最大公因子

Greatest Common Divisor is one of the basic subjects in computational number theory, it has a wide application in encryption and analysis of cryptography.

摘要最大公因子计算是计算数论的基础课题之1，它在密码算法和密码分析中有着非常广泛的应用。

Firstly, this thesis introduce the related concepts of the algorithm and some GCD algorithms that current existing, then list a few basic properties of Greatest Common Divisor.

本文首先介绍了算法的相关概念和当前现有的GCD算法，然后列出了最大公因子的几个基本性质。

This work gives an algorithm to simplify the rational curves in this situation. After the approximate proper index is defined, it is computed by solving the semi-algebra system. The greatest common divisor is obtained according to the computing process of approximate proper index.

为此，讨论了这类有误差的有理参数曲线，定义了近似非恰当参数形式和近似非恰当指数，并通过半代数系统计算近似非恰当指数；在给出近似非恰当指数的同时，得到近似最大公因子。

Based on a formal analysis of lifting decomposition, the hierarchical structure concept of the decomposition set, as well as the lifting decomposition technique of the polyphase matrix' greatest mth-order common divisor, is proposed to conquer the difficulties in the practical computation of and the optimal search in the huge decomposition set.

本文在形式化分析Lifting分解原理的基础上，提出了分解集合的分级结构概念以及多相矩阵的m阶最大公因子Lifling分解技术，克服了分解集合求解问题的高复杂性所带来的实际计算与搜索困难；进一步地，从数值稳定性及计算代价两方面研究了分解的评价问题，设计出两种实用的分解稳定性准则；最后，结合分级结构技术提出一种最优分解算法。

The modular inverse operation by extended Euclidean algorithm and the binary extended Euclidean algorithm are analyzed, and the improved modular inverse operation by binary extended Euclidean algorithm is presented in this paper.

基于现有的求最大公因子的方法，分析利用扩展欧几里德求模逆的方法，以及二进制扩展欧几里德算法，提出了利用二进制扩展欧几里德算法求模逆的方法，给出了几种算法性能比较的测试环境和测试结果。

This paper gives a method that through elementary transformming the row of the matrix , the greatest common factor of the Euclidean Ring＇s factors can be found.

给出了利用矩阵的初等行变换求欧氏环中多个元素的最大公因子的方法。

The algorithms of basic operations for large integer,addition,subtraction and comparison,are presented based on mixed radix representation,the algorithms of multiplication,division, modulo ,and greatest common divisor are conveyed from addition machins.

将大数采用混合基表示，对大数的加法、减法与比较运算给出相应的算法，并对加法机器上的乘法、除法、模运算以及求最大公因子的算法进行了移

Highest common factor H.C.F.

最高公因式，最高公因子，最大公因数

The primary theory of numbers aspect related integer property basic content.

摘要本论文主要讨论了整数的离散性、代数性质、有序性、整除性、最大公因数与最小公倍数、素因子分解、同余等初等数论方面的有关整数性质的基本内容。

In this paper, we introduce the concepts of the great common P-divisor, least common P-multiple of two distinct nonzero elements x, y in arbitrary unique factorization domain R, and denote them byp, and p respectively.

在本文中，作为通常的整数环Z上的最大公因子和最小公倍数的推广，我们在惟一分解整环R上定义了最大公P-因子和最小公P-倍元，分别记为_P和_P。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。