“congruence relation”的概念、定义、翻译、参考文献-科学参考

congruence relation

Computer

1. An equivalence relation defined on the integers in the following manner. Let m be 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
$a \equiv b (modulo m)$
One of the most important uses of the congruence relation in computing is in generating random integers. A sequence
$s_{0}, s_{1}, s_{2}, \dots$
of integers between 0 and (m–1) inclusive can be generated by the relation
$s_{n + 1} \equiv a s_{n} + c (modulo m)$
The values of a, c, and m must be suitably chosen.
2. An equivalence relation R (defined on a set S on which a dyadic operation ° is defined) with the property that whenever
$\begin{array}{l} x R u and y R v \\ then (x ° y) R (u ° v) \end{array}$
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.

单词	congruence relation
释义	congruence relation Computer 1. An equivalence relation defined on the integers in the following manner. Let m be 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 $a \equiv b (modulo m)$ One of the most important uses of the congruence relation in computing is in generating random integers. A sequence $s_{0}, s_{1}, s_{2}, \dots$ of integers between 0 and (m–1) inclusive can be generated by the relation $s_{n + 1} \equiv a s_{n} + c (modulo m)$ The values of a, c, and m must be suitably chosen. 2. An equivalence relation R (defined on a set S on which a dyadic operation ° is defined) with the property that whenever $\begin{array}{l} x R u and y R v \\ then (x ° y) R (u ° v) \end{array}$ 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.
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