IRREDUCIBLE
irreducible
(adjective) incapable of being made smaller or simpler; “an irreducible minimum”; “an irreducible formula”; “an irreducible hernia”
Source: WordNet® 3.1
Etymology
Adjective
irreducible (comparative more irreducible, superlative most irreducible)
Not able to be reduced or lessened.
Antonym: unincreasable
Not able to be brought to a simpler or reduced form.
(mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x2 + 1).
(number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
(number theory, of an integer) Unable to be factored into smaller integers; prime.
(algebra, of an element of a ring) that its only divisors are units and associates.
(topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
(group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
Antonyms
• reducible
Noun
irreducible (plural irreducibles)
(mathematics) Such a polynomial
Source: Wiktionary
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.
2. (Math.)
Definition: 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.
– Ir`re*du"ci*ble*ness, n.
– -- Ir`re*du"ci*bly, adv.
Source: Webster’s Unabridged Dictionary 1913 Edition
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