irreducible background

irreducible

/ˌɪɹɪˈdjuːsɪbəl/

Illustration irreducible - Image 1

noun

不可约多项式, 素多项式

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. "

在玛丽亚的代数课上，她学到不可约多项式（素多项式）是一种不能在特定域（例如实数域）上分解成更简单多项式的多项式。

Illustration irreducible - Image 1

adjective

不可约的，不能简化的

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. "

医生说肿胀是由一个不可复位性骨折引起的，意思是说不通过手术是无法让骨头恢复原位的。

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Illustration irreducible - Image 1

adjective

不可简化的，不能约分的

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. "

他们之间的冲突已经到了一个不可简化的地步，他们简直无法再达成任何共识了。

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Illustration irreducible - Image 1

adjective

不可约的，不能分解的

(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. "

在代数课上，老师解释说，多项式 x² + 4 在实数范围内是不可约的，因为它不能被分解成系数为实数的更简单的多项式因子。

Illustration irreducible - Image 1

adjective

最简的，既约的

(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是最简的，因为3和5除了1以外没有其他的公约数。

Illustration irreducible - Image 1

adjective

不可约的，素数的.

(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. "

数字7是不可约的，因为它只能被1和它本身整除，也就是一个素数。

Illustration irreducible - Image 1

adjective

不可约的，既约的

(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). "

在数论的世界里，数字7被认为是不可约的，因为它唯一的因子是1、-1、7和-7（这些因子要么是单位，要么是7的相伴数）。

Illustration irreducible - Image 1

adjective

不可约的, 不能简化的

(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. "

由于它无法在不失去其本质特征的前提下进一步简化，这位数学家将这个几何体描述为不可约的。

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Illustration irreducible - Image 1

adjective

不可约的，不能简化的

(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. "

团队合作这个复杂的概念，虽然看起来有很多方面，但可以分解到最根本的、不可约的要素：个人责任。

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