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In this paper, we present a parametric $F_{4}$ algorithm (so-
called P$F_{4}$) which can be considered as a generalization of Faugere's
F4 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 P$F_{4}$
algorithm takes as input a parametric polynomial ideal and two monomial
orderings on the variables and the parameters and returns a Grobner
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].
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