org.apache.commons.math3.fraction

## Class BigFraction

- java.lang.Object
- - java.lang.Number
  - - org.apache.commons.math3.fraction.BigFraction

- All Implemented Interfaces:
    Serializable, Comparable<BigFraction>, FieldElement<BigFraction>

      public class BigFraction
      extends Number
      implements FieldElement<BigFraction>, Comparable<BigFraction>, Serializable

  Representation of a rational number without any overflow. This class is immutable.
  Since:
    2.0
  Version:
    $Id: BigFraction.java 1547633 2013-12-03 23:03:06Z tn $
  See Also:
    Serialized Form

- - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `static BigFraction` | `FOUR_FIFTHS` A fraction representing "4/5".
    `static BigFraction` | `MINUS_ONE` A fraction representing "-1 / 1".
    `static BigFraction` | `ONE` A fraction representing "1".
    `static BigFraction` | `ONE_FIFTH` A fraction representing "1/5".
    `static BigFraction` | `ONE_HALF` A fraction representing "1/2".
    `static BigFraction` | `ONE_QUARTER` A fraction representing "1/4".
    `static BigFraction` | `ONE_THIRD` A fraction representing "1/3".
    `static BigFraction` | `THREE_FIFTHS` A fraction representing "3/5".
    `static BigFraction` | `THREE_QUARTERS` A fraction representing "3/4".
    `static BigFraction` | `TWO` A fraction representing "2 / 1".
    `static BigFraction` | `TWO_FIFTHS` A fraction representing "2/5".
    `static BigFraction` | `TWO_QUARTERS` A fraction representing "2/4".
    `static BigFraction` | `TWO_THIRDS` A fraction representing "2/3".
    `static BigFraction` | `ZERO` A fraction representing "0".

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `BigFraction(BigInteger num)` Create a `BigFraction` equivalent to the passed `BigInteger`, ie "num / 1".
    `BigFraction(BigInteger num, BigInteger den)` Create a `BigFraction` given the numerator and denominator as `BigInteger`.
    `BigFraction(double value)` Create a fraction given the double value.
    `BigFraction(double value, double epsilon, int maxIterations)` Create a fraction given the double value and maximum error allowed.
    `BigFraction(double value, int maxDenominator)` Create a fraction given the double value and maximum denominator.
    `BigFraction(int num)` Create a `BigFraction` equivalent to the passed `int`, ie "num / 1".
    `BigFraction(int num, int den)` Create a `BigFraction` given the numerator and denominator as simple `int`.
    `BigFraction(long num)` Create a `BigFraction` equivalent to the passed long, ie "num / 1".
    `BigFraction(long num, long den)` Create a `BigFraction` given the numerator and denominator as simple `long`.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `BigFraction` | `abs()` Returns the absolute value of this `BigFraction`.
    `BigFraction` | `add(BigFraction fraction)` Adds the value of this fraction to another, returning the result in reduced form.
    `BigFraction` | `add(BigInteger bg)` Adds the value of this fraction to the passed `BigInteger`, returning the result in reduced form.
    `BigFraction` | `add(int i)` Adds the value of this fraction to the passed `integer`, returning the result in reduced form.
    `BigFraction` | `add(long l)` Adds the value of this fraction to the passed `long`, returning the result in reduced form.
    `BigDecimal` | `bigDecimalValue()` Gets the fraction as a `BigDecimal`.
    `BigDecimal` | `bigDecimalValue(int roundingMode)` Gets the fraction as a `BigDecimal` following the passed rounding mode.
    `BigDecimal` | `bigDecimalValue(int scale, int roundingMode)` Gets the fraction as a `BigDecimal` following the passed scale and rounding mode.
    `int` | `compareTo(BigFraction object)` Compares this object to another based on size.
    `BigFraction` | `divide(BigFraction fraction)` Divide the value of this fraction by another, returning the result in reduced form.
    `BigFraction` | `divide(BigInteger bg)` Divide the value of this fraction by the passed `BigInteger`, ie `this * 1 / bg`, returning the result in reduced form.
    `BigFraction` | `divide(int i)` Divide the value of this fraction by the passed `int`, ie `this * 1 / i`, returning the result in reduced form.
    `BigFraction` | `divide(long l)` Divide the value of this fraction by the passed `long`, ie `this * 1 / l`, returning the result in reduced form.
    `double` | `doubleValue()` Gets the fraction as a `double`.
    `boolean` | `equals(Object other)` Test for the equality of two fractions.
    `float` | `floatValue()` Gets the fraction as a `float`.
    `BigInteger` | `getDenominator()` Access the denominator as a `BigInteger`.
    `int` | `getDenominatorAsInt()` Access the denominator as a `int`.
    `long` | `getDenominatorAsLong()` Access the denominator as a `long`.
    `BigFractionField` | `getField()` Get the `Field` to which the instance belongs.
    `BigInteger` | `getNumerator()` Access the numerator as a `BigInteger`.
    `int` | `getNumeratorAsInt()` Access the numerator as a `int`.
    `long` | `getNumeratorAsLong()` Access the numerator as a `long`.
    `static BigFraction` | `getReducedFraction(int numerator, int denominator)` Creates a `BigFraction` instance with the 2 parts of a fraction Y/Z.
    `int` | `hashCode()` Gets a hashCode for the fraction.
    `int` | `intValue()` Gets the fraction as an `int`.
    `long` | `longValue()` Gets the fraction as a `long`.
    `BigFraction` | `multiply(BigFraction fraction)` Multiplies the value of this fraction by another, returning the result in reduced form.
    `BigFraction` | `multiply(BigInteger bg)` Multiplies the value of this fraction by the passed `BigInteger`, returning the result in reduced form.
    `BigFraction` | `multiply(int i)` Multiply the value of this fraction by the passed `int`, returning the result in reduced form.
    `BigFraction` | `multiply(long l)` Multiply the value of this fraction by the passed `long`, returning the result in reduced form.
    `BigFraction` | `negate()` Return the additive inverse of this fraction, returning the result in reduced form.
    `double` | `percentageValue()` Gets the fraction percentage as a `double`.
    `BigFraction` | `pow(BigInteger exponent)` Returns a `BigFraction` whose value is `(thisexponent)`, returning the result in reduced form.
    `double` | `pow(double exponent)` Returns a `double` whose value is `(thisexponent)`, returning the result in reduced form.
    `BigFraction` | `pow(int exponent)` Returns a `BigFraction` whose value is `(this<sup>exponent</sup>)`, returning the result in reduced form.
    `BigFraction` | `pow(long exponent)` Returns a `BigFraction` whose value is `(thisexponent)`, returning the result in reduced form.
    `BigFraction` | `reciprocal()` Return the multiplicative inverse of this fraction.
    `BigFraction` | `reduce()` Reduce this `BigFraction` to its lowest terms.
    `BigFraction` | `subtract(BigFraction fraction)` Subtracts the value of another fraction from the value of this one, returning the result in reduced form.
    `BigFraction` | `subtract(BigInteger bg)` Subtracts the value of an `BigInteger` from the value of this `BigFraction`, returning the result in reduced form.
    `BigFraction` | `subtract(int i)` Subtracts the value of an `integer` from the value of this `BigFraction`, returning the result in reduced form.
    `BigFraction` | `subtract(long l)` Subtracts the value of a `long` from the value of this `BigFraction`, returning the result in reduced form.
    `String` | `toString()` Returns the `String` representing this fraction, ie "num / dem" or just "num" if the denominator is one.

    - ### Methods inherited from class java.lang.Number

      `byteValue, shortValue`

    - ### Methods inherited from class java.lang.Object

      `clone, finalize, getClass, notify, notifyAll, wait, wait, wait`

- - ### Field Detail

    - #### TWO

          public static final BigFraction TWO

      A fraction representing "2 / 1".

    - #### ONE

          public static final BigFraction ONE

      A fraction representing "1".

    - #### ZERO

          public static final BigFraction ZERO

      A fraction representing "0".

    - #### MINUS_ONE

          public static final BigFraction MINUS_ONE

      A fraction representing "-1 / 1".

    - #### FOUR_FIFTHS

          public static final BigFraction FOUR_FIFTHS

      A fraction representing "4/5".

    - #### ONE_FIFTH

          public static final BigFraction ONE_FIFTH

      A fraction representing "1/5".

    - #### ONE_HALF

          public static final BigFraction ONE_HALF

      A fraction representing "1/2".

    - #### ONE_QUARTER

          public static final BigFraction ONE_QUARTER

      A fraction representing "1/4".

    - #### ONE_THIRD

          public static final BigFraction ONE_THIRD

      A fraction representing "1/3".

    - #### THREE_FIFTHS

          public static final BigFraction THREE_FIFTHS

      A fraction representing "3/5".

    - #### THREE_QUARTERS

          public static final BigFraction THREE_QUARTERS

      A fraction representing "3/4".

    - #### TWO_FIFTHS

          public static final BigFraction TWO_FIFTHS

      A fraction representing "2/5".

    - #### TWO_QUARTERS

          public static final BigFraction TWO_QUARTERS

      A fraction representing "2/4".

    - #### TWO_THIRDS

          public static final BigFraction TWO_THIRDS

      A fraction representing "2/3".

  - ### Constructor Detail

    - #### BigFraction

          public BigFraction(BigInteger num)

      Create a `BigFraction` equivalent to the passed `BigInteger`, ie "num / 1".

      Parameters:
        `num` - the numerator.

    - #### BigFraction

          public BigFraction(BigInteger num,
                     BigInteger den)

      Create a `BigFraction` given the numerator and denominator as `BigInteger`. The `BigFraction` is reduced to lowest terms.
      Parameters:
        `num` - the numerator, must not be `null`.
        `den` - the denominator, must not be `null`.
      Throws:
        `ZeroException` - if the denominator is zero.
        `NullArgumentException` - if either of the arguments is null

    - #### BigFraction

          public BigFraction(double value)
                      throws MathIllegalArgumentException

      Create a fraction given the double value.

      This constructor behaves differently from `BigFraction(double, double, int)`. It converts the double value exactly, considering its internal bits representation. This works for all values except NaN and infinities and does not requires any loop or convergence threshold.

      Since this conversion is exact and since double numbers are sometimes approximated, the fraction created may seem strange in some cases. For example, calling `new BigFraction(1.0 / 3.0)` does not create the fraction 1/3, but the fraction 6004799503160661 / 18014398509481984 because the double number passed to the constructor is not exactly 1/3 (this number cannot be stored exactly in IEEE754).

      Parameters:
        `value` - the double value to convert to a fraction.
      Throws:
        `MathIllegalArgumentException` - if value is NaN or infinite
      See Also:
        `BigFraction(double, double, int)`

    - #### BigFraction

          public BigFraction(double value,
                     double epsilon,
                     int maxIterations)
                      throws FractionConversionException

      Create a fraction given the double value and maximum error allowed.

      References:

      - Continued Fraction equations (11) and (22)-(26)
      Parameters:
        `value` - the double value to convert to a fraction.
        `epsilon` - maximum error allowed. The resulting fraction is within `epsilon` of `value`, in absolute terms.
        `maxIterations` - maximum number of convergents.
      Throws:
        `FractionConversionException` - if the continued fraction failed to converge.
      See Also:
        `BigFraction(double)`

    - #### BigFraction

          public BigFraction(double value,
                     int maxDenominator)
                      throws FractionConversionException

      Create a fraction given the double value and maximum denominator.

      References:

      - Continued Fraction equations (11) and (22)-(26)
      Parameters:
        `value` - the double value to convert to a fraction.
        `maxDenominator` - The maximum allowed value for denominator.
      Throws:
        `FractionConversionException` - if the continued fraction failed to converge.

    - #### BigFraction

          public BigFraction(int num)

      Create a `BigFraction` equivalent to the passed `int`, ie "num / 1".

      Parameters:
        `num` - the numerator.

    - #### BigFraction

          public BigFraction(int num,
                     int den)

      Create a `BigFraction` given the numerator and denominator as simple `int`. The `BigFraction` is reduced to lowest terms.

      Parameters:
        `num` - the numerator.
        `den` - the denominator.

    - #### BigFraction

          public BigFraction(long num)

      Create a `BigFraction` equivalent to the passed long, ie "num / 1".

      Parameters:
        `num` - the numerator.

    - #### BigFraction

          public BigFraction(long num,
                     long den)

      Create a `BigFraction` given the numerator and denominator as simple `long`. The `BigFraction` is reduced to lowest terms.

      Parameters:
        `num` - the numerator.
        `den` - the denominator.

  - ### Method Detail

    - #### getReducedFraction

          public static BigFraction getReducedFraction(int numerator,
                                       int denominator)

      Creates a `BigFraction` instance with the 2 parts of a fraction Y/Z.

      Any negative signs are resolved to be on the numerator.

      Parameters:
        `numerator` - the numerator, for example the three in 'three sevenths'.
        `denominator` - the denominator, for example the seven in 'three sevenths'.
      Returns:
        a new fraction instance, with the numerator and denominator reduced.
      Throws:
        `ArithmeticException` - if the denominator is `zero`.

    - #### abs

          public BigFraction abs()

      Returns the absolute value of this `BigFraction`.

      Returns:
        the absolute value as a `BigFraction`.

    - #### add

          public BigFraction add(BigInteger bg)
                          throws NullArgumentException

      Adds the value of this fraction to the passed `BigInteger`, returning the result in reduced form.

      Parameters:
        `bg` - the `BigInteger` to add, must'nt be `null`.
      Returns:
        a `BigFraction` instance with the resulting values.
      Throws:
        `NullArgumentException` - if the `BigInteger` is `null`.

    - #### add

          public BigFraction add(int i)

      Adds the value of this fraction to the passed `integer`, returning the result in reduced form.

      Parameters:
        `i` - the `integer` to add.
      Returns:
        a `BigFraction` instance with the resulting values.

    - #### add

          public BigFraction add(long l)

      Adds the value of this fraction to the passed `long`, returning the result in reduced form.

      Parameters:
        `l` - the `long` to add.
      Returns:
        a `BigFraction` instance with the resulting values.

    - #### add

          public BigFraction add(BigFraction fraction)

      Adds the value of this fraction to another, returning the result in reduced form.

      Specified by:
        `add` in interface `FieldElement<BigFraction>`
      Parameters:
        `fraction` - the `BigFraction` to add, must not be `null`.
      Returns:
        a `BigFraction` instance with the resulting values.
      Throws:
        `NullArgumentException` - if the `BigFraction` is `null`.

    - #### bigDecimalValue

          public BigDecimal bigDecimalValue()

      Gets the fraction as a `BigDecimal`. This calculates the fraction as the numerator divided by denominator.

      Returns:
        the fraction as a `BigDecimal`.
      Throws:
        `ArithmeticException` - if the exact quotient does not have a terminating decimal expansion.
      See Also:
        `BigDecimal`

    - #### bigDecimalValue

          public BigDecimal bigDecimalValue(int roundingMode)

      Gets the fraction as a `BigDecimal` following the passed rounding mode. This calculates the fraction as the numerator divided by denominator.

      Parameters:
        `roundingMode` - rounding mode to apply. see `BigDecimal` constants.
      Returns:
        the fraction as a `BigDecimal`.
      Throws:
        `IllegalArgumentException` - if `roundingMode` does not represent a valid rounding mode.
      See Also:
        `BigDecimal`

    - #### bigDecimalValue

          public BigDecimal bigDecimalValue(int scale,
                                   int roundingMode)

      Gets the fraction as a `BigDecimal` following the passed scale and rounding mode. This calculates the fraction as the numerator divided by denominator.

      Parameters:
        `scale` - scale of the `BigDecimal` quotient to be returned. see `BigDecimal` for more information.
        `roundingMode` - rounding mode to apply. see `BigDecimal` constants.
      Returns:
        the fraction as a `BigDecimal`.
      See Also:
        `BigDecimal`

    - #### compareTo

          public int compareTo(BigFraction object)

      Compares this object to another based on size.

      Specified by:
        `compareTo` in interface `Comparable<BigFraction>`
      Parameters:
        `object` - the object to compare to, must not be `null`.
      Returns:
        -1 if this is less than `object`, +1 if this is greater than `object`, 0 if they are equal.
      See Also:
        `Comparable.compareTo(java.lang.Object)`

    - #### divide

          public BigFraction divide(BigInteger bg)

      Divide the value of this fraction by the passed `BigInteger`, ie `this * 1 / bg`, returning the result in reduced form.

      Parameters:
        `bg` - the `BigInteger` to divide by, must not be `null`
      Returns:
        a `BigFraction` instance with the resulting values
      Throws:
        `NullArgumentException` - if the `BigInteger` is `null`
        `MathArithmeticException` - if the fraction to divide by is zero

    - #### divide

          public BigFraction divide(int i)

      Divide the value of this fraction by the passed `int`, ie `this * 1 / i`, returning the result in reduced form.

      Parameters:
        `i` - the `int` to divide by
      Returns:
        a `BigFraction` instance with the resulting values
      Throws:
        `MathArithmeticException` - if the fraction to divide by is zero

    - #### divide

          public BigFraction divide(long l)

      Divide the value of this fraction by the passed `long`, ie `this * 1 / l`, returning the result in reduced form.

      Parameters:
        `l` - the `long` to divide by
      Returns:
        a `BigFraction` instance with the resulting values
      Throws:
        `MathArithmeticException` - if the fraction to divide by is zero

    - #### divide

          public BigFraction divide(BigFraction fraction)

      Divide the value of this fraction by another, returning the result in reduced form.

      Specified by:
        `divide` in interface `FieldElement<BigFraction>`
      Parameters:
        `fraction` - Fraction to divide by, must not be `null`.
      Returns:
        a `BigFraction` instance with the resulting values.
      Throws:
        `NullArgumentException` - if the `fraction` is `null`.
        `MathArithmeticException` - if the fraction to divide by is zero

    - #### doubleValue

          public double doubleValue()

      Gets the fraction as a `double`. This calculates the fraction as the numerator divided by denominator.

      Specified by:
        `doubleValue` in class `Number`
      Returns:
        the fraction as a `double`
      See Also:
        `Number.doubleValue()`

    - #### equals

          public boolean equals(Object other)

      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.

      Overrides:
        `equals` in class `Object`
      Parameters:
        `other` - fraction to test for equality to this fraction, can be `null`.
      Returns:
        true if two fractions are equal, false if object is `null`, not an instance of `BigFraction`, or not equal to this fraction instance.
      See Also:
        `Object.equals(java.lang.Object)`

    - #### floatValue

          public float floatValue()

      Gets the fraction as a `float`. This calculates the fraction as the numerator divided by denominator.

      Specified by:
        `floatValue` in class `Number`
      Returns:
        the fraction as a `float`.
      See Also:
        `Number.floatValue()`

    - #### getDenominator

          public BigInteger getDenominator()

      Access the denominator as a `BigInteger`.

      Returns:
        the denominator as a `BigInteger`.

    - #### getDenominatorAsInt

          public int getDenominatorAsInt()

      Access the denominator as a `int`.

      Returns:
        the denominator as a `int`.

    - #### getDenominatorAsLong

          public long getDenominatorAsLong()

      Access the denominator as a `long`.

      Returns:
        the denominator as a `long`.

    - #### getNumerator

          public BigInteger getNumerator()

      Access the numerator as a `BigInteger`.

      Returns:
        the numerator as a `BigInteger`.

    - #### getNumeratorAsInt

          public int getNumeratorAsInt()

      Access the numerator as a `int`.

      Returns:
        the numerator as a `int`.

    - #### getNumeratorAsLong

          public long getNumeratorAsLong()

      Access the numerator as a `long`.

      Returns:
        the numerator as a `long`.

    - #### hashCode

          public int hashCode()

      Gets a hashCode for the fraction.

      Overrides:
        `hashCode` in class `Object`
      Returns:
        a hash code value for this object.
      See Also:
        `Object.hashCode()`

    - #### intValue

          public int intValue()

      Gets the fraction as an `int`. This returns the whole number part of the fraction.

      Specified by:
        `intValue` in class `Number`
      Returns:
        the whole number fraction part.
      See Also:
        `Number.intValue()`

    - #### longValue

          public long longValue()

      Gets the fraction as a `long`. This returns the whole number part of the fraction.

      Specified by:
        `longValue` in class `Number`
      Returns:
        the whole number fraction part.
      See Also:
        `Number.longValue()`

    - #### multiply

          public BigFraction multiply(BigInteger bg)

      Multiplies the value of this fraction by the passed `BigInteger`, returning the result in reduced form.

      Parameters:
        `bg` - the `BigInteger` to multiply by.
      Returns:
        a `BigFraction` instance with the resulting values.
      Throws:
        `NullArgumentException` - if `bg` is `null`.

    - #### multiply

          public BigFraction multiply(int i)

      Multiply the value of this fraction by the passed `int`, returning the result in reduced form.

      Specified by:
        `multiply` in interface `FieldElement<BigFraction>`
      Parameters:
        `i` - the `int` to multiply by.
      Returns:
        a `BigFraction` instance with the resulting values.

    - #### multiply

          public BigFraction multiply(long l)

      Multiply the value of this fraction by the passed `long`, returning the result in reduced form.

      Parameters:
        `l` - the `long` to multiply by.
      Returns:
        a `BigFraction` instance with the resulting values.

    - #### multiply

          public BigFraction multiply(BigFraction fraction)

      Multiplies the value of this fraction by another, returning the result in reduced form.

      Specified by:
        `multiply` in interface `FieldElement<BigFraction>`
      Parameters:
        `fraction` - Fraction to multiply by, must not be `null`.
      Returns:
        a `BigFraction` instance with the resulting values.
      Throws:
        `NullArgumentException` - if `fraction` is `null`.

    - #### negate

          public BigFraction negate()

      Return the additive inverse of this fraction, returning the result in reduced form.

      Specified by:
        `negate` in interface `FieldElement<BigFraction>`
      Returns:
        the negation of this fraction.

    - #### percentageValue

          public double percentageValue()

      Gets the fraction percentage as a `double`. This calculates the fraction as the numerator divided by denominator multiplied by 100.

      Returns:
        the fraction percentage as a `double`.

    - #### pow

          public BigFraction pow(int exponent)

      Returns a `BigFraction` whose value is `(this<sup>exponent</sup>)`, returning the result in reduced form.

      Parameters:
        `exponent` - exponent to which this `BigFraction` is to be raised.
      Returns:
        `thisexponent`.

    - #### pow

          public BigFraction pow(long exponent)

      Returns a `BigFraction` whose value is `(thisexponent)`, returning the result in reduced form.

      Parameters:
        `exponent` - exponent to which this `BigFraction` is to be raised.
      Returns:
        `thisexponent` as a `BigFraction`.

    - #### pow

          public BigFraction pow(BigInteger exponent)

      Returns a `BigFraction` whose value is `(thisexponent)`, returning the result in reduced form.

      Parameters:
        `exponent` - exponent to which this `BigFraction` is to be raised.
      Returns:
        `thisexponent` as a `BigFraction`.

    - #### pow

          public double pow(double exponent)

      Returns a `double` whose value is `(thisexponent)`, returning the result in reduced form.

      Parameters:
        `exponent` - exponent to which this `BigFraction` is to be raised.
      Returns:
        `thisexponent`.

    - #### reciprocal

          public BigFraction reciprocal()

      Return the multiplicative inverse of this fraction.

      Specified by:
        `reciprocal` in interface `FieldElement<BigFraction>`
      Returns:
        the reciprocal fraction.

    - #### reduce

          public BigFraction reduce()

      Reduce this `BigFraction` to its lowest terms.

      Returns:
        the reduced `BigFraction`. It doesn't change anything if the fraction can be reduced.

    - #### subtract

          public BigFraction subtract(BigInteger bg)

      Subtracts the value of an `BigInteger` from the value of this `BigFraction`, returning the result in reduced form.

      Parameters:
        `bg` - the `BigInteger` to subtract, cannot be `null`.
      Returns:
        a `BigFraction` instance with the resulting values.
      Throws:
        `NullArgumentException` - if the `BigInteger` is `null`.

    - #### subtract

          public BigFraction subtract(int i)

      Subtracts the value of an `integer` from the value of this `BigFraction`, returning the result in reduced form.

      Parameters:
        `i` - the `integer` to subtract.
      Returns:
        a `BigFraction` instance with the resulting values.

    - #### subtract

          public BigFraction subtract(long l)

      Subtracts the value of a `long` from the value of this `BigFraction`, returning the result in reduced form.

      Parameters:
        `l` - the `long` to subtract.
      Returns:
        a `BigFraction` instance with the resulting values.

    - #### subtract

          public BigFraction subtract(BigFraction fraction)

      Subtracts the value of another fraction from the value of this one, returning the result in reduced form.

      Specified by:
        `subtract` in interface `FieldElement<BigFraction>`
      Parameters:
        `fraction` - `BigFraction` to subtract, must not be `null`.
      Returns:
        a `BigFraction` instance with the resulting values
      Throws:
        `NullArgumentException` - if the `fraction` is `null`.

    - #### toString

          public String toString()

      Returns the `String` representing this fraction, ie "num / dem" or just "num" if the denominator is one.

      Overrides:
        `toString` in class `Object`
      Returns:
        a string representation of the fraction.
      See Also:
        `Object.toString()`

    - #### getField

          public BigFractionField getField()

      Get the `Field` to which the instance belongs.
      Specified by:
        `getField` in interface `FieldElement<BigFraction>`
      Returns:
        `Field` to which the instance belongs

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