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1)  right greatest common divisor
右最大公因子
1.
Offers the concept of right greatest common divisor of two matrices over an Euclidean ring and expression,and considrs its some properties.
给出一个Euclid环上两个矩阵的右最大公因子的概念及其表示式 ,并讨论了其性质 。
2)  right greatest common divisor in row simplest form
行最简形右最大公因子
3)  greatest common divisor
最大公因子
1.
In this paper, the concepts of the least common multiple of polynomial matrices and the prime polynomial matrix are introduced, and some algebraic properties of the greatest common divisor and of the least common multiple of polynomial matrices are given.
讨论了多项式矩阵最大公因子与最小公倍的有关性质,同时给出了多项式矩阵的分解定理。
2.
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
3.
In this paper,an algorithm,which is called the extended Euclidean algorithm,is derived such that x and y can be simultaneously computed when the greatest common divisor ( a,b ) is computed by the Euclidean algorithm.
给出一种算法使得在用辗转互除计算最大公因子 (a,b)的同时能够计算出 x和 y来 。
4)  greatest common factor
最大公因子
1.
A united method for greatest common factor and least common multiple in euclidean ring;
欧氏环中最大公因子与最小公倍子的统一求法
2.
A new method to solve the greatest common factor of several polymerizations on polymerization ring is introduced.
介绍了一种P[x]上的多项式组最大公因子的求法 。
3.
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。
5)  maximal common factor
最大公因子
1.
A theorem for any A∈M 2Z (M 2Z is the ring of all integral 2×2 matrices) and any integer m and n , there are X, Y∈M 2Z such that A=X+Y and det X=m , det Y=n if and only if ( m-n ) is divisible by the maximal common factor of all elements of A is proved.
证明了一个定理:对任意的A∈M2Z(M2Z表示所有的2阶整数方阵组成的环)和任意的整数m和n,则存在X,Y∈M2Z,使A=X+Y且detX=m,detY=n的充分必要条件是矩阵A的所有元素的最大公因子能整除(m-n)。
6)  right common divisor
右公因子
补充资料:故右散骑常侍舒国公褚公挽词
【诗文】:
阳翟疏丰构,临平演庆源。学筵尊授几,儒服宠乘轩。
审谕留中密,开陈与上言。徂晖一不借,空有赐东园。



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【出处】:
全唐诗:卷73_43
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