# Package org.jscience.mathematics.structure

Provides mathematical sets (identified by the class parameter) associated to binary operations, such as multiplication or addition, satisfying certain axioms.

See: Description

Interface Summary Interface Description Field<F> This interface represents an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed.GroupAdditive<G> This interface represents a structure with a binary additive operation (+), satisfying the group axioms (associativity, neutral element, inverse element and closure).GroupMultiplicative<G> This interface represents a structure with a binary multiplicative operation (\xc2\xb7), satisfying the group axioms (associativity, neutral element, inverse element and closure).Ring<R> This interface represents an algebraic structure with two binary operations addition and multiplication (+ and \xc2\xb7), such that (R, +) is an abelian group, (R, \xc2\xb7) is a monoid and the multiplication distributes over the addition.Structure<T> This interface represents a mathematical structure on a set (type).VectorSpace<V,F extends Field> This interface represents a vector space over a field with two operations, vector addition and scalar multiplication.VectorSpaceNormed<V,F extends Field> This interface represents a vector space on which a positive vector length or size is defined.

## Package org.jscience.mathematics.structure Description

Provides mathematical sets (identified by the class parameter) associated to binary operations, such as multiplication or addition, satisfying certain axioms.

For example, `Real`

is a `Field<Real>`

, but `LargeInteger`

is only a `Ring<LargeInteger>`

as its elements do not have multiplicative inverse (except for one).

To implement a structure means not only that some operations are now available but also that some properties (such as associativity and distributivity) must be verified. For example, the declaration:

**class** Quaternions **implements** Field<Quaternions>

Indicates that addition (+), multiplication (\xc2\xb7) and their respective inverses are automatically defined for Quaternions objects; but also that (\xc2\xb7) is distributive over (+), both operations (+) and (\xc2\xb7) are associative and (+) is commutative.**SCaVis 2.0 © jWork.ORG**