Irreducible

Pronunciation

• IPA: /ˌɪrɪˈdjuːsɪbÉ™l/

Origin

- + reducible

Full definition of irreducible

Adjective

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

• reducible
• (unable to be reduced) unincreasable

Derived terms

• irreducibility
• irrep

Noun

1. (mathematics) Such a polynomial