Irreducible

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. (Math.) 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.