Background for irreducible

irreducible

/ˌɪɹɪˈdjuːsɪbəl/

Illustration irreducible - Image 1

noun

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. "

Illustration irreducible - Image 1

adjective

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. "

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Illustration irreducible - Image 1

adjective

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. "

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Illustration irreducible - Image 1

adjective

(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. "

Illustration irreducible - Image 1

adjective

(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. "

Illustration irreducible - Image 1

adjective

(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. "

Illustration irreducible - Image 1

adjective

(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). "

Illustration irreducible - Image 1

adjective

(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. "

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Illustration irreducible - Image 1

adjective

(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. "

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