## org.apache.commons.math3
Interface FieldElement<T>

Type Parameters:
  `T` - the type of the field elements

All Known Implementing Classes:
  BigFraction, BigReal, Complex, Decimal64, DerivativeStructure, Dfp, DfpDec, Fraction

    public interface FieldElement<T>

Interface representing field elements.

Since:
  2.0
Version:
  $Id: FieldElement.java 1416643 2012-12-03 19:37:14Z tn $
See Also:
  `Field`

Method Summary
`T` `add(T a)` Compute this + a.
`T` `divide(T a)` Compute this ÷ a.
`Field<T>` `getField()` Get the `Field` to which the instance belongs.
`T` `multiply(int n)` Compute n × this.
`T` `multiply(T a)` Compute this × a.
`T` `negate()` Returns the additive inverse of `this` element.
`T` `reciprocal()` Returns the multiplicative inverse of `this` element.
`T` `subtract(T a)` Compute this - a.

Method Detail

### add

    T add(T a)
          throws NullArgumentException

  Compute this + a.

  Parameters:
    `a` - element to add
  Returns:
    a new element representing this + a
  Throws:
    `NullArgumentException` - if `addend` is `null`.

### subtract

    T subtract(T a)
               throws NullArgumentException

  Compute this - a.

  Parameters:
    `a` - element to subtract
  Returns:
    a new element representing this - a
  Throws:
    `NullArgumentException` - if `a` is `null`.

### negate

    T negate()

  Returns the additive inverse of `this` element.

  Returns:
    the opposite of `this`.

### multiply

    T multiply(int n)

  Compute n × this. Multiplication by an integer number is defined as the following sum
  n × this = ∑i=1n this.

  Parameters:
    `n` - Number of times `this` must be added to itself.
  Returns:
    A new element representing n × this.

### multiply

    T multiply(T a)
               throws NullArgumentException

  Compute this × a.

  Parameters:
    `a` - element to multiply
  Returns:
    a new element representing this × a
  Throws:
    `NullArgumentException` - if `a` is `null`.

### divide

    T divide(T a)
             throws NullArgumentException,
                    MathArithmeticException

  Compute this ÷ a.

  Parameters:
    `a` - element to add
  Returns:
    a new element representing this ÷ a
  Throws:
    `NullArgumentException` - if `a` is `null`.
    `MathArithmeticException` - if `a` is zero

### reciprocal

    T reciprocal()
                 throws MathArithmeticException

  Returns the multiplicative inverse of `this` element.

  Returns:
    the inverse of `this`.
  Throws:
    `MathArithmeticException` - if `this` is zero

### getField

    Field<T> getField()

  Get the `Field` to which the instance belongs.

  Returns:
    `Field` to which the instance belongs

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