English Dictionary

Euclidean algorithm

名詞

歴史的

(historical) Any of certain algorithms first described in Euclid's Elements.

日本語の意味

ユークリッドの『原論』で初めて記載されたアルゴリズムの総称。特に、2つの整数の最大公約数を求める互除法を指すことが多い。

Scholars debated whether the Euclidean algorithm referred to a single method or a family of procedures in antiquity.

学者たちは、ユークリッド『原論』に記述された算法が古代において単一の方法を指すのか、それとも一連の手続き群を指すのかを議論した。

意味（1）

(historical) Any of certain algorithms first described in Euclid's Elements.

The Euclidean algorithms for finding a compound ratio also allowed a ratio and an inverse ratio, and more than two ratios to be compounded, since each compounded pair is equivalent to a single ratio between lines.

意味（2）

(arithmetic, number theory) Specifically, a method, based on a division algorithm, for finding the greatest common divisor (gcd) of two given integers; any of certain variations or generalisations of said method.

In a quadratic field Q (√), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known. We prove that for D<-19 even remainder sequences with possibly nondecreasing norms cannot determine the GCD of arbitrary inputs.

Euclidean algorithms （ plural ）