different between irreducible vs irreducibly

English

Etymology

ir- +? reducible

Pronunciation

• IPA^(key): /?????dju?s?b?l/

Adjective

irreducible (comparative more irreducible, superlative most irreducible)

1. Not able to be reduced or lessened.

   Antonym: unincreasable

2. Not able to be brought to a simpler or reduced form.
3. (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
4. (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
5. (number theory, of an integer) Unable to be factored into smaller integers; prime.
6. (algebra, of an element of a ring) that its only divisors are units and associates.
7. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
8. (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.

Antonyms

• reducible

Derived terms

Translations

Noun

irreducible (plural irreducibles)

1. (mathematics) Such a polynomial

English

Etymology

irreducible +? -ly

Adverb

irreducibly (comparative more irreducibly, superlative most irreducibly)

1. In an irreducible manner, or state.