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irreducible Definition

ir·re·duc·ible (ir′i do̵̅o̅s′ə bəl, -dyo̵̅o̅s′-)

adjective

that cannot be reduced

Related Forms:

irreducible Synonyms

irreducible

modif.

immutable, irrevocable, unchangeable, intransmutable, incapable of being diminished, indelible, indestructible, imperishable, indissoluble, inextinguishable, basic, fundamental; see also firm 1, permanent 2.

irreducible Usage Examples

Modifies a noun

  • semigroups: The output is a set of irreducible numerical semigroups containing it.
  • polynomial: It can be an integer or an irreducible polynomial over the field S.
  • subgroup: Up to conjugacy, all irreducible subgroups of GL(n, q ) arise in that way.
  • complexity: Contrary to claims about irreducible complexity, the entire ensemble of proteins is not needed.
  • representation: However, even the most basic properties of the irreducible representations are unknown in general.
  • character: For any generic table, there has to be a fixed number of types of irreducible characters of G q, too.

Modifying Another Word

  • absolutely: The result was a contradiction which was absolutely irreducible within the limits of formal democracy.
  • computationally: For [ computationally irreducible ] complex systems there is no other way to predict their evolution than by tracking it.
  • not: If there are any absorbing states, the chain is not irreducible.

Used with adjective complement

  • call: The aim of the project is to study various constructions of the " minimal " representations of the classical groups, called irreducible.