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Paper   IPM / M / 17694
School of Mathematics
  Title:   A parametric $F_{4}$ algorithm
1.  Mahdi Dehghani Darmian
2.  Amir Hashemi
  Status:   Published
  Journal: IJMSI
  Vol.:  19
  Year:  2024
  Pages:   117-133
  Supported by:  IPM
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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