منابع مشابه
Greatest common divisor
In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), highest common factor (hcf), or greatest commonmeasure (gcm), of two or more integers (when at least one of them is not zero), is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.[1][2] This notion can be extended to polynomials, see ...
متن کاملEuclid’s Algorithm for the Greatest Common Divisor
People have been using numbers, and operations on them like division, for a very long time for practical purposes like dividing up the money left by parents for children, or distributing ears of corn equally to groups of people, and more generally to conduct all sorts of business dealings. It may be a bit of a surprise that things like calculating divisors of numbers also form the core of today...
متن کاملThe complexity of greatest common divisor computations
We study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers. We prove the NP-completeness of finding an optimal set of multipliers with respect to either the L0 metric or the L∞ norm. We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give an upper bound on the size of the lar...
متن کاملMultidimensional Greatest Common Divisor and Lehmer Algorithms
A class of multidimensional greatest common divisor algorithms is studied. Their connection with the Jacobi algorithm is established and used to obtain theoretical properties such as the existence of digit frequencies. A technique of D. H. Lehmer's for Euclid's algorithm is generalized for efficient computation of the multidimensional algorithms. For triples of integers, two algorithms of inter...
متن کاملBarnett's Theorems About the Greatest Common Divisor of Several Univariate Polynomials Through Bezout-like Matrices
This article provides a new presentation of Barnett’s theorems giving the degree (resp. coefficients) of the greatest common divisor of several univariate polynomials with coefficients in an integral domain by means of the rank (resp. linear dependencies of the columns) of several Bezout-like matrices. This new presentation uses Bezout or hybrid Bezout matrices instead of polynomials evaluated ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1989
ISSN: 0024-3795
DOI: 10.1016/0024-3795(89)90572-7