Package 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)