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irreducible Definition

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

adjective

that cannot be reduced

irreducible Related Forms

ir′·re·duc′·ibil·ity noun ir′·re·duc·ibly adverb

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.