快速计算gcd

Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI:10.1145/800125.804045

R. Moenck

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引用次数: 102

摘要

基于Schönhage的整数最大公约数算法推广到所有具有快速乘法算法的欧几里得域。结果表明，如果两个精度为N的元素可以在O(N logn)内相乘，则它们的GCD可以在O(N loga+1 N)内计算出来。因此，可以推导出一种新的更快的多元多项式GCD算法，并使用该算法对有理函数进行处理。

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Fast computation of GCDs

An integer greatest common divisor (GCD) algorithm due to Schönhage is generalized to hold in all euclidean domains which possess a fast multiplication algorithm. It is shown that if two N precision elements can be multiplied in O(N loga N), then their GCD can be computed in O(N loga+1 N). As a consequence, a new faster algorithm for multivariate polynomial GCD's can be derived and with that new bounds for rational function manipulation.

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来源期刊

Proceedings of the fifth annual ACM symposium on Theory of computing

CiteScore

7.80

自引率

0.00%

发文量