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In this paper, we propose an efficient method to solve polynomial systems whose equations are left invariant by the action of a finite group G. The idea is to simultaneously compute a truncated SAGBI-Gr¨obner bases (a generalisation of Gr¨obner bases to ideals of subalgebras of polynomial ring) and a Gr¨obner basis in the invariant ring… (More)
—The link between Gröbner basis and linear algebra was described by Lazard [4,5] where he realized the Gröbner basis computation could be archived by applying Gaussian elimination over Macaulay's matrix. In this paper, we indicate how same technique may be used to SAGBI-Gröbner basis computations in invariant rings.
There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new elimination method to solve and analyse interval polynomial systems, in general case. This method is based on… (More)
—The aim of this paper is to review some of standard fact on Miura curves. We give some easy theorem in number theory to define Miura curves, then we present a new implementation of Arita algorithm for Miura curves.