/*
    * 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.fraction;
  
  import java.io.Serializable;
  import java.math.BigInteger;
  import java.util.function.Function;
  import java.util.function.Predicate;
  import java.util.stream.Stream;
  
  import org.hipparchus.FieldElement;
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.exception.MathIllegalStateException;
  import org.hipparchus.exception.MathRuntimeException;
  import org.hipparchus.fraction.ConvergentsIterator.ConvergenceStep;
  import org.hipparchus.util.ArithmeticUtils;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathUtils;
  import org.hipparchus.util.Pair;
  import org.hipparchus.util.Precision;
  
  /**
   * Representation of a rational number.
   */
  public class Fraction
      extends Number
      implements FieldElement<Fraction>, Comparable<Fraction>, Serializable {
  
      /** A fraction representing "2 / 1". */
      public static final Fraction TWO = new Fraction(2, 1);
  
      /** A fraction representing "1". */
      public static final Fraction ONE = new Fraction(1, 1);
  
      /** A fraction representing "0". */
      public static final Fraction ZERO = new Fraction(0, 1);
  
      /** A fraction representing "4/5". */
      public static final Fraction FOUR_FIFTHS = new Fraction(4, 5);
  
      /** A fraction representing "1/5". */
      public static final Fraction ONE_FIFTH = new Fraction(1, 5);
  
      /** A fraction representing "1/2". */
      public static final Fraction ONE_HALF = new Fraction(1, 2);
  
      /** A fraction representing "1/4". */
      public static final Fraction ONE_QUARTER = new Fraction(1, 4);
  
      /** A fraction representing "1/3". */
      public static final Fraction ONE_THIRD = new Fraction(1, 3);
  
      /** A fraction representing "3/5". */
      public static final Fraction THREE_FIFTHS = new Fraction(3, 5);
  
      /** A fraction representing "3/4". */
      public static final Fraction THREE_QUARTERS = new Fraction(3, 4);
  
      /** A fraction representing "2/5". */
      public static final Fraction TWO_FIFTHS = new Fraction(2, 5);
  
      /** A fraction representing "2/4". */
      public static final Fraction TWO_QUARTERS = new Fraction(2, 4);
  
      /** A fraction representing "2/3". */
      public static final Fraction TWO_THIRDS = new Fraction(2, 3);
  
      /** A fraction representing "-1 / 1". */
      public static final Fraction MINUS_ONE = new Fraction(-1, 1);
  
      /** Serializable version identifier */
      private static final long serialVersionUID = 3698073679419233275L;
  
      /** The default epsilon used for convergence. */
      private static final double DEFAULT_EPSILON = 1e-5;
  
      /** Convert a convergence step to the corresponding double fraction. */
      private static final Function<ConvergenceStep, Fraction> STEP_TO_FRACTION = //
                      s -> new Fraction((int) s.getNumerator(), (int) s.getDenominator());
  
     /** The denominator. */
     private final int denominator;
 
     /** The numerator. */
     private final int numerator;
 
     /**
      * Create a fraction given the double value.
      * @param value the double value to convert to a fraction.
      * @throws MathIllegalStateException if the continued fraction failed to
      *         converge.
      */
     public Fraction(double value) throws MathIllegalStateException {
         this(value, DEFAULT_EPSILON, 100);
     }
 
     /**
      * Create a fraction given the double value and maximum error allowed.
      * <p>
      * References:
      * <ul>
      * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">
      * Continued Fraction</a> equations (11) and (22)-(26)</li>
      * </ul>
      *
      * @param value the double value to convert to a fraction.
      * @param epsilon maximum error allowed.  The resulting fraction is within
      *        {@code epsilon} of {@code value}, in absolute terms.
      * @param maxIterations maximum number of convergents
      * @throws MathIllegalStateException if the continued fraction failed to
      *         converge.
      */
     public Fraction(double value, double epsilon, int maxIterations)
         throws MathIllegalStateException {
         ConvergenceStep converged = convergent(value, maxIterations, s -> {
             double quotient = s.getFractionValue();
             return Precision.equals(quotient, value, 1) || FastMath.abs(quotient - value) < epsilon;
         }).getKey();
         if (FastMath.abs(converged.getFractionValue() - value) < epsilon) {
             this.numerator   = (int) converged.getNumerator();
             this.denominator = (int) converged.getDenominator();
         } else {
             throw new MathIllegalStateException(LocalizedCoreFormats.FAILED_FRACTION_CONVERSION,
                                                 value, maxIterations);
         }
     }
 
     /**
      * Create a fraction given the double value and maximum denominator.
      * <p>
      * References:
      * <ul>
      * <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">
      * Continued Fraction</a> equations (11) and (22)-(26)</li>
      * </ul>
      *
      * @param value the double value to convert to a fraction.
      * @param maxDenominator The maximum allowed value for denominator
      * @throws MathIllegalStateException if the continued fraction failed to
      *         converge
      */
     public Fraction(double value, int maxDenominator)
         throws MathIllegalStateException {
         final int maxIterations = 100;
         ConvergenceStep[] lastValid = new ConvergenceStep[1];
         try {
             convergent(value, maxIterations, s -> {
                 if (s.getDenominator() < maxDenominator) {
                     lastValid[0] = s;
                 }
                 return Precision.equals(s.getFractionValue(), value, 1);
             });
         } catch (MathIllegalStateException e) { // NOPMD - ignore overflows and just take the last valid result
         }
         if (lastValid[0] != null) {
             this.numerator   = (int) lastValid[0].getNumerator();
             this.denominator = (int) lastValid[0].getDenominator();
         } else {
             throw new MathIllegalStateException(LocalizedCoreFormats.FAILED_FRACTION_CONVERSION,
                                                 value, maxIterations);
         }
     }
 
     /**
      * Create a fraction from an int.
      * The fraction is num / 1.
      * @param num the numerator.
      */
     public Fraction(int num) {
         this(num, 1);
     }
 
     /**
      * Create a fraction given the numerator and denominator.  The fraction is
      * reduced to lowest terms.
      * @param num the numerator.
      * @param den the denominator.
      * @throws MathRuntimeException if the denominator is {@code zero}
      */
     public Fraction(int num, int den) {
         if (den == 0) {
             throw new MathRuntimeException(LocalizedCoreFormats.ZERO_DENOMINATOR_IN_FRACTION,
                                            num, den);
         }
         if (den < 0) {
             if (num == Integer.MIN_VALUE ||
                 den == Integer.MIN_VALUE) {
                 throw new MathRuntimeException(LocalizedCoreFormats.OVERFLOW_IN_FRACTION,
                                                num, den);
             }
             num = -num;
             den = -den;
         }
         // reduce numerator and denominator by greatest common denominator.
         final int d = ArithmeticUtils.gcd(num, den);
         if (d > 1) {
             num /= d;
             den /= d;
         }
 
         // move sign to numerator.
         if (den < 0) {
             num = -num;
             den = -den;
         }
         this.numerator   = num;
         this.denominator = den;
     }
 
     /**
      * A test to determine if a series of fractions has converged.
      */
     @FunctionalInterface
     public interface ConvergenceTest {
         /**
          * Evaluates if the fraction formed by {@code numerator/denominator} satisfies
          * this convergence test.
          *
          * @param numerator   the numerator
          * @param denominator the denominator
          * @return if this convergence test is satisfied
          */
         boolean test(int numerator, int denominator); // NOPMD - this is not a Junit test, PMD false positive here
     }
 
     /** Generate a {@link Stream stream} of convergents from a real number.
      * @param value value to approximate
      * @param maxConvergents maximum number of convergents.
      * @return stream of {@link Fraction} convergents approximating  {@code value}
      * @since 2.1
      */
     public static Stream<Fraction> convergents(final double value, final int maxConvergents) {
         if (FastMath.abs(value) > Integer.MAX_VALUE) {
             throw new MathIllegalStateException(LocalizedCoreFormats.FRACTION_CONVERSION_OVERFLOW, value, value, 1l);
         }
         return ConvergentsIterator.convergents(value, maxConvergents).map(STEP_TO_FRACTION);
     }
 
     /**
      * Returns the last element of the series of convergent-steps to approximate the
      * given value.
      * <p>
      * The series terminates either at the first step that satisfies the given
      * {@code convergenceTest} or after at most {@code maxConvergents} elements. The
      * returned Pair consists of that terminal {@link Fraction} and a
      * {@link Boolean} that indicates if it satisfies the given convergence tests.
      * If the returned pair's value is {@code false} the element at position
      * {@code maxConvergents} was examined but failed to satisfy the
      * {@code convergenceTest}. A caller can then decide to accept the result
      * nevertheless or to discard it. This method is usually faster than
      * {@link #convergents(double, int)} if only the terminal element is of
      * interest.
      *
      * @param value           value to approximate
      * @param maxConvergents  maximum number of convergents to examine
      * @param convergenceTest the test if the series has converged at a step
      * @return the pair of last element of the series of convergents and a boolean
      *         indicating if that element satisfies the specified convergent test
      */
     public static Pair<Fraction, Boolean> convergent(double value, int maxConvergents, ConvergenceTest convergenceTest) {
         Pair<ConvergenceStep, Boolean> converged = convergent(value, maxConvergents, s -> {
             assertNoIntegerOverflow(s, value);
             return convergenceTest.test((int) s.getNumerator(), (int) s.getDenominator());
         });
         return Pair.create(STEP_TO_FRACTION.apply(converged.getKey()), converged.getValue());
     }
 
     /** Create a convergent-steps to approximate the given value.
      * @param value           value to approximate
      * @param maxConvergents  maximum number of convergents to examine
      * @param convergenceTests the test if the series has converged at a step
      * @return the pair of last element of the series of convergents and a boolean
      *         indicating if that element satisfies the specified convergent test
      */
     private static Pair<ConvergenceStep, Boolean> convergent(double value, int maxConvergents,
                                                              Predicate<ConvergenceStep> convergenceTests) {
         if (FastMath.abs(value) > Integer.MAX_VALUE) {
             throw new MathIllegalStateException(LocalizedCoreFormats.FRACTION_CONVERSION_OVERFLOW, value, value, 1l);
         }
         return ConvergentsIterator.convergent(value, maxConvergents, s -> {
             assertNoIntegerOverflow(s, value);
             return convergenceTests.test(s);
         });
     }
 
     /** Check no overflow occurred.
      * @param s convergent
      * @param value corresponding value
      */
     private static void assertNoIntegerOverflow(ConvergenceStep s, double value) {
         if (s.getNumerator() > Integer.MAX_VALUE || s.getDenominator() > Integer.MAX_VALUE) {
             throw new MathIllegalStateException(LocalizedCoreFormats.FRACTION_CONVERSION_OVERFLOW, value,
                     s.getNumerator(), s.getDenominator());
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public double getReal() {
         return doubleValue();
     }
 
     /** Check if a fraction is an integer.
      * @return true of fraction is an integer
      */
     public boolean isInteger() {
         return denominator == 1;
     }
 
     /** Returns the signum function of this fraction.
      * <p>
      * The return value is -1 if the specified value is negative;
      * 0 if the specified value is zero; and 1 if the specified value is positive.
      * </p>
      * @return the signum function of this fraction
      * @since 1.7
      */
     public int signum() {
         return Integer.signum(numerator);
     }
 
     /**
      * Returns the absolute value of this fraction.
      * @return the absolute value.
      */
     public Fraction abs() {
         Fraction ret;
         if (numerator >= 0) {
             ret = this;
         } else {
             ret = negate();
         }
         return ret;
     }
 
     /**
      * Compares this object to another based on size.
      * @param object the object to compare to
      * @return -1 if this is less than {@code object}, +1 if this is greater
      *         than {@code object}, 0 if they are equal.
      */
     @Override
     public int compareTo(Fraction object) {
         long nOd = ((long) numerator) * object.denominator;
         long dOn = ((long) denominator) * object.numerator;
         return Long.compare(nOd, dOn);
     }
 
     /**
      * Gets the fraction as a {@code double}. This calculates the fraction as
      * the numerator divided by denominator.
      * @return the fraction as a {@code double}
      */
     @Override
     public double doubleValue() {
         return (double)numerator / (double)denominator;
     }
 
     /**
      * Test for the equality of two fractions.  If the lowest term
      * numerator and denominators are the same for both fractions, the two
      * fractions are considered to be equal.
      * @param other fraction to test for equality to this fraction
      * @return true if two fractions are equal, false if object is
      *         {@code null}, not an instance of {@link Fraction}, or not equal
      *         to this fraction instance.
      */
     @Override
     public boolean equals(Object other) {
         if (this == other) {
             return true;
         }
         if (other instanceof Fraction) {
             // since fractions are always in lowest terms, numerators and
             // denominators can be compared directly for equality.
             Fraction rhs = (Fraction)other;
             return (numerator == rhs.numerator) &&
                 (denominator == rhs.denominator);
         }
         return false;
     }
 
     /**
      * Gets the fraction as a {@code float}. This calculates the fraction as
      * the numerator divided by denominator.
      * @return the fraction as a {@code float}
      */
     @Override
     public float floatValue() {
         return (float)doubleValue();
     }
 
     /**
      * Rational number greatest common divisor.
      *
      * @param s fraction.
      * @return gcd(this, s).
      * @since 3.1
      */
     public Fraction gcd(Fraction s) {
       if (s.isZero()) {
         return this;
       }
       if (this.isZero()) {
         return s;
       }
       int p = ArithmeticUtils.gcd(numerator, s.numerator);
       int q = ArithmeticUtils.lcm(denominator, s.denominator);
       return new Fraction(p, q);
     }
 
     /**
      * Rational number least common multiple.
      *
      * @param s fraction.
      * @return lcm(this, s).
      * @since 3.1
      */
     public Fraction lcm(Fraction s) {
       if (s.isZero()) {
         return ZERO;
       }
       if (this.isZero()) {
         return ZERO;
       }
       return new Fraction(ArithmeticUtils.lcm(numerator, s.numerator),
                           ArithmeticUtils.gcd(denominator, s.denominator));
     }
 
     /**
      * Access the denominator.
      * @return the denominator.
      */
     public int getDenominator() {
         return denominator;
     }
 
     /**
      * Access the numerator.
      * @return the numerator.
      */
     public int getNumerator() {
         return numerator;
     }
 
     /**
      * Gets a hashCode for the fraction.
      * @return a hash code value for this object
      */
     @Override
     public int hashCode() {
         return 37 * (37 * 17 + numerator) + denominator;
     }
 
     /**
      * Gets the fraction as an {@code int}. This returns the whole number part
      * of the fraction.
      * @return the whole number fraction part
      */
     @Override
     public int intValue() {
         return (int)doubleValue();
     }
 
     /**
      * Gets the fraction as a {@code long}. This returns the whole number part
      * of the fraction.
      * @return the whole number fraction part
      */
     @Override
     public long longValue() {
         return (long)doubleValue();
     }
 
     /**
      * Return the additive inverse of this fraction.
      * @return the negation of this fraction.
      */
     @Override
     public Fraction negate() {
         if (numerator==Integer.MIN_VALUE) {
             throw new MathRuntimeException(LocalizedCoreFormats.OVERFLOW_IN_FRACTION, numerator, denominator);
         }
         return new Fraction(-numerator, denominator);
     }
 
     /**
      * Return the multiplicative inverse of this fraction.
      * @return the reciprocal fraction
      */
     @Override
     public Fraction reciprocal() {
         return new Fraction(denominator, numerator);
     }
 
     /**
      * Adds the value of this fraction to another, returning the result in reduced form.
      * The algorithm follows Knuth, 4.5.1.
      *
      * @param fraction  the fraction to add, must not be {@code null}
      * @return a {@code Fraction} instance with the resulting values
      * @throws org.hipparchus.exception.NullArgumentException if the fraction is {@code null}
      * @throws MathRuntimeException if the resulting numerator or denominator exceeds
      *  {@code Integer.MAX_VALUE}
      */
     @Override
     public Fraction add(Fraction fraction) {
         return addSub(fraction, true /* add */);
     }
 
     /**
      * Add an integer to the fraction.
      * @param i the {@code integer} to add.
      * @return this + i
      */
     public Fraction add(final int i) {
         return new Fraction(numerator + i * denominator, denominator);
     }
 
     /**
      * Subtracts the value of another fraction from the value of this one,
      * returning the result in reduced form.
      *
      * @param fraction  the fraction to subtract, must not be {@code null}
      * @return a {@code Fraction} instance with the resulting values
      * @throws org.hipparchus.exception.NullArgumentException if the fraction is {@code null}
      * @throws MathRuntimeException if the resulting numerator or denominator
      *   cannot be represented in an {@code int}.
      */
     @Override
     public Fraction subtract(Fraction fraction) {
         return addSub(fraction, false /* subtract */);
     }
 
     /**
      * Subtract an integer from the fraction.
      * @param i the {@code integer} to subtract.
      * @return this - i
      */
     public Fraction subtract(final int i) {
         return new Fraction(numerator - i * denominator, denominator);
     }
 
     /**
      * Implement add and subtract using algorithm described in Knuth 4.5.1.
      *
      * @param fraction the fraction to subtract, must not be {@code null}
      * @param isAdd true to add, false to subtract
      * @return a {@code Fraction} instance with the resulting values
      * @throws org.hipparchus.exception.NullArgumentException if the fraction is {@code null}
      * @throws MathRuntimeException if the resulting numerator or denominator
      *   cannot be represented in an {@code int}.
      */
     private Fraction addSub(Fraction fraction, boolean isAdd) {
         MathUtils.checkNotNull(fraction, LocalizedCoreFormats.FRACTION);
 
         // zero is identity for addition.
         if (numerator == 0) {
             return isAdd ? fraction : fraction.negate();
         }
         if (fraction.numerator == 0) {
             return this;
         }
         // if denominators are randomly distributed, d1 will be 1 about 61%
         // of the time.
         int d1 = ArithmeticUtils.gcd(denominator, fraction.denominator);
         if (d1==1) {
             // result is ( (u*v' +/- u'v) / u'v')
             int uvp = ArithmeticUtils.mulAndCheck(numerator, fraction.denominator);
             int upv = ArithmeticUtils.mulAndCheck(fraction.numerator, denominator);
             return new Fraction
                 (isAdd ? ArithmeticUtils.addAndCheck(uvp, upv) :
                  ArithmeticUtils.subAndCheck(uvp, upv),
                  ArithmeticUtils.mulAndCheck(denominator, fraction.denominator));
         }
         // the quantity 't' requires 65 bits of precision; see knuth 4.5.1
         // exercise 7.  we're going to use a BigInteger.
         // t = u(v'/d1) +/- v(u'/d1)
         BigInteger uvp = BigInteger.valueOf(numerator)
                                    .multiply(BigInteger.valueOf(fraction.denominator / d1));
         BigInteger upv = BigInteger.valueOf(fraction.numerator)
                                    .multiply(BigInteger.valueOf(denominator / d1));
         BigInteger t = isAdd ? uvp.add(upv) : uvp.subtract(upv);
         // but d2 doesn't need extra precision because
         // d2 = gcd(t,d1) = gcd(t mod d1, d1)
         int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue();
         int d2 = (tmodd1==0)?d1:ArithmeticUtils.gcd(tmodd1, d1);
 
         // result is (t/d2) / (u'/d1)(v'/d2)
         BigInteger w = t.divide(BigInteger.valueOf(d2));
         if (w.bitLength() > 31) {
             throw new MathRuntimeException(LocalizedCoreFormats.NUMERATOR_OVERFLOW_AFTER_MULTIPLY,
                                            w);
         }
         return new Fraction (w.intValue(),
                 ArithmeticUtils.mulAndCheck(denominator/d1,
                                             fraction.denominator/d2));
     }
 
     /**
      * Multiplies the value of this fraction by another, returning the
      * result in reduced form.
      *
      * @param fraction  the fraction to multiply by, must not be {@code null}
      * @return a {@code Fraction} instance with the resulting values
      * @throws org.hipparchus.exception.NullArgumentException if the fraction is {@code null}
      * @throws MathRuntimeException if the resulting numerator or denominator exceeds
      *  {@code Integer.MAX_VALUE}
      */
     @Override
     public Fraction multiply(Fraction fraction) {
         MathUtils.checkNotNull(fraction, LocalizedCoreFormats.FRACTION);
         if (numerator == 0 || fraction.numerator == 0) {
             return ZERO;
         }
         // knuth 4.5.1
         // make sure we don't overflow unless the result *must* overflow.
         int d1 = ArithmeticUtils.gcd(numerator, fraction.denominator);
         int d2 = ArithmeticUtils.gcd(fraction.numerator, denominator);
         return getReducedFraction
                 (ArithmeticUtils.mulAndCheck(numerator/d1, fraction.numerator/d2),
                  ArithmeticUtils.mulAndCheck(denominator/d2, fraction.denominator/d1));
     }
 
     /**
      * Multiply the fraction by an integer.
      * @param i the {@code integer} to multiply by.
      * @return this * i
      */
     @Override
     public Fraction multiply(final int i) {
         return multiply(new Fraction(i));
     }
 
     /**
      * Divide the value of this fraction by another.
      *
      * @param fraction  the fraction to divide by, must not be {@code null}
      * @return a {@code Fraction} instance with the resulting values
      * @throws IllegalArgumentException if the fraction is {@code null}
      * @throws MathRuntimeException if the fraction to divide by is zero
      * @throws MathRuntimeException if the resulting numerator or denominator exceeds
      *  {@code Integer.MAX_VALUE}
      */
     @Override
     public Fraction divide(Fraction fraction) {
         MathUtils.checkNotNull(fraction, LocalizedCoreFormats.FRACTION);
         if (fraction.numerator == 0) {
             throw new MathRuntimeException(LocalizedCoreFormats.ZERO_FRACTION_TO_DIVIDE_BY,
                                            fraction.numerator, fraction.denominator);
         }
         return multiply(fraction.reciprocal());
     }
 
     /**
      * Divide the fraction by an integer.
      * @param i the {@code integer} to divide by.
      * @return this * i
      */
     public Fraction divide(final int i) {
         return divide(new Fraction(i));
     }
 
     /**
      * Gets the fraction percentage as a {@code double}. This calculates the
      * fraction as the numerator divided by denominator multiplied by 100.
      *
      * @return the fraction percentage as a {@code double}.
      */
     public double percentageValue() {
         return 100 * doubleValue();
     }
 
     /**
      * Creates a {@code Fraction} instance with the 2 parts
      * of a fraction Y/Z.
      * <p>
      * Any negative signs are resolved to be on the numerator.
      *
      * @param numerator  the numerator, for example the three in 'three sevenths'
      * @param denominator  the denominator, for example the seven in 'three sevenths'
      * @return a new fraction instance, with the numerator and denominator reduced
      * @throws MathRuntimeException if the denominator is {@code zero}
      */
     public static Fraction getReducedFraction(int numerator, int denominator) {
         if (denominator == 0) {
             throw new MathRuntimeException(LocalizedCoreFormats.ZERO_DENOMINATOR_IN_FRACTION,
                                            numerator, denominator);
         }
         if (numerator==0) {
             return ZERO; // normalize zero.
         }
         // allow 2^k/-2^31 as a valid fraction (where k>0)
         if (denominator==Integer.MIN_VALUE && (numerator&1)==0) {
             numerator/=2; denominator/=2;
         }
         if (denominator < 0) {
             if (numerator==Integer.MIN_VALUE ||
                 denominator==Integer.MIN_VALUE) {
                 throw new MathRuntimeException(LocalizedCoreFormats.OVERFLOW_IN_FRACTION,
                                                numerator, denominator);
             }
             numerator = -numerator;
             denominator = -denominator;
         }
         // simplify fraction.
         int gcd = ArithmeticUtils.gcd(numerator, denominator);
         numerator /= gcd;
         denominator /= gcd;
         return new Fraction(numerator, denominator);
     }
 
     /**
      * Returns the {@code String} representing this fraction, ie
      * "num / dem" or just "num" if the denominator is one.
      *
      * @return a string representation of the fraction.
      * @see java.lang.Object#toString()
      */
     @Override
     public String toString() {
         if (denominator == 1) {
             return Integer.toString(numerator);
         } else if (numerator == 0) {
             return "0";
         } else {
             return numerator + " / " + denominator;
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public FractionField getField() {
         return FractionField.getInstance();
     }
 
 }