org.tensorics.core.math.structures.ringlike

Interface Field<T>

Type Parameters:

T - the type of elements of the field.

All Superinterfaces:

Ring<T>, RinglikeStructure<T>, Semiring<T>, Structure<T>

All Known Subinterfaces:

OrderedField<T>

All Known Implementing Classes:

AbstractOrderedField, DoubleField

public interface Field<T>
extends Ring<T>

Represents the algebraic structure 'field'. It means that it represents a set of elements together with two binary operations (+, *) with the following properties:

• both, + and * are associative: a + (b + c) = (a + b) + c; a * (b * c) = (a * b) * c.
• both, + and * have an identity element (Called '0' for +, '1' for *): a + 0 = a; a * 1 = a.
• both, + and * have an inverse element (Called '-a' for +, '1/a' for *): a + (-a) = 0; a * 1/a = 1.
• both, + and * are commutative: a + b = b + a; a * b = b * a.
• * is distributive over +: a * (b + c) = a * b + a * c.

In other words, both addition and multiplication (without 0) are abelian groups.

See Also:

http://en.wikipedia.org/wiki/Field_(mathematics)

Method Summary

Modifier and Type	Method and Description
AbelianGroup<T>	multiplicationStructure() Returns the grouplike structure representing the multiplication of elements.

Methods inherited from interface org.tensorics.core.math.structures.ringlike.Ring

additionStructure

Method Detail

multiplicationStructure

AbelianGroup<T> multiplicationStructure()

Description copied from interface: RinglikeStructure

Returns the grouplike structure representing the multiplication of elements.

Specified by:

multiplicationStructure in interface RinglikeStructure<T>

Specified by:

multiplicationStructure in interface Semiring<T>

Returns:

the group like structure for multiplication