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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;

/**
 * Interface representing a field.
 * 
 * Classes implementing this interface will often be singletons.
 * 
 * @param  the type of the field elements
 * @see FieldElement
 * @since 2.0
 */
public interface Field {

    /** Get the additive identity of the field.
     * 
     * The additive identity is the element e₀ of the field such that
     * for all elements a of the field, the equalities a + e₀ =
     * e₀ + a = a hold.
     * 
     * @return additive identity of the field
     */
    T getZero();

    /** Get the multiplicative identity of the field.
     * 
     * The multiplicative identity is the element e₁ of the field such that
     * for all elements a of the field, the equalities a × e₁ =
     * e₁ × a = a hold.
     * 
     * @return multiplicative identity of the field
     */
    T getOne();

    /**
     * Returns the runtime class of the FieldElement.
     *
     * @return The {@code Class} object that represents the runtime
     *         class of this object.
     */
    Class> getRuntimeClass();

}