A Parametric F₄ Algorithm

In this paper, we present a parametric F 4 algorithm (socalled PF 4 ) which can be considered as a generalization of Faugère's F 4 algorithm [8] to polynomial ideals with parametric coefficients.Our approach is based on the F 4 algorithm, Montes DisPGB algorithm [21] and the parametric linear algebra method developed in [6].The PF 4 algorithm takes as input a parametric polynomial ideal and two monomial orderings on the variables and the parameters and returns a Gröbner system of the ideal with respect to a compatible elimination product of the given monomial orderings.We have implemented our new algorithm in Maple and give timings to compare its performance with those of (our implementation) of the Kapur et al. algorithm [16] and the DisPGB algorithm [21].