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A New Algorithm for Discussing Gröbner Bases with Parameters

✍ Scribed by Antonio Montes

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 372 KB
Volume: 33
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.2001.0504

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✦ Synopsis

Let F be a set of polynomials in the variables x = x 1 , . . . , xn with coefficients in R[a], where R is a UFD and a = a 1 , . . . , am a set of parameters. In this paper we present a new algorithm for discussing Gröbner bases with parameters. The algorithm obtains all the cases over the parameters leading to different reduced Gröbner basis, when the parameters in F are substituted in an extension field K of R. This new algorithm improves Weispfenning's comprehensive Gröbner basis CGB algorithm, obtaining a reduced complete set of compatible and disjoint cases. A final improvement determines the minimal singular variety outside of which the Gröbner basis of the generic case specializes properly. These constructive methods provide a very satisfactory discussion and rich geometrical interpretation in the applications.

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