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diff --git a/src/main/java/org/apache/commons/math3/util/BigRealField.java b/src/main/java/org/apache/commons/math3/util/BigRealField.java
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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.util;
+
+import org.apache.commons.math3.Field;
+import org.apache.commons.math3.FieldElement;
+
+import java.io.Serializable;
+
+/**
+ * Representation of real numbers with arbitrary precision field.
+ *
+ * <p>This class is a singleton.
+ *
+ * @see BigReal
+ * @since 2.0
+ */
+public class BigRealField implements Field<BigReal>, Serializable {
+
+    /** Serializable version identifier */
+    private static final long serialVersionUID = 4756431066541037559L;
+
+    /** Private constructor for the singleton. */
+    private BigRealField() {}
+
+    /**
+     * Get the unique instance.
+     *
+     * @return the unique instance
+     */
+    public static BigRealField getInstance() {
+        return LazyHolder.INSTANCE;
+    }
+
+    /** {@inheritDoc} */
+    public BigReal getOne() {
+        return BigReal.ONE;
+    }
+
+    /** {@inheritDoc} */
+    public BigReal getZero() {
+        return BigReal.ZERO;
+    }
+
+    /** {@inheritDoc} */
+    public Class<? extends FieldElement<BigReal>> getRuntimeClass() {
+        return BigReal.class;
+    }
+
+    // CHECKSTYLE: stop HideUtilityClassConstructor
+    /**
+     * Holder for the instance.
+     *
+     * <p>We use here the Initialization On Demand Holder Idiom.
+     */
+    private static class LazyHolder {
+        /** Cached field instance. */
+        private static final BigRealField INSTANCE = new BigRealField();
+    }
+
+    // CHECKSTYLE: resume HideUtilityClassConstructor
+
+    /**
+     * Handle deserialization of the singleton.
+     *
+     * @return the singleton instance
+     */
+    private Object readResolve() {
+        // return the singleton instance
+        return LazyHolder.INSTANCE;
+    }
+}