Elsevier

Journal of Symbolic Computation

Volume 40, Issue 3, September 2005, Pages 1087-1105
Journal of Symbolic Computation

Using resultants for SAGBI basis verification in the univariate polynomial ring

https://doi.org/10.1016/j.jsc.2004.06.002Get rights and content
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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.

MSC

12Y05
68W30
13P99

Keywords

SAGBI basis
Resultant
Reduction
Subalgebra
Univariate polynomial ring

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