| 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,
{@link org.jscience.mathematics.number.Real Real} is a
{@link org.jscience.mathematics.structure.Field Field<Real>},
but
{@link org.jscience.mathematics.number.LargeInteger LargeInteger} is only a
{@link org.jscience.mathematics.structure.Ring 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.
|
| Java Source File Name | Type | Comment |
| Field.java | Interface | This interface represents an algebraic structure in which the operations of
addition, subtraction, multiplication and division (except division by zero)
may be performed. |
| GroupAdditive.java | Interface | This interface represents a structure with a binary additive
operation (+), satisfying the group axioms (associativity, neutral element,
inverse element and closure). |
| GroupMultiplicative.java | Interface | This interface represents a structure with a binary multiplicative
operation (·), satisfying the group axioms (associativity, neutral element,
inverse element and closure). |
| Ring.java | Interface | 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.java | Interface | This interface represents a mathematical structure on a set (type). |
| VectorSpace.java | Interface | This interface represents a vector space over a field with two operations,
vector addition and scalar multiplication. |
| VectorSpaceNormed.java | Interface | This interface represents a vector space on which a positive vector length
or size is defined. |