com.numericalmethod.suanshu.mathstructure

Interface Field<F>

Type Parameters:

F - a field

All Superinterfaces:

AbelianGroup<F>, Monoid<F>, Ring<F>, java.io.Serializable

All Known Implementing Classes:

Complex, Real

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:

Wikipedia: Field (mathematics)

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static class	Field.InverseNonExistent This is the exception thrown when the inverse of a field element does not exist.

Method Summary

Modifier and Type	Method and Description
F	divide(F that) / : F × F → F That is the same as this.multiply(that.inverse())
F	inverse() For each a in F, there exists an element b in F such that a × b = b × a = 1.

Methods inherited from interface com.numericalmethod.suanshu.mathstructure.AbelianGroup

add, minus, opposite, ZERO

Methods inherited from interface com.numericalmethod.suanshu.mathstructure.Monoid

multiply, ONE

Method Detail

inverse

F inverse()
   throws Field.InverseNonExistent

For each a in F, there exists an element b in F such that a × b = b × a = 1. That is, it is the object such as

this.multiply(this.inverse()) == this.ONE

Returns:

1 / this if it exists

Throws:

Field.InverseNonExistent - if the inverse does not exist

See Also:

Wikipedia: Multiplicative inverse

divide

F divide(F that)
  throws Field.InverseNonExistent

/ : F × F → F

That is the same as

this.multiply(that.inverse())

Parameters:

that - the denominator

Returns:

this / that

Throws:

Field.InverseNonExistent - if the inverse does not exist