en عمومى General پژوهشي Research paper <p dir="rtl">&rlm;&lrm;<br> <span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:Calibri,sans-serif"><span lang="FA" dir="RTL" style="font-family:"Arial",sans-serif"></span></span></span></span></p> <p dir="rtl"></p> <div style="text-align: justify;">In this paper, we present a parametric F₄ algorithm (socalled PF₄) which can be considered as a generalization of Faug&eacute;re&rsquo;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 PF_4&nbsp;algorithm takes as input a parametric polynomial ideal and two monomial orderings on the variables and the parameters and returns a Gr&ouml;bner 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].</div> Gröbner bases, Gröbner systems, F4 algorithm, PF4 algorithm, PGBMain algorithm, DisPGB algorithm. 117 133 http://ijmsi.ir/browse.php?a_code=A-10-5225-1&slc_lang=en&sid=1 Mahdi Dehghani Darmain m.dehghanidarmian@gmail.com 100319475328460010645 100319475328460010645 Yes Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran Amir Hashemi amir.hashemi@ipm.ir 100319475328460010646 100319475328460010646 No Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran