irreducible

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English[edit]

Etymology[edit]

ir- +‎ reducible

Pronunciation[edit]

  • IPA(key): /ˌɪrɪˈdjuːsɪbəl/

Adjective[edit]

irreducible (comparative more irreducible, superlative most irreducible)

  1. Not able to be reduced or lessened.
  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 (x^2 + 1).
  4. (mathematics, of an integer) Unable to be factored into smaller integers; prime.
  5. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
  6. (group theory, of a representation) impossible to divide further into representations of lower dimension by means of any similarity transformation

Antonyms[edit]

Derived terms[edit]

Noun[edit]

irreducible (plural irreducibles)

  1. (mathematics) Such a polynomial