irreducible

irreducible
    adj 1: incapable of being made smaller or simpler; "an
           irreducible minimum"; "an irreducible formula"; "an
           irreducible hernia" [ant: {reducible}]
    

Irreducible \Ir`re*du"ci*ble\, a.
   1. Incapable of being reduced, or brought into a different
      state; incapable of restoration to its proper or normal
      condition; as, an irreducible hernia.
      [1913 Webster]

   2. (Math.) Incapable of being reduced to a simpler form of
      expression; as, an irreducible formula.
      [1913 Webster]

   {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. -- {Ir`re*du"ci*ble*ness}, n. --
      -- {Ir`re*du"ci*bly}, adv.
      [1913 Webster]
    

90 Moby Thesaurus words for "irreducible":
      a certain, an, any, any one, atomic, austere, bare, basic,
      called for, chaste, deep-seated, either, elementary, esoteric,
      essential, exclusive, fundamental, homely, homespun, homogeneous,
      immanent, implanted, implicit, inalienable, indicated,
      indispensable, individual, indivisible, indwelling, inextricable,
      infixed, ingrained, inherent, inner, integral, internal, intrinsic,
      inward, inwrought, irreductible, irreplaceable, lone, mere,
      monadic, monistic, monolithic, necessary, needed, needful,
      of a piece, one, plain, prerequisite, primal, primary, private,
      pure, pure and simple, required, requisite, resident, secret,
      severe, simon-pure, simple, single, singular, sole, solid,
      solitary, spare, stark, subjective, unadorned, unalienable,
      unanalyzable, unchallengeable, uncluttered, undifferenced,
      undifferentiated, undivided, unforgoable, uniform, unique, unitary,
      unquestionable, unsolvable, vital, wanted, whole