英和和英

発音

• IPA^(key): /ˌɪɹɪˈdjuːsɪbəl/

形容詞

irreducible (comparative more irreducible, superlative most irreducible)

1. Not able to be reduced or lessened.
   • 1948 January and February, Cecil J. Allen, “British Locomotive Practice and Performance”, in Railway Magazine, page 48:

     With each reduction in the number of railways, there must come, eventually, a decline in interest, if only through reduction in variety; and when it comes to one nationalised railway only we have reached the irreducible minimum.

   Antonym: unincreasable

2. Not able to be brought to a simpler or reduced form.
3. (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
4. (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
5. (number theory, of an integer) Unable to be factored into smaller integers; prime.
6. (algebra, of an element of a ring) that its only divisors are units and associates.
7. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
8. (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.

反意語

• reducible

派生語

名詞

irreducible (複数形 irreducibles)

1. (mathematics) Such a polynomial