001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.numbers.field;
018
019/**
020 * Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>.
021 *
022 * @param <T> Type of the field elements.
023 */
024public interface Field<T> {
025    /**
026     * Add the elements.
027     *
028     * @param a Field element.
029     * @param b Field element.
030     * @return {@code a + b}.
031     */
032    T add(T a, T b);
033
034    /**
035     * Subtract the element {@code b} from {@code a}.
036     *
037     * @param a Field element.
038     * @param b Field element.
039     * @return {@code a - b}.
040     */
041    T subtract(T a, T b);
042
043    /**
044     * Negate the element.
045     *
046     * @param a Field element.
047     * @return {@code -a}.
048     */
049    T negate(T a);
050
051    /**
052     * Multiply the element {@code a} by a specified number of times {@code n}.
053     *
054     * @param a Field element.
055     * @param n Number of times {@code a} must be added to itself.
056     * @return {@code n a}.
057     */
058    T multiply(int n, T a);
059
060    /**
061     * Multiply the elements.
062     *
063     * @param a Field element.
064     * @param b Field element.
065     * @return {@code a * b}.
066     */
067    T multiply(T a, T b);
068
069    /**
070     * Divide the element {@code a} by {@code b}.
071     *
072     * @param a Field element.
073     * @param b Field element.
074     * @return <code>a * b<sup>-1</sup></code>.
075     */
076    T divide(T a, T b);
077
078    /**
079     * Return the reciprocal (multiplicative inverse).
080     *
081     * @param a Field element.
082     * @return <code>a<sup>-1</sup></code>.
083     */
084    T reciprocal(T a);
085
086    /**
087     * Return the value of one.
088     *
089     * @return the field element {@code 1} such that for all {@code a},
090     * {@code 1 * a == a}.
091     */
092    T one();
093
094    /**
095     * Return the value of zero.
096     *
097     * @return the field element {@code 0} such that for all {@code a},
098     * {@code 0 + a == a}.
099     */
100    T zero();
101}