separabelt

Separabelt is a term used in Norwegian, Swedish, and Danish to denote something that can be separated into distinct parts or components. In everyday language, it describes objects that can be disassembled or analyses that can be broken into independent factors. In scientific and technical contexts, separability is a formal property that often implies that a system can be studied piecewise without loss of generality.

In mathematics, separable concepts appear in several areas. A separable differential equation is one that can be rewritten as dy/dx = g(x)h(y) and solved by integrating both sides after rearrangement; for example, dy/y = x dx integrates to ln|y| = x^2/2 + C. In algebra, a polynomial is separable if its roots are distinct in its splitting field, and a field extension L/K is separable if the minimal polynomial of every element of L over K has distinct roots.

In linguistics, separable verbs are a characteristic of some Germanic languages, where a prefix can detach and appear as a distinct word in a sentence. Example: German aufstehen: Ich stehe heute früh auf. The verb and prefix 'auf' separate in finite clauses.

In physics and computer science, separability describes the possibility of decomposing a system into independent subsystems. In quantum mechanics, a state is separable if it can be written as a product of states of its parts; otherwise it is entangled.

Separabelt derives from Latin separabilis via European languages; English uses separable and separability with the same root. See also separable equation, separable extension, separable state.