A new algorithm for discussing Grobner bases with parameters

摘要

Let F be a set of polynomials in the variables x = x_1, ..., x_n with coefficients in R[a], where R is a UFD and a = a_1, ..., a_m a set of parameters. In this paper we Present a new algorithm for discussing Grobner bases with parameters. The algorithm Obtains all the cases over the parameters leading to different reduced Grobner basis, When the parameters in F are substituted in an extension field K of R. This new algo- Rithm improves Weispfenning's comprehensive Grobner basis CGB algorithm, obtaining A reduced complete set of compatible and disjoint cases.