra</term>
<term xml:lang="it">differential geometry</term>
<term xml:lang="it">algèbre différentielle</term>
<term xml:lang="it">géométrie différentielle</term>
<term xml:lang="it">décomposition triangulaire</term>
<term xml:lang="it">raisonnement automatique</term>
</keywords>
<classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode>
<classCode scheme="halTypology" n="COMM">Conference papers</classCode>
</textClass>
<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.</abstract>
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Reasoning about Surfaces Using Differential Zero and Ideal Decomposition

Reasoning about Surfaces Using Differential Zero and Ideal Decomposition

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