TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 19
IS - 1
PY - 2024
Y1 - 2024/4/01
TI - A Parametric $ F_4 $ Algorithm
TT -
N2 - In this paper, we present a parametric F4 algorithm (socalled PF4) which can be considered as a generalization of Faugére’s F4 algorithm [8] to polynomial ideals with parametric coefficients. Our approach is based on the F4 algorithm, Montes DisPGB algorithm [21] and the parametric linear algebra method developed in [6]. The PF4 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].
SP - 117
EP - 133
AU - Dehghani Darmain, Mahdi
AU - Hashemi, Amir
AD - Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran
KW - Gröbner bases
KW - Gröbner systems
KW - F4 algorithm
KW - PF4 algorithm
KW - PGBMain algorithm
KW - DisPGB algorithm.
UR - http://ijmsi.ir/article-1-1718-en.html
DO - 10.61186/ijmsi.19.1.117
ER -