Irreducible case
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. [1913 Webster]

2. (Math.) Incapable of being reduced to a simpler form of expression; as, an irreducible formula. [1913 Webster]

{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. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

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• IRREDUCIBLE CASE —    name given to a cubic equation which cannot be solved by the rule of CARDAN (q.v. CARDAN, JEROME) …   The Nuttall Encyclopaedia

• 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. [1913 Webster] 2. (Math.) Incapable of being reduced to a simpler form of …   The Collaborative International Dictionary of English

• Irreducible complexity — This article covers irreducible complexity as used by those who argue for intelligent design. For information on irreducible complexity as used in Systems Theory, see Irreducible complexity (Emergence). Irreducible complexity (IC) is an argument… …   Wikipedia

• Subdirect irreducible — In algebra, a subdirect irreducible is an algebra that cannot be factored as a subdirect product of simpler algebras. Subdirect irreducibles play a somewhat analogous role in algebra to primes in number theory. TOC =Definition=In algebra, a… …   Wikipedia

• Complejidad irreducible — Existen desacuerdos sobre la neutralidad en el punto de vista de la versión actual de este artículo o sección. En la página de discusión puedes consultar el debate al respecto …   Wikipedia Español

• 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. [1913 Webster] 2. (Math.) Incapable of being reduced to a… …   The Collaborative International Dictionary of English

• Irreducibly — 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. [1913 Webster] 2. (Math.) Incapable of being reduced to a… …   The Collaborative International Dictionary of English

• Reductive dual pair — In the mathematical field of representation theory, a reductive dual pair is a pair of subgroups (G,G ′) of the isometry group Sp(W) of a symplectic vector space W, such that G is the centralizer of G ′ in Sp(W) and vice versa, and these groups… …   Wikipedia

• Cubic function — This article is about cubic equations in one variable. For cubic equations in two variables, see elliptic curve. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis where y = 0). It has 2 critical points. Here …   Wikipedia

• Casus irreducibilis — In algebra, casus irreducibilis (Latin for the irreducible case ) is one of the cases that may arise in attempting to solve a cubic equation with integer coefficients with roots that are expressed with radicals. Specifically, if a cubic… …   Wikipedia