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Journals and Conferences
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)
In this paper we will introduce a brief introduction to theory of Gröbner bases and some applications of Gröbner bases to graph coloring problem, automatic geometric theorem proving and cryptography. Keywords—Gröbner bases, Application of Gröbner bases, Automatic Geometric Theorem Proving, Graph Coloring, Cryptography.
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 SAGBIGröbner basis computations in invariant rings. . Keywords— Gröbner basis, SAGBIGröbner… (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. Keywords—Miura curve, discrete logarithm problem, algebraic curve cryptography, Jacobian group.