“modular arithmetic”的概念、定义、翻译、参考文献-科学参考

modular arithmetic

Mathematics

See modulo N arithmetic.

Computer

Arithmetic based on the concept of the congruence relation defined on the integers and used in computing to circumvent the problem of performing arithmetic on very large numbers.
Let m₁, m₂,…, m_k be integers, no two of which have a common factor greater than one. Given a large positive integer n it is possible to compute the remainders or residues r₁, r₂,…, r_k such that
$\begin{array}{l} n \equiv r_{1} (mod m_{1}) \\ n \equiv r_{2} (mod m_{2}) \\ \dots \\ n \equiv r_{k} (mod m_{k}) \end{array}$
Provided n is less than
$m_{1} \times m_{2} \times \dots \times m_{k}$
n can be represented by
$(r_{1}, r_{2}, \dots, r_{k})$
This can be regarded as an internal representation of n. Addition, subtraction, and multiplication of two large numbers then involves the addition, subtraction, and multiplication of corresponding pairs, e.g.
$\begin{array}{l} (r_{1}, \dots, r_{k}) + (s_{1}, \dots, s_{k}) = \\ (r_{1} + s_{1}, \dots, r_{k} + s_{k}) \end{array}$
Determining the sign of an integer or comparing relative magnitudes are less straightforward.

单词	modular arithmetic
释义	modular arithmetic Mathematics See modulo N arithmetic. Computer Arithmetic based on the concept of the congruence relation defined on the integers and used in computing to circumvent the problem of performing arithmetic on very large numbers. Let m₁, m₂,…, m_k be integers, no two of which have a common factor greater than one. Given a large positive integer n it is possible to compute the remainders or residues r₁, r₂,…, r_k such that $\begin{array}{l} n \equiv r_{1} (mod m_{1}) \\ n \equiv r_{2} (mod m_{2}) \\ \dots \\ n \equiv r_{k} (mod m_{k}) \end{array}$ Provided n is less than $m_{1} \times m_{2} \times \dots \times m_{k}$ n can be represented by $(r_{1}, r_{2}, \dots, r_{k})$ This can be regarded as an internal representation of n. Addition, subtraction, and multiplication of two large numbers then involves the addition, subtraction, and multiplication of corresponding pairs, e.g. $\begin{array}{l} (r_{1}, \dots, r_{k}) + (s_{1}, \dots, s_{k}) = \\ (r_{1} + s_{1}, \dots, r_{k} + s_{k}) \end{array}$ Determining the sign of an integer or comparing relative magnitudes are less straightforward.
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