added Field and FieldElement interfaces to allow algorithms

operate on any type of field.
This change is related to the discussion on dev list
http://markmail.org/message/h2rmq6wo7nwqzx4w

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@766482 13f79535-47bb-0310-9956-ffa450edef68

src/java/org/apache/commons/math/Field.java

@@ -0,0 +1,53 @@
+/*
+ * 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.math;
+
+import java.io.Serializable;
+
+/**
+ * Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>.
+ * <p>
+ * Classes implementing this interface will often be singletons.
+ * </p>
+ * @param <T> the type of the field elements
+ * @see FieldElement
+ * @version $Revision$ $Date$
+ * @since 2.0
+ */
+public interface Field<T> extends Serializable {
+
+    /** Get the additive identity of the field.
+     * <p>
+     * The additive identity is the element e<sub>0</sub> of the field such that
+     * for all elements a of the field, the equalities a + e<sub>0</sub> =
+     * e<sub>0</sub> + a = a hold.
+     * </p>
+     * @return additive identity of the field
+     */
+    T getZero();
+
+    /** Get the multiplicative identity of the field.
+     * <p>
+     * The multiplicative identity is the element e<sub>1</sub> of the field such that
+     * for all elements a of the field, the equalities a &times; e<sub>1</sub> =
+     * e<sub>1</sub> &times; a = a hold.
+     * </p>
+     * @return multiplicative identity of the field
+     */
+    T getOne();
+
+}

src/java/org/apache/commons/math/FieldElement.java

@@ -0,0 +1,61 @@
+/*
+ * 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.math;
+
+import java.io.Serializable;
+
+/**
+ * Interface representing <a href="http://mathworld.wolfram.com/Field.html">field</a> elements.
+ * @param <T> the type of the field elements
+ * @see Field
+ * @version $Revision$ $Date$
+ * @since 2.0
+ */
+public interface FieldElement<T> extends Serializable {
+
+    /** Compute this + a.
+     * @param a element to add
+     * @return a new element representing this + a
+     */
+    T add(T a);
+
+    /** Compute this - a.
+     * @param a element to subtract
+     * @return a new element representing this - a
+     */
+    T subtract(T a);
+
+    /** Compute this &times; a.
+     * @param a element to multiply
+     * @return a new element representing this &times; a
+     */
+    T multiply(T a);
+
+    /** Compute this &divide; a.
+     * @param a element to add
+     * @return a new element representing this &divide; a
+     * @exception ArithmeticException if a is the zero of the
+     * additive operation (i.e. additive identity)
+     */
+    T divide(T a) throws ArithmeticException;
+
+    /** Get the {@link Field} to which the instance belongs.
+     * @return {@link Field} to which the instance belongs
+     */
+    Field<T> getField();
+
+}