irreducible
/ˌɪɹɪˈdjuːsɪbəl/ adjective, noun
Forms irreducibles
- adjective Not able to be reduced or lessened.
- adjective Not able to be brought to a simpler or reduced form.
- adjective (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
- adjective (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
- adjective (number theory, of an integer) Unable to be factored into smaller integers; prime.
- adjective (algebra, of an element of a ring) Whose only divisors are units and associates.
- adjective (algebraic geometry, of an algebraic variety) Inexpressible as the union of two proper algebraic subvarieties.
- adjective (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
- noun (mathematics) Such a polynomial
Antonyms
Webster’s 1913
- adjective Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.
- adjective Incapable of being reduced to a simpler form of expression; as, an irreducible formula. Irreducible case (Alg.), a particular case in the solution of a cubic equation, in which the formula commonly employed contains an imaginary quantity, and therefore fails in its application.
Sources: Wiktionary · Webster’s 1913 — from the Wiktionary entry “irreducible”, CC BY-SA 4.0. Details