Practical Divide-and-Conquer Algorithms for Polynomial Arithmetic

被引：8

作者：

Hart, William ^{[1
]}

Novocin, Andrew ^{[2
]}

机构：

[1] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

[2] LIP, INRIA, ENS, F-69364 Lyon 07, France

来源：

COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING | 2011年 / 6885卷

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1007/978-3-642-23568-9_16

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We investigate two practical divide-and-conquer style algorithms for univariate polynomial arithmetic. First we revisit an algorithm originally described by Brent and Kung for composition of power series, showing that it can be applied practically to composition of polynomials in Z[x] given in the standard monomial basis. We offer a complexity analysis, showing that it is asymptotically fast, avoiding coefficient explosion in Z[x]. Secondly we provide an improvement to Mulders' polynomial division algorithm. We show that it is particularly efficient compared with the multimodular algorithm. The algorithms are straightforward to implement and available in the open source FLINT C library. We offer a practical comparison of our implementations with various computer algebra systems.

引用

页码：200 / +

页数：3

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