| 术语 | congruence relation |
| 释义 | congruence relation 同余关系,全等关系 1. An equivalence relation defined on the integers in the following manner. Letmbe some given but fixed positive integer and let a and b be arbitrary integers. Then a is congruent to b modulo m if and only if (a-b) is divisible by m. It is customary to write this as a≡b (modulo m).One of the most important uses of the congruence relation in computing is in generating random integers. A sequence S&-{0},S&-{1},S&-{2},… of integers between 0 and (m-1) inclusive can be generated by the relation S&-{n+1}≡aS&-{n}+c(modulo m). The values of a, c and m must be suitably chosen. 一种以下列方式定义在整数集合上的等价关系:设m为某一给定但是固定的正整数,a和b 为任意整数,当且仅当a-b之差能被m除尽时,则a和b按模m同余,记为a≡b(modulo m)。 在计算机技术中,同余关系最重要的应用之一是产生随机整数。一个介于0和m-1,包括 m-1在内的整数序列S&-{0},S&-{1},S&-{2},…可由S&-{n+1}≡aS&-{n}+c(modulo m)关系产生。 a,c和m的值必须适当加以选择。 2. An equivalence relation R (defined on a set S on which a dyadic operation o is defined) with the property that whenever x R u and y R v, then (x o y) R (u o v). This is often referred to as the substitution property. Congruence relations can be defined for such algebraic structures as certain kinds of algebras, automata, groups, monoids, and for the integers, the latter is the congruence modulo m of def. 1. 一种具有下列性质的等价关系R(R定义在集合S上,在该集合S上定义了一种二元操作)。每当x R u和y R v,则有(x o y)R(u o v)。这通常称之为置换性。 可为像某类代数学、自动机、群、独异点那样的代数结构,也可为整数定义同余关系,而后者就是1.中的按模m定义的同余关系。 |
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