/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3;

import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NullArgumentException;


Interface representing field elements.
Type parameters:
<T> – the type of the field elements
See Also:
Field
Since:
2.0/**
 * Interface representing <a href="http://mathworld.wolfram.com/Field.html">field</a> elements.
 * @param <T> the type of the field elements
 * @see Field
 * @since 2.0
 */
public interface FieldElement<T> {

    
Compute this + a.
Params:
a – element to add
Throws:
NullArgumentException – if a is null.
Returns:
a new element representing this + a/** Compute this + a.
     * @param a element to add
     * @return a new element representing this + a
     * @throws NullArgumentException if {@code a} is {@code null}.
     */
    T add(T a) throws NullArgumentException;

    
Compute this - a.
Params:
a – element to subtract
Throws:
NullArgumentException – if a is null.
Returns:
a new element representing this - a/** Compute this - a.
     * @param a element to subtract
     * @return a new element representing this - a
     * @throws NullArgumentException if {@code a} is {@code null}.
     */
    T subtract(T a) throws NullArgumentException;

    
Returns the additive inverse of this element. 
Returns:
the opposite of this./**
     * Returns the additive inverse of {@code this} element.
     * @return the opposite of {@code this}.
     */
    T negate();

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

n × this = ∑i=1n this.

Params:
n – Number of times this must be added to itself.
Returns:
A new element representing n × this./** Compute n &times; this. Multiplication by an integer number is defined
     * as the following sum
     * <center>
     * n &times; this = &sum;<sub>i=1</sub><sup>n</sup> this.
     * </center>
     * @param n Number of times {@code this} must be added to itself.
     * @return A new element representing n &times; this.
     */
    T multiply(int n);

    
Compute this × a.
Params:
a – element to multiply
Throws:
NullArgumentException – if a is null.
Returns:
a new element representing this × a/** Compute this &times; a.
     * @param a element to multiply
     * @return a new element representing this &times; a
     * @throws NullArgumentException if {@code a} is {@code null}.
     */
    T multiply(T a) throws NullArgumentException;

    
Compute this ÷ a.
Params:
a – element to divide by
Throws:
NullArgumentException – if a is null.
MathArithmeticException – if a is zero
Returns:
a new element representing this ÷ a/** Compute this &divide; a.
     * @param a element to divide by
     * @return a new element representing this &divide; a
     * @throws NullArgumentException if {@code a} is {@code null}.
     * @throws MathArithmeticException if {@code a} is zero
     */
    T divide(T a) throws NullArgumentException, MathArithmeticException;

    
Returns the multiplicative inverse of this element. 
Throws:
MathArithmeticException – if this is zero
Returns:
the inverse of this./**
     * Returns the multiplicative inverse of {@code this} element.
     * @return the inverse of {@code this}.
     * @throws MathArithmeticException if {@code this} is zero
     */
    T reciprocal() throws MathArithmeticException;

    
Get the Field to which the instance belongs. 
Returns:
Field to which the instance belongs/** Get the {@link Field} to which the instance belongs.
     * @return {@link Field} to which the instance belongs
     */
    Field<T> getField();
}