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Package org.jscience.mathematics.structure

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

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

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

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For example, \n `Real` is a \n `Field<Real>`,\n but\n `LargeInteger` is only a \n `Ring<LargeInteger>` as its \n elements do not have multiplicative inverse (except for one).

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

``class Quaternions implements Field<Quaternions>``
\n Indicates that addition (+), multiplication (\xc2\xb7) and their respective inverses \n are automatically defined for Quaternions objects; but also that (\xc2\xb7) is distributive over (+),\n both operations (+) and (\xc2\xb7) are associative and (+) is commutative.

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