irreducible background

irreducible

/ˌɪɹɪˈdjuːsɪbəl/

Illustration irreducible - Image 1

noun

既約多項式

Such a polynomial

Examples :

"In her algebra class, Maria learned that an irreducible is a polynomial that cannot be factored into simpler polynomials over a specified field, like the real numbers. "

マリアは代数学の授業で、既約多項式とは、実数などの指定された体上で、より単純な多項式に因数分解できない多項式であることを学びました。

Illustration irreducible - Image 1

adjective

還元できない、不可分の

Not able to be reduced or lessened.

Examples :

"The doctor said the swelling was caused by an irreducible fracture, meaning they couldn't fix it without surgery. "

医者は、腫れは不可分の骨折によって引き起こされたと言い、それは手術なしでは治せないという意味だった。

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Illustration irreducible - Image 1

adjective

還元できない, 既約の

Not able to be brought to a simpler or reduced form.

Examples :

"The conflict between them had reached an irreducible point; they simply couldn't agree on anything anymore. "

彼らの間の対立は既約点に達し、もはや何も合意することができなかった。

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Illustration irreducible - Image 1

adjective

既約の

(of a polynomial) Unable to be factorized into polynomials of lower degree, as (x2 + 1).

Examples :

"In algebra class, the teacher explained that the polynomial x² + 4 is irreducible over real numbers because it cannot be broken down into simpler polynomial factors with real number coefficients. "

代数の授業で、教師は、多項式x² + 4は、実数係数を持つより単純な多項式因子に分解できないため、実数上で既約であると説明しました。

Illustration irreducible - Image 1

adjective

約分できない

(of a fraction) Whose numerator and denominator share no common factor greater than 1.

Examples :

"The fraction 3/5 is irreducible because 3 and 5 have no common factors other than 1. "

分数3/5は、3と5が1以外の共通の約数を持たないため、約分できません。

Illustration irreducible - Image 1

adjective

既約の, 素数の

(of an integer) Unable to be factored into smaller integers; prime.

Examples :

"The number 7 is irreducible because it can only be divided evenly by 1 and itself. "

7は1と自分自身でしか割り切れないため、既約です。

Illustration irreducible - Image 1

adjective

既約の

(of an element of a ring) that its only divisors are units and associates.

Examples :

"In the world of number theory, the number 7 is considered irreducible because its only factors are 1, -1, 7, and -7 (which are either units or associates of 7). "

数論の世界では、7の約数は1、-1、7、-7のみであるため（これらは単位元または7の関連元である）、7は既約とみなされます。

Illustration irreducible - Image 1

adjective

既約の

(of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.

Examples :

"Because it cannot be simplified further without losing its essential characteristics, the geometric object was described by the mathematician as irreducible. "

本質的な特性を失うことなく、これ以上単純化できないため、数学者はその幾何学的対象を既約であると説明した。

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Illustration irreducible - Image 1

adjective

既約の

(of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.

Examples :

"The complex concept of teamwork, while appearing multifaceted, can be broken down to the irreducible element of individual accountability. "

多面的なように見えても、チームワークという複雑な概念は、個人の説明責任という既約要素に分解できる。

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