/*
 * 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.math;

/**
 * Interface representing
 * <a href="http://mathworld.wolfram.com/Field.html">field</a> elements.
 * 
 * @param <T>
 *            the type of the field elements
 * @see Field
 * @version $Revision$ $Date$
 * @since 2.0
 */
public interface FieldElement<T> {

	/**
	 * Compute this + a.
	 * 
	 * @param a
	 *            element to add
	 * @return a new element representing this + a
	 */
	T add(T a);

	/**
	 * Compute this - a.
	 * 
	 * @param a
	 *            element to subtract
	 * @return a new element representing this - a
	 */
	T subtract(T a);

	/**
	 * Compute this &times; a.
	 * 
	 * @param a
	 *            element to multiply
	 * @return a new element representing this &times; a
	 */
	T multiply(T a);

	/**
	 * Compute this &divide; a.
	 * 
	 * @param a
	 *            element to add
	 * @return a new element representing this &divide; a
	 * @exception ArithmeticException
	 *                if a is the zero of the additive operation (i.e. additive
	 *                identity)
	 */
	T divide(T a) throws ArithmeticException;

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

}