Packages

case class Rational(num: Long, den: Long = 1l) extends Fractional[Rational] with Ordered[Rational] with Product with Serializable

The Rational class is used to represent and operate on rational numbers. Internally, a rational number is represented as two long integers. Externally, two forms are supported:

a/b = 2/3 via: Rational ("2/3"), 'toString' (a, b) = (2, 3) via: create ("(2, 3)") 'toString2'

Rational number can be created without loss of precision using the constructor, 'apply', 'create' or 'fromBigDecimal' methods. Other methods may lose precision.

num

the numerator (e.g., 2)

den

the denominator (e.g., 3)

Linear Supertypes
Product, Equals, Ordered[Rational], Comparable[Rational], Fractional[Rational], Numeric[Rational], Ordering[Rational], PartialOrdering[Rational], Equiv[Rational], Serializable, Serializable, Comparator[Rational], AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Rational
  2. Product
  3. Equals
  4. Ordered
  5. Comparable
  6. Fractional
  7. Numeric
  8. Ordering
  9. PartialOrdering
  10. Equiv
  11. Serializable
  12. Serializable
  13. Comparator
  14. AnyRef
  15. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Instance Constructors

  1. new Rational(num: Long, den: Long = 1l)

    num

    the numerator (e.g., 2)

    den

    the denominator (e.g., 3)

Type Members

  1. class FractionalOps extends scala.math.Fractional.Ops
    Definition Classes
    Fractional
  2. class Ops extends AnyRef
    Definition Classes
    Numeric

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. def !=~(q: Rational): Boolean

    Return whether two rational numbers are not nearly equal.

    Return whether two rational numbers are not nearly equal.

    q

    the compare 'this' with q

  3. final def ##(): Int
    Definition Classes
    AnyRef → Any
  4. def *(l: Long): Rational

    Multiply a rational number times a long.

    Multiply a rational number times a long.

    l

    multiply this times long l

  5. def *(q: Rational): Rational

    Multiply two rational numbers 'this * q'.

    Multiply two rational numbers 'this * q'.

    q

    multiply this times rational q

  6. def +(l: Long): Rational

    Add a rational number plus a long.

    Add a rational number plus a long.

    l

    add long l to this

  7. def +(q: Rational): Rational

    Add two rational numbers 'this + q'.

    Add two rational numbers 'this + q'.

    q

    add rational q to this

  8. def -(l: Long): Rational

    Subtract: a rational number minus a long.

    Subtract: a rational number minus a long.

    l

    subtract long l from this

  9. def -(q: Rational): Rational

    Subtract two rational numbers 'this - q'.

    Subtract two rational numbers 'this - q'.

    q

    subtract rational q from this

  10. def /(l: Long): Rational

    Divide a rational number div a long.

    Divide a rational number div a long.

    l

    divide this by long l

  11. def /(q: Rational): Rational

    Divide two rational numbers 'this / q'.

    Divide two rational numbers 'this / q'.

    q

    divide this by rational q

  12. def <(that: Rational): Boolean
    Definition Classes
    Ordered
  13. def <=(that: Rational): Boolean
    Definition Classes
    Ordered
  14. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  15. def =~(q: Rational): Boolean

    Return whether two rational numbers are nearly equal.

    Return whether two rational numbers are nearly equal.

    q

    the compare 'this' with q

  16. def >(that: Rational): Boolean
    Definition Classes
    Ordered
  17. def >=(that: Rational): Boolean
    Definition Classes
    Ordered
  18. def abs: Rational

    Return the absolute value of this rational number.

  19. def abs(x: Rational): Rational
    Definition Classes
    Numeric
  20. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  21. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  22. def compare(q: Rational): Int

    Compare this rational number with that rational number 'q'.

    Compare this rational number with that rational number 'q'.

    q

    that rational number

    Definition Classes
    Rational → Ordered
  23. def compare(q: Rational, p: Rational): Int

    Compare two rational numbers (negative for <, zero for ==, positive for >).

    Compare two rational numbers (negative for <, zero for ==, positive for >).

    q

    the first rational number to compare

    p

    the second rational number to compare

    Definition Classes
    Rational → Ordering → Comparator
  24. def compareTo(that: Rational): Int
    Definition Classes
    Ordered → Comparable
  25. val den: Long
  26. def div(q: Rational, l: Long): Rational
  27. def div(q: Rational, p: Rational): Rational
    Definition Classes
    Rational → Fractional
  28. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  29. def equals(c: Any): Boolean

    Override equals to determine whether this rational number equals rational 'c'.

    Override equals to determine whether this rational number equals rational 'c'.

    c

    the rational number to compare with this

    Definition Classes
    Rational → Equals → Comparator → AnyRef → Any
  30. def equiv(x: Rational, y: Rational): Boolean
    Definition Classes
    Ordering → PartialOrdering → Equiv
  31. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  32. def fromBigDecimal(y: BigDecimal): Rational

    Create a rational number from a BigDecimal number.

    Create a rational number from a BigDecimal number.

    y

    the BigDecimal used to create the rational number

  33. def fromInt(n: Int): Rational

    Create a rational number from an Int.

    Create a rational number from an Int.

    n

    the Int used to create the rational number

    Definition Classes
    Rational → Numeric
  34. def fromLong(n: Long): Rational

    Create a rational number from a Long.

    Create a rational number from a Long.

    n

    the Long used to create the rational number

  35. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  36. def gt(x: Rational, y: Rational): Boolean
    Definition Classes
    Ordering → PartialOrdering
  37. def gteq(x: Rational, y: Rational): Boolean
    Definition Classes
    Ordering → PartialOrdering
  38. def hashCode(): Int

    Must also override hashCode to be be compatible with equals.

    Must also override hashCode to be be compatible with equals.

    Definition Classes
    Rational → AnyRef → Any
  39. def in(set: Set[Rational]): Boolean

    Determine whether 'this' is in the given set.

  40. def in(lim: (Rational, Rational)): Boolean

    Determine whether 'this' is within the given bounds

    Determine whether 'this' is within the given bounds

    lim

    the given (lower, upper) bounds

  41. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  42. def isIntegral: Boolean

    Determine whether this rational number is integral.

  43. def lt(x: Rational, y: Rational): Boolean
    Definition Classes
    Ordering → PartialOrdering
  44. def lteq(x: Rational, y: Rational): Boolean
    Definition Classes
    Ordering → PartialOrdering
  45. def max(q: Rational): Rational

    Return the maximum of this and that rational numbers.

    Return the maximum of this and that rational numbers.

    q

    that rational number to compare with this

  46. def max(x: Rational, y: Rational): Rational
    Definition Classes
    Ordering
  47. def min(q: Rational): Rational

    Return the minimum of this and that rational numbers.

    Return the minimum of this and that rational numbers.

    q

    that rational number to compare with this

  48. def min(x: Rational, y: Rational): Rational
    Definition Classes
    Ordering
  49. def minus(q: Rational, l: Long): Rational
  50. def minus(q: Rational, p: Rational): Rational
    Definition Classes
    Rational → Numeric
  51. implicit def mkNumericOps(lhs: Rational): FractionalOps
    Definition Classes
    Fractional → Numeric
  52. implicit def mkOrderingOps(lhs: Rational): Rational.Ops
    Definition Classes
    Ordering
  53. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  54. def near_eq(q: Rational, p: Rational): Boolean
  55. def negate(q: Rational): Rational
    Definition Classes
    Rational → Numeric
  56. def not_in(set: Set[Rational]): Boolean

    Determine whether 'this' is not in the given set.

  57. def not_in(lim: (Rational, Rational)): Boolean

    Determine whether 'this' is not within the given bounds

    Determine whether 'this' is not within the given bounds

    lim

    the given (lower, upper) bounds

  58. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  59. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  60. val num: Long
  61. def on[U](f: (U) ⇒ Rational): Ordering[U]
    Definition Classes
    Ordering
  62. def one: Rational
    Definition Classes
    Numeric
  63. def plus(q: Rational, l: Long): Rational
  64. def plus(q: Rational, p: Rational): Rational
    Definition Classes
    Rational → Numeric
  65. def pow(q: Rational, l: Long): Rational
  66. def pow(q: Rational, p: Rational): Rational
  67. def reduce(): Rational

    Reduce the magnitude of the numerator and denonimator by dividing both by their Greatest Common Divisor (GCD).

  68. def reverse: Ordering[Rational]
    Definition Classes
    Ordering → PartialOrdering
  69. def reversed(): Comparator[Rational]
    Definition Classes
    Comparator
  70. def root(q: Rational, l: Long): Rational

    Take the 'l'-th root of the rational number 'q'.

    Take the 'l'-th root of the rational number 'q'.

    l

    the long root

  71. def signum(x: Rational): Int
    Definition Classes
    Numeric
  72. def sqrt: Rational

    Return the square root of that rational number.

  73. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  74. def thenComparing[U <: Comparable[_ >: U]](arg0: Function[_ >: Rational, _ <: U]): Comparator[Rational]
    Definition Classes
    Comparator
  75. def thenComparing[U](arg0: Function[_ >: Rational, _ <: U], arg1: Comparator[_ >: U]): Comparator[Rational]
    Definition Classes
    Comparator
  76. def thenComparing(arg0: Comparator[_ >: Rational]): Comparator[Rational]
    Definition Classes
    Comparator
  77. def thenComparingDouble(arg0: ToDoubleFunction[_ >: Rational]): Comparator[Rational]
    Definition Classes
    Comparator
  78. def thenComparingInt(arg0: ToIntFunction[_ >: Rational]): Comparator[Rational]
    Definition Classes
    Comparator
  79. def thenComparingLong(arg0: ToLongFunction[_ >: Rational]): Comparator[Rational]
    Definition Classes
    Comparator
  80. def times(q: Rational, l: Long): Rational
  81. def times(q: Rational, p: Rational): Rational
    Definition Classes
    Rational → Numeric
  82. def toBigDecimal: BigDecimal
  83. def toBigDecimal(q: Rational): BigDecimal

    Convert that/this rational number to a BigDecimal number.

    Convert that/this rational number to a BigDecimal number.

    q

    that rational number to convert

  84. def toDouble: Double
  85. def toDouble(q: Rational): Double

    Convert that/this rational number to a Double.

    Convert that/this rational number to a Double.

    q

    that rational number to convert

    Definition Classes
    Rational → Numeric
  86. def toFloat: Float
  87. def toFloat(q: Rational): Float

    Convert that/this rational number to a Float.

    Convert that/this rational number to a Float.

    q

    that rational number to convert

    Definition Classes
    Rational → Numeric
  88. def toInt: Int
  89. def toInt(q: Rational): Int

    Convert that/this rational number to an Int.

    Convert that/this rational number to an Int.

    q

    that rational number to convert

    Definition Classes
    Rational → Numeric
  90. def toLong: Long
  91. def toLong(q: Rational): Long

    Convert this rational number to a Long.

    Convert this rational number to a Long.

    q

    that rational number to convert

    Definition Classes
    Rational → Numeric
  92. def toRational: Rational
  93. def toRational(q: Rational): Rational

    Convert that/this rational number to a Rational.

    Convert that/this rational number to a Rational.

    q

    that rational number to convert

  94. def toString(): String

    Convert this rational number to a String of the form 'a/b'.

    Convert this rational number to a String of the form 'a/b'.

    Definition Classes
    Rational → AnyRef → Any
  95. def toString2: String

    Convert this rational number to a String of the form '(a, b)'.

  96. def tryCompare(x: Rational, y: Rational): Some[Int]
    Definition Classes
    Ordering → PartialOrdering
  97. def unary_-(): Rational

    Compute the unary minus (-).

  98. val val1: Long

    General alias for the parts of a complex number

  99. val val2: Long

    General alias for the parts of a complex number

  100. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  101. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  102. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  103. def zero: Rational
    Definition Classes
    Numeric
  104. def ~^(l: Long): Rational

    Raise a rational number to the 'l'-th power.

    Raise a rational number to the 'l'-th power.

    l

    the long power/exponent

  105. def ~^(q: Rational): Rational

    Raise a rational number to the 'q'-th power.

    Raise a rational number to the 'q'-th power.

    q

    the rational power/exponent

  106. def ↑(l: Long): Rational
  107. def ∈(set: Set[Rational]): Boolean
  108. def ∈(lim: (Rational, Rational)): Boolean
  109. def ∉(set: Set[Rational]): Boolean
  110. def ∉(lim: (Rational, Rational)): Boolean
  111. def ≈(q: Rational): Boolean
  112. def ≉(q: Rational): Boolean
  113. def ≠(q: Rational): Boolean

    Compare 'this' rational number with that rational number 'q' for inequality.

    Compare 'this' rational number with that rational number 'q' for inequality.

    q

    that rational number

  114. def ≤(q: Rational): Boolean

    Compare 'this' rational number with that rational number 'q' for less than or equal to.

    Compare 'this' rational number with that rational number 'q' for less than or equal to.

    q

    that rational number

  115. def ≥(q: Rational): Boolean

    Compare 'this' rational number with that rational number 'q' for greater than or equal to.

    Compare 'this' rational number with that rational number 'q' for greater than or equal to.

    q

    that rational number

Inherited from Product

Inherited from Equals

Inherited from Ordered[Rational]

Inherited from Comparable[Rational]

Inherited from Fractional[Rational]

Inherited from Numeric[Rational]

Inherited from Ordering[Rational]

Inherited from PartialOrdering[Rational]

Inherited from Equiv[Rational]

Inherited from Serializable

Inherited from Serializable

Inherited from Comparator[Rational]

Inherited from AnyRef

Inherited from Any

Ungrouped