1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.numbers.field;
18
19 /**
20 * Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>.
21 *
22 * @param <T> Type of the field elements.
23 */
24 public interface Field<T> {
25 /**
26 * @param a Field element.
27 * @param b Field element.
28 * @return {@code a + b}.
29 */
30 T add(T a, T b);
31
32 /**
33 * @param a Field element.
34 * @param b Field element.
35 * @return {@code a - b}.
36 */
37 T subtract(T a, T b);
38
39 /**
40 * @param a Field element.
41 * @return {@code -a}.
42 */
43 T negate(T a);
44
45 /**
46 * @param a Field element.
47 * @param n Number of times {@code a} must be added to itself.
48 * @return {@code n a}.
49 */
50 T multiply(int n, T a);
51
52 /**
53 * @param a Field element.
54 * @param b Field element.
55 * @return {@code a * b}.
56 */
57 T multiply(T a, T b);
58
59 /**
60 * @param a Field element.
61 * @param b Field element.
62 * @return <code>a * b<sup>-1</sup></code>.
63 */
64 T divide(T a, T b);
65
66 /**
67 * @param a Field element.
68 * @return <code>a<sup>-1</sup></code>.
69 */
70 T reciprocal(T a);
71
72 /**
73 * @return the field element {@code 1} such that for all {@code a},
74 * {@code 1 * a == a}.
75 */
76 T one();
77
78 /**
79 * @return the field element {@code 0} such that for all {@code a},
80 * {@code 0 + a == a}.
81 */
82 T zero();
83 }