Definition of Irreducibleness. Meaning of Irreducibleness. Synonyms of Irreducibleness

Here you will find one or more explanations in English for the word Irreducibleness. Also in the bottom left of the page several parts of wikipedia pages related to the word Irreducibleness and, of course, Irreducibleness synonyms and on the right images related to the word Irreducibleness.

Definition of Irreducibleness

Irreducibleness
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. 2. (Math.) 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.

Meaning of Irreducibleness from wikipedia

- high-level system on its components; qualities produced this way are irreducible to the system's constituent parts. The whole is other than the sum of...
- specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic...
- Irreducible complexity (IC) is the argument that certain biological systems with multiple interacting parts would not function if one of the parts were...
- In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials...
- absolutely irreducible if it is irreducible over the complex field. For example, x 2 + y 2 − 1 {\displaystyle x^{2}+y^{2}-1} is absolutely irreducible, but...
- In algebraic geometry, an irreducible algebraic set or irreducible variety is an algebraic set that cannot be written as the union of two proper algebraic...
- sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable into...
- An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers...
- In mathematics, the concept of irreducibility is used in several ways. A polynomial over a field may be an irreducible polynomial if it cannot be factored...
- In algebra, an irreducible element of an integral domain is a non-zero element that is not invertible (that is, is not a unit), and is not the product...