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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.

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/*
 * 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.
 * @param  the type of the field elements
 * @see Field
 * @since 2.0
 */
public interface FieldElement {

    /** 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.
     * @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 {@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.
     * 
     * @param n Number of times {@code this} must be added to itself.
     * @return A new element representing n × this.
     */
    T multiply(int n);

    /** Compute this × a.
     * @param a element to multiply
     * @return a new element representing this × a
     * @throws NullArgumentException if {@code a} is {@code null}.
     */
    T multiply(T a) throws NullArgumentException;

    /** Compute this ÷ a.
     * @param a element to divide by
     * @return a new element representing this ÷ 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 {@code this} element.
     * @return the inverse of {@code this}.
     * @throws MathArithmeticException if {@code this} is zero
     */
    T reciprocal() throws MathArithmeticException;

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