Package org.jscience.mathematics.structure

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.

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: [code]class Quaternions implements Field[/code] Indicates that addition (+), multiplication (·) and their respective inverses are automatically defined for Quaternions objects; but also that (·) is distributive over (+), both operations (+) and (·) are associative and (+) is commutative.

  • Interfaces
    Class
    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 (·), 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 ·), such that (R, +) is an abelian group, (R, ·) 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.