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

Type Parameters:
`T` - the type of the field elements
All Known Subinterfaces:
RealFieldElement<T>
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 \$
`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

```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