Using resultants for SAGBI basis verification in the univariate polynomial ring

Anna Torstensson; Victor Ufnarovski; Hans Öfverbeck

doi:10.1016/j.jsc.2004.06.002

Using resultants for SAGBI basis verification in the univariate polynomial ring

Anna Torstensson, Victor Ufnarovski, Hans Öfverbeck

Research output: Contribution to journal › Article › peer-review

Abstract

A resultant-type identity for univariate polynomials is proved and used to characterise SAGBI bases of subalgebras generated by two polynomials. A new equivalent condition, expressed in terms of the degree of a field extension, for a pair of univariate polynomials to form a SAGBI basis is derived.

Original language	English
Pages (from-to)	1087-1105
Journal	Journal of Symbolic Computation
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/j.jsc.2004.06.002
Publication status	Published - 2005

Subject classification (UKÄ)

Mathematics

Free keywords

subalgebra
reduction
SAGBI basis
resultant
univariate polynomial
ring

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10.1016/j.jsc.2004.06.002

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@article{1ecfe20acc044661bd7f030f0409d16a,

title = "Using resultants for SAGBI basis verification in the univariate polynomial ring",

abstract = "A resultant-type identity for univariate polynomials is proved and used to characterise SAGBI bases of subalgebras generated by two polynomials. A new equivalent condition, expressed in terms of the degree of a field extension, for a pair of univariate polynomials to form a SAGBI basis is derived.",

keywords = "subalgebra, reduction, SAGBI basis, resultant, univariate polynomial, ring",

author = "Anna Torstensson and Victor Ufnarovski and Hans {\"O}fverbeck",

year = "2005",

doi = "10.1016/j.jsc.2004.06.002",

language = "English",

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journal = "Journal of Symbolic Computation",

issn = "0747-7171",

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TY - JOUR

T1 - Using resultants for SAGBI basis verification in the univariate polynomial ring

AU - Torstensson, Anna

AU - Ufnarovski, Victor

AU - Öfverbeck, Hans

PY - 2005

Y1 - 2005

N2 - A resultant-type identity for univariate polynomials is proved and used to characterise SAGBI bases of subalgebras generated by two polynomials. A new equivalent condition, expressed in terms of the degree of a field extension, for a pair of univariate polynomials to form a SAGBI basis is derived.

AB - A resultant-type identity for univariate polynomials is proved and used to characterise SAGBI bases of subalgebras generated by two polynomials. A new equivalent condition, expressed in terms of the degree of a field extension, for a pair of univariate polynomials to form a SAGBI basis is derived.

KW - subalgebra

KW - reduction

KW - SAGBI basis

KW - resultant

KW - univariate polynomial

KW - ring

U2 - 10.1016/j.jsc.2004.06.002

DO - 10.1016/j.jsc.2004.06.002

M3 - Article

SN - 0747-7171

VL - 40

SP - 1087

EP - 1105

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - 3

ER -

Using resultants for SAGBI basis verification in the univariate polynomial ring

Abstract

Subject classification (UKÄ)

Free keywords

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