Using resultants for SAGBI basis verification in the univariate polynomial ring

Summary, in English

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.

• Author: Anna Torstensson; Victor Ufnarovski; Hans Öfverbeck
• Department/s: Mathematics (Faculty of Engineering); Mathematics (Faculty of Sciences); Algebra
• Publishing year: 2005
• Language: English
• Pages: 1087-1105
• Publication/Series: Journal of Symbolic Computation
• Volume: 40
• Issue: 3
• Links: http://dx.doi.org/10.1016/j.jsc.2004.06.002
• Document type: Journal article
• Publisher: Elsevier
• Topic: Mathematics
• Keywords: subalgebra; reduction; SAGBI basis; resultant; univariate polynomial; ring
• Status: Published
• Research group: Algebra
• ISBN/ISSN/Other: ISSN: 0747-7171