Welcome to the resource topic for 2009/151
Title:
Euclid’s Algorithm, Guass’ Elimination and Buchberger’s Algorithm
Authors: Shaohua Zhang
Abstract:It is known that Euclid’s algorithm, Guass’ elimination and Buchberger’s algorithm play important roles in algorithmic number theory, symbolic computation and cryptography, and even in science and engineering. The aim of this paper is to reveal again the relations of these three algorithms, and, simplify Buchberger’s algorithm without using multivariate division algorithm. We obtain an algorithm for computing the greatest common divisor of several positive integers, which can be regarded as the generalization of Euclid’s algorithm. This enables us to re-find the Guass’ elimination and further simplify Buchberger’s algorithm for computing Gröbner bases of polynomial ideals in modern Computational Algebraic Geometry.
ePrint: https://eprint.iacr.org/2009/151
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