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.core; 018 019/** 020 * Multiplication. 021 * 022 * @param <T> Type of elements. 023 */ 024public interface Multiplication<T> { 025 /** 026 * Binary multiplication. 027 * 028 * @param a Element. 029 * @return {@code this * a}. 030 */ 031 T multiply(T a); 032 033 /** 034 * Identity element. 035 * 036 * @return the field element such that for all {@code a}, 037 * {@code one().multiply(a).equals(a)} is {@code true}. 038 */ 039 T one(); 040 041 /** 042 * Multiplicative inverse. 043 * 044 * @return <code>this<sup>-1</sup></code>. 045 */ 046 T reciprocal(); 047 048 /** 049 * Check if this is a neutral element of multiplication, i.e. {@code this.multiply(a)} returns 050 * {@code a} or an element representing the same value as {@code a}. 051 * 052 * <p>The default implementation calls {@link Object#equals(Object) equals(one())}. 053 * Implementations may want to employ more a efficient method. This may even 054 * be required if an implementation has multiple representations of {@code one} and its 055 * {@code equals} method differentiates between them. 056 * 057 * @return {@code true} if {@code this} is a neutral element of multiplication. 058 * @see #one() 059 * @since 1.2 060 */ 061 default boolean isOne() { 062 return this.equals(one()); 063 } 064}