Separability may refer to:

Mathematics

Separable algebra In mathematics, a separable algebra is a kind of semisimple algebra. It is a generalization to associative algebras of the notion of a separable field extension. Definition and first properties A homomorphism of (unital, but not necessarily ...

, a generalization to associative algebras of the notion of a separable field extension * Separable differential equation, in which

separation of variables In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary differential equation, ordinary and partial differential equations, in which algebra allows one to rewrite an equation so tha ...

is achieved by various means *

Separable extension In field theory (mathematics), field theory, a branch of algebra, an algebraic field extension E/F is called a separable extension if for every \alpha\in E, the minimal polynomial (field theory), minimal polynomial of \alpha over is a separable po ...

, in field theory, an algebraic field extension *

Separable filter A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into two 1-dimensional filters. This reduces the computational costs on an N\times M image wit ...

, a product of two or more simple filters in image processing * Separable ordinary differential equation, a class of equations that can be separated into a pair of integrals *

Separable partial differential equation A separable partial differential equation can be broken into a set of equations of lower dimensionality (fewer independent variables) by a method of separation of variables. It generally relies upon the problem having some special form or symmetry ...

, a class of equations that can be broken down into differential equations in fewer independent variables *

Separable permutation In combinatorics, combinatorial mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by Direct sum of permutations, direct sums and Skew sum of permutations, skew sums. Separable permutations may ...

, a permutation that can be obtained by direct sums and skew sums of the trivial permutation *

Separable polynomial In mathematics, a polynomial ''P''(''X'') over a given field ''K'' is separable if its roots are distinct in an algebraic closure of ''K'', that is, the number of distinct roots is equal to the degree of the polynomial. This concept is closely ...

, a polynomial whose number of distinct roots is equal to its degree *

Separable sigma algebra Separability may refer to: Mathematics * Separable algebra, a generalization to associative algebras of the notion of a separable field extension * Separable differential equation, in which separation of variables is achieved by various means ...

, a separable space in measure theory *

Separable space In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence ( x_n )_^ of elements of the space such that every nonempty open subset of the space contains at least one elemen ...

, a topological space that contains a countable, dense subset *

Linear separability In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being col ...

, a geometric property of a pair of sets of points in Euclidean geometry *

Recursively inseparable sets In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated" with a computable set.Monk 1976, p. 100 These sets arise in the study of computability th ...

, in computability theory, pairs of sets of natural numbers that cannot be "separated" with a recursive set

Other uses

* Separable states, in quantum mechanics, states without quantum entanglement *

Separation process A separation process is a method that converts a mixture or a solution of chemical substances into two or more distinct product mixtures, a scientific process of separating two or more substances in order to obtain purity. At least one product mi ...

, in chemistry, a method that converts a mixture of substances into two or more distinct product mixtures {{disambiguation