OcrV1, France, Analysis, bibRecord, 000306

Lower bounds for diophantine approximations

Identifieur interne : 000306 ( France/Analysis ); précédent : 000305; suivant : 000307

Lower bounds for diophantine approximations

Auteurs : M. Giusti [France] ; J. Heintz [Espagne] ; K. H Gele [Espagne] ; J. E. Morais [Espagne] ; L. M. Pardo [Espagne] ; J. L. Monta A [Espagne]

Source :

Journal of Pure and Applied Algebra [ 0022-4049 ] ; 1997.

RBID : ISTEX:E0BC2FAF7D2237578CD73E8A597435B1DE60CD3E

Abstract

We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new procedure for the decision of consistency of polynomial equation systems whose bit complexity is subexponential, too. As a byproduct, we analyze the division of a polynomial modulo a reduced complete intersection ideal and from this, we obtain an intrinsic lower bound for the logarithmic height of diophantine approximations to a given solution of a zero-dimensional polynomial equation system. This result represents a multivariate version of Liouville's classical theorem on approximation of algebraic numbers by rationals. A special feature of our procedures is their polynomial character with respect to the mentioned geometric invariants when instead of bit operations only arithmetic operations are counted at unit cost. Technically our paper relies on the use of straight-line programs as a data structure for the encoding of polynomials, on a new symbolic application of Newton's algorithm to the Implicit Function Theorem and on a special, basis independent trace formula for affine Gorenstein algebras.

Url:

https://api.istex.fr/document/E0BC2FAF7D2237578CD73E8A597435B1DE60CD3E/fulltext/pdf

DOI: 10.1016/S0022-4049(97)00015-7

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Istex, to step Corpus: 003128
to stream Istex, to step Curation: 002E87
to stream Istex, to step Checkpoint: 001846
to stream Main, to step Merge: 002526
to stream Main, to step Curation: 002396
to stream Main, to step Exploration: 002396
to stream France, to step Extraction: 000306

Links to Exploration step

ISTEX:E0BC2FAF7D2237578CD73E8A597435B1DE60CD3E

Le document en format XML

<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Lower bounds for diophantine approximations</title>
<author><name sortKey="Giusti, M" sort="Giusti, M" uniqKey="Giusti M" first="M." last="Giusti">M. Giusti</name>
</author>
<author><name sortKey="Heintz, J" sort="Heintz, J" uniqKey="Heintz J" first="J." last="Heintz">J. Heintz</name>
</author>
<author><name sortKey="H Gele, K" sort="H Gele, K" uniqKey="H Gele K" first="K." last="H Gele">K. H Gele</name>
</author>
<author><name sortKey="Morais, J E" sort="Morais, J E" uniqKey="Morais J" first="J. E." last="Morais">J. E. Morais</name>
</author>
<author><name sortKey="Pardo, L M" sort="Pardo, L M" uniqKey="Pardo L" first="L. M." last="Pardo">L. M. Pardo</name>
</author>
<author><name sortKey="Monta A, J L" sort="Monta A, J L" uniqKey="Monta A J" first="J. L." last="Monta A">J. L. Monta A</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:E0BC2FAF7D2237578CD73E8A597435B1DE60CD3E</idno>
<date when="1997" year="1997">1997</date>
<idno type="doi">10.1016/S0022-4049(97)00015-7</idno>
<idno type="url">https://api.istex.fr/document/E0BC2FAF7D2237578CD73E8A597435B1DE60CD3E/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">003128</idno>
<idno type="wicri:Area/Istex/Curation">002E87</idno>
<idno type="wicri:Area/Istex/Checkpoint">001846</idno>
<idno type="wicri:doubleKey">0022-4049:1997:Giusti M:lower:bounds:for</idno>
<idno type="wicri:Area/Main/Merge">002526</idno>
<idno type="wicri:Area/Main/Curation">002396</idno>
<idno type="wicri:Area/Main/Exploration">002396</idno>
<idno type="wicri:Area/France/Extraction">000306</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a">Lower bounds for diophantine approximations</title>
<author><name sortKey="Giusti, M" sort="Giusti, M" uniqKey="Giusti M" first="M." last="Giusti">M. Giusti</name>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</affiliation>
<affiliation wicri:level="3"><country xml:lang="fr">France</country>
<wicri:regionArea>GAGE, Centre de Mathématiques, École Polytechnique, F-91128 Palaiseau Cedex</wicri:regionArea>
<placeName><region type="region" nuts="2">Île-de-France</region>
<settlement type="city">Palaiseau</settlement>
</placeName>
</affiliation>
</author>
<author><name sortKey="Heintz, J" sort="Heintz, J" uniqKey="Heintz J" first="J." last="Heintz">J. Heintz</name>
<affiliation wicri:level="4"><country xml:lang="fr">Espagne</country>
<wicri:regionArea>Departamento de Matentáticas, Estadistica y Computación, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander</wicri:regionArea>
<placeName><region nuts="2" type="communauté">Cantabrie</region>
<settlement type="city">Santander</settlement>
</placeName>
<orgName type="university">Université de Cantabrie</orgName>
</affiliation>
</author>
<author><name sortKey="H Gele, K" sort="H Gele, K" uniqKey="H Gele K" first="K." last="H Gele">K. H Gele</name>
<affiliation wicri:level="4"><country xml:lang="fr">Espagne</country>
<wicri:regionArea>Departamento de Matentáticas, Estadistica y Computación, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander</wicri:regionArea>
<placeName><region nuts="2" type="communauté">Cantabrie</region>
<settlement type="city">Santander</settlement>
</placeName>
<orgName type="university">Université de Cantabrie</orgName>
</affiliation>
</author>
<author><name sortKey="Morais, J E" sort="Morais, J E" uniqKey="Morais J" first="J. E." last="Morais">J. E. Morais</name>
<affiliation wicri:level="4"><country xml:lang="fr">Espagne</country>
<wicri:regionArea>Departamento de Matentáticas, Estadistica y Computación, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander</wicri:regionArea>
<placeName><region nuts="2" type="communauté">Cantabrie</region>
<settlement type="city">Santander</settlement>
</placeName>
<orgName type="university">Université de Cantabrie</orgName>
</affiliation>
</author>
<author><name sortKey="Pardo, L M" sort="Pardo, L M" uniqKey="Pardo L" first="L. M." last="Pardo">L. M. Pardo</name>
<affiliation wicri:level="4"><country xml:lang="fr">Espagne</country>
<wicri:regionArea>Departamento de Matentáticas, Estadistica y Computación, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander</wicri:regionArea>
<placeName><region nuts="2" type="communauté">Cantabrie</region>
<settlement type="city">Santander</settlement>
</placeName>
<orgName type="university">Université de Cantabrie</orgName>
</affiliation>
</author>
<author><name sortKey="Monta A, J L" sort="Monta A, J L" uniqKey="Monta A J" first="J. L." last="Monta A">J. L. Monta A</name>
<affiliation wicri:level="2"><country xml:lang="fr">Espagne</country>
<wicri:regionArea>Departamento de Matemática e Informática, Campus de Arrosadia, Universidad Pública de Navarra, E-31006 Pamplona</wicri:regionArea>
<placeName><region nuts="2" type="communauté">Communauté forale de Navarre</region>
</placeName>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Journal of Pure and Applied Algebra</title>
<title level="j" type="abbrev">JPAA</title>
<idno type="ISSN">0022-4049</idno>
<imprint><publisher>ELSEVIER</publisher>
<date type="published" when="1997">1997</date>
<biblScope unit="volume">117–118</biblScope>
<biblScope unit="supplement">C</biblScope>
<biblScope unit="page" from="277">277</biblScope>
<biblScope unit="page" to="317">317</biblScope>
</imprint>
<idno type="ISSN">0022-4049</idno>
</series>
<idno type="istex">E0BC2FAF7D2237578CD73E8A597435B1DE60CD3E</idno>
<idno type="DOI">10.1016/S0022-4049(97)00015-7</idno>
<idno type="PII">S0022-4049(97)00015-7</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0022-4049</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new procedure for the decision of consistency of polynomial equation systems whose bit complexity is subexponential, too. As a byproduct, we analyze the division of a polynomial modulo a reduced complete intersection ideal and from this, we obtain an intrinsic lower bound for the logarithmic height of diophantine approximations to a given solution of a zero-dimensional polynomial equation system. This result represents a multivariate version of Liouville's classical theorem on approximation of algebraic numbers by rationals. A special feature of our procedures is their polynomial character with respect to the mentioned geometric invariants when instead of bit operations only arithmetic operations are counted at unit cost. Technically our paper relies on the use of straight-line programs as a data structure for the encoding of polynomials, on a new symbolic application of Newton's algorithm to the Implicit Function Theorem and on a special, basis independent trace formula for affine Gorenstein algebras.</div>
</front>
</TEI>
<affiliations><list><country><li>Espagne</li>
<li>France</li>
</country>
<region><li>Cantabrie</li>
<li>Communauté forale de Navarre</li>
<li>Île-de-France</li>
</region>
<settlement><li>Palaiseau</li>
<li>Santander</li>
</settlement>
<orgName><li>Université de Cantabrie</li>
</orgName>
</list>
<tree><country name="France"><noRegion><name sortKey="Giusti, M" sort="Giusti, M" uniqKey="Giusti M" first="M." last="Giusti">M. Giusti</name>
</noRegion>
<name sortKey="Giusti, M" sort="Giusti, M" uniqKey="Giusti M" first="M." last="Giusti">M. Giusti</name>
</country>
<country name="Espagne"><region name="Cantabrie"><name sortKey="Heintz, J" sort="Heintz, J" uniqKey="Heintz J" first="J." last="Heintz">J. Heintz</name>
</region>
<name sortKey="H Gele, K" sort="H Gele, K" uniqKey="H Gele K" first="K." last="H Gele">K. H Gele</name>
<name sortKey="Monta A, J L" sort="Monta A, J L" uniqKey="Monta A J" first="J. L." last="Monta A">J. L. Monta A</name>
<name sortKey="Morais, J E" sort="Morais, J E" uniqKey="Morais J" first="J. E." last="Morais">J. E. Morais</name>
<name sortKey="Pardo, L M" sort="Pardo, L M" uniqKey="Pardo L" first="L. M." last="Pardo">L. M. Pardo</name>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Ticri/CIDE/explor/OcrV1/Data/France/Analysis

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000306 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/France/Analysis/biblio.hfd -nk 000306 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Ticri/CIDE
   |area=    OcrV1
   |flux=    France
   |étape=   Analysis
   |type=    RBID
   |clé=     ISTEX:E0BC2FAF7D2237578CD73E8A597435B1DE60CD3E
   |texte=   Lower bounds for diophantine approximations
}}

This area was generated with Dilib version V0.6.32.
Data generation: Sat Nov 11 16:53:45 2017. Site generation: Mon Mar 11 23:15:16 2024

	Serveur d'exploration sur l'OCR
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur l'OCR

Lower bounds for diophantine approximations

Lower bounds for diophantine approximations

Source :

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri