Interface Field<F>

Type Parameters:
F - a field
All Superinterfaces:
AbelianGroup<F>, Monoid<F>, Ring<F>
All Known Implementing Classes:
Complex, Real, VariancebtX

public interface Field<F> extends Ring<F>
As an algebraic structure, every field is a ring, but not every ring is a field. That is, it has the notion of addition, subtraction, multiplication, satisfying certain axioms. The most important difference is that a field allows for division (though not division by zero), while a ring may not possess a multiplicative inverse. In addition, the multiplication operation in a field is required to be commutative.
See Also:
  • Nested Class Summary

    Nested Classes
    Modifier and Type
    static class 
    This is the exception thrown when the inverse of a field element does not exist.
  • Method Summary

    Modifier and Type
    divide(F that)
    / : F × F → F
    For each a in F, there exists an element b in F such that a × b = b × a = 1.

    Methods inherited from interface dev.nm.algebra.structure.AbelianGroup

    add, minus, opposite, ZERO

    Methods inherited from interface dev.nm.algebra.structure.Monoid

    multiply, ONE