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Description
Interface Summary  

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. 
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 (·) and their respective inverses
are automatically defined for Quaternions objects; but also that (·) is distributive over (+),
both operations (+) and (·) are associative and (+) is commutative.

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