D defs.my
Entry 2 senses Webster, 1913

Irreducible

· Ir·re·du·ci·ble · IPA /ˌɪɹɪˈdjuːsɪbəl/
01 a. Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducib…
  1. 1.
    Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.
  2. 2.
    Incapable of being reduced to a simpler form of expression; as, an irreducible formula.(Math.)
Phrases & compounds
Irreducible case — 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.