A new algorithm for discussing Gröbner bases with parameters

  • Authors:

  • Antonio Montes

  • Affiliations:

  • Univ. Politécnica de Catalunya, Spain

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2002

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Abstract

Let F be a set of polynomials in the variables __ x=x1, . . . , xnwith coefficients in R [__ a ], where R is a UFD and __ a=a1, . . . , ama set of parameters. In this paper we present a new algorithm for discussing Grbner bases with parameters. The algorithm obtains all the cases over the parameters leading to different reduced Grbner basis, when the parameters in F are substituted in an extension field K of R. This new algorithm improves Weispfenning's comprehensive Grbner 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 Grbner basis of the generic case specializes properly. These constructive methods provide a very satisfactory discussion and rich geometrical interpretation in the applications. Copyright 2002 Academic Press