一种计算截断结果的快速算法

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation Pub Date : 2016-07-20 DOI:10.1145/2930889.2930931

G. Moroz, É. Schost

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引用次数: 11

摘要

设P和Q是K[x,y]中阶不超过d的两个多项式，其中K是一个域。用R∈K[x]表示P和Q关于y的结果，我们给出了在K的O~(kd)算术运算中计算R mod xk的算法，其中的~O符号表示我们省略了多对数因子。这是对最先进的算法的改进，这些算法需要在计算前k个系数之前在O~(d3)次操作中计算R。

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A Fast Algorithm for Computing the Truncated Resultant

Let P and Q be two polynomials in K[x,y] with degree at most d, where K is a field. Denoting by R ∈ K[x] the resultant of P and Q with respect to y, we present an algorithm to compute R mod xk in O~(kd) arithmetic operations in K, where the ~O notation indicates that we omit polylogarithmic factors. This is an improvement over state-of-the-art algorithms that require to compute R in O~(d3) operations before computing its first k coefficients.

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Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation

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