Encoding algebraic power series

Herwig Hauser; Mariemi E. Alonso; Francisco J. Castro-Jiménez

doi:10.1007/s10208-017-9354-z

Encoding algebraic power series

Herwig Hauser, Mariemi E. Alonso, Francisco J. Castro-Jiménez

Institut für Mathematik

Veröffentlichungen: Beitrag in Fachzeitschrift › Artikel › Peer Reviewed

Abstract

The division algorithm for ideals of algebraic power series satisfying Hironaka's box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series. In particular, the codes of the reduced standard basis of the ideal can be constructed effectively.

Originalsprache	Englisch
Seiten (von - bis)	789–833
Seitenumfang	45
Fachzeitschrift	Foundations of Computational Mathematics
Jahrgang	18
Ausgabenummer	3
Frühes Online-Datum	2017
DOIs	https://doi.org/10.1007/s10208-017-9354-z
Publikationsstatus	Veröffentlicht - Juni 2018

ÖFOS 2012

101001 Algebra
101005 Computeralgebra
101009 Geometrie
101008 Funktionentheorie

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10.1007/s10208-017-9354-z

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Zitationsweisen

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abstract = "The division algorithm for ideals of algebraic power series satisfying Hironaka's box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series. In particular, the codes of the reduced standard basis of the ideal can be constructed effectively.",

keywords = "ALGORITHM, Algebraic power series, COMBINATORIAL DECOMPOSITIONS, EQUATIONS, GENERAL NERON DESINGULARIZATION, Grbner and standard bases, Henselization, INVOLUTIVE BASES, Polynomial codes, Power series division, QUADRANT, QUARTER PLANE, RESOLUTION, SINGULARITIES, WALKS, Gr{\"o}bner and standard bases",

author = "Herwig Hauser and Alonso, {Mariemi E.} and Castro-Jim{\'e}nez, {Francisco J.}",

note = "Publisher Copyright: {\textcopyright} 2017, SFoCM.",

year = "2018",

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doi = "10.1007/s10208-017-9354-z",

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AU - Castro-Jiménez, Francisco J.

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KW - COMBINATORIAL DECOMPOSITIONS

KW - EQUATIONS

KW - GENERAL NERON DESINGULARIZATION

KW - Grbner and standard bases

KW - Henselization

KW - INVOLUTIVE BASES

KW - Polynomial codes

KW - Power series division

KW - QUADRANT

KW - QUARTER PLANE

KW - RESOLUTION

KW - SINGULARITIES

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