论文标题
有效地计算加权最大的常见除数
Computing efficiently the weighted greatest common divisor
论文作者
论文摘要
在本文中，我们提供了一些加权最大的常见分隔线的基本属性，并讨论如何加快计算加权最大的常见除数的速度。通过订购“权重”，我们可以将操作显着缩短到计算WGCD。如果没有通过订购权重来计算WGCD的有效算法，并使用$ \ gcd $，我们大大减少了要计算WGCD的数字。作为本文的最终结果，我们证明：如果$ \ Mathbf {x} =（x_ {0}，\ dots，x_ {n}）\ in \ in \ Mathbb {z}^{n+1} $，带权衡$ q_ {0} \ leq \ cdots \ leq q_ {n} $，然后$ {\ rm wgcd} _W（\ Mathbf {x}）= {\ rm wgcd} \ gcd（x_i，\ dots，x_n）$和$ y_0 \ leq y_1 \ leq \ dots \ leq y_n $。
In this paper we included some basic properties for weighted greatest common divisors, and discuss how to speed up computing the weighted greatest common divisor. By ordering the 'weights' we are able to significantly shorten the operations to computing wgcd. In the absence of an efficient algorithm for computing wgcd by ordering the weights, and using $\gcd$, we significantly reduce the numbers for which we want to compute wgcd. As a final result in this paper we prove that: If $\mathbf{x} = (x_{0},\dots ,x_{n})\in \mathbb{Z}^{n+1}$, with weights $\mathfrak{w}=(q_{0},\dots ,q_{n})$ and $q_{0}\leq \cdots \leq q_{n}$, then ${\rm wgcd}_w(\mathbf{x}) = {\rm wgcd}_w(y_0,y_1,\dots,y_n)$, where $y_i = \gcd(x_i,\dots,x_n)$, and $y_0\leq y_1 \leq\dots \leq y_n$.
