Abdolali Basiri

Publications

3 Some Applications of Gröbner bases

Authors: Hassan Noori, Abdolali Basiri, Sajjad Rahmany

Abstract:

In this paper we will introduce a brief introduction to theory of Gr¨obner bases and some applications of Gr¨obner bases to graph coloring problem, automatic geometric theorem proving and cryptography.

Keywords: Cryptography, Graph Coloring, Gr¨obner bases, Application of Gr¨obner bases, Automatic Geometric Theorem Proving

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2 Computing SAGB-Gröbner Basis of Ideals of Invariant Rings by Using Gaussian Elimination

Authors: Abdolali Basiri, Sajjad Rahmany

Abstract:

The link between Gröbner basis and linear algebra was described by Lazard [4,5] where he realized the Gr┬¿obner 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.

Keywords: Reduction, Grobner basis, SAGBI- Gröbner basis, Invariant ring, permutation groups

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1 A New Method for Computing the Inverse Ideal in a Coordinate Ring

Authors: Abdolali Basiri

Abstract:

In this paper we present an efficient method for inverting an ideal in the ideal class group of a Cab curve by extending the method which is presented in [3]. More precisely we introduce a useful generator for the inverse ideal as a K[X]-module.

Keywords: Cab Curves, Ideal Class Group

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