scalation.math

Rational

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
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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
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  1. Public
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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. final def ##(): Int

    Definition Classes
    AnyRef → Any
  3. def *(l: Long): Rational

    Multiply a rational number times a long.

    Multiply a rational number times a long.

    l

    multiply this times long l

  4. def *(q: Rational): Rational

    Multiply two rational numbers (this * q).

    Multiply two rational numbers (this * q).

    q

    multiply this times rational q

  5. def +(l: Long): Rational

    Add a rational number plus a long.

    Add a rational number plus a long.

    l

    add long l to this

  6. def +(q: Rational): Rational

    Add two rational numbers (this + q)

    Add two rational numbers (this + q)

    q

    add rational q to this

  7. def -(l: Long): Rational

    Subtract: a rational number minus a long.

    Subtract: a rational number minus a long.

    l

    subtract long l from this

  8. def -(q: Rational): Rational

    Subtract two rational numbers (this - q).

    Subtract two rational numbers (this - q).

    q

    subtract rational q from this

  9. def /(l: Long): Rational

    Divide a rational number div a long.

    Divide a rational number div a long.

    l

    divide this by long l

  10. def /(q: Rational): Rational

    Divide two rational numbers (this / q)

    Divide two rational numbers (this / q)

    q

    divide this by rational q

  11. def <(that: Rational): Boolean

    Definition Classes
    Ordered
  12. def <=(that: Rational): Boolean

    Definition Classes
    Ordered
  13. final def ==(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  14. def >(that: Rational): Boolean

    Definition Classes
    Ordered
  15. def >=(that: Rational): Boolean

    Definition Classes
    Ordered
  16. def abs: Rational

    Return the absolute value of this rational number.

  17. def abs(x: Rational): Rational

    Definition Classes
    Numeric
  18. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  19. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  20. 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
  21. 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
  22. def compareTo(that: Rational): Int

    Definition Classes
    Ordered → Comparable
  23. val den: Long

    the denominator (e.

    the denominator (e.g., 3)

  24. def div(q: Rational, l: Long): Rational

  25. def div(q: Rational, p: Rational): Rational

    Definition Classes
    Rational → Fractional
  26. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  27. 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
  28. def equiv(x: Rational, y: Rational): Boolean

    Definition Classes
    Ordering → PartialOrdering → Equiv
  29. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  30. 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

  31. def fromDouble(y: Double): Rational

    Create a rational number from a Double.

    Create a rational number from a Double.

    y

    the Double used to create the rational number

  32. def fromFloat(y: Float): Rational

    Create a rational number from a Float.

    Create a rational number from a Float.

    y

    the Float 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
  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. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  40. def isIntegral: Boolean

    Determine whether this rational number is integral.

  41. def lt(x: Rational, y: Rational): Boolean

    Definition Classes
    Ordering → PartialOrdering
  42. def lteq(x: Rational, y: Rational): Boolean

    Definition Classes
    Ordering → PartialOrdering
  43. 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

  44. def max(x: Rational, y: Rational): Rational

    Definition Classes
    Ordering
  45. 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

  46. def min(x: Rational, y: Rational): Rational

    Definition Classes
    Ordering
  47. def minus(q: Rational, l: Long): Rational

  48. def minus(q: Rational, p: Rational): Rational

    Definition Classes
    Rational → Numeric
  49. implicit def mkNumericOps(lhs: Rational): FractionalOps

    Definition Classes
    Fractional → Numeric
  50. implicit def mkOrderingOps(lhs: Rational): Rational.Ops

    Definition Classes
    Ordering
  51. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  52. def negate(q: Rational): Rational

    Definition Classes
    Rational → Numeric
  53. final def notify(): Unit

    Definition Classes
    AnyRef
  54. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  55. val num: Long

    the numerator (e.

    the numerator (e.g., 2)

  56. def on[U](f: (U) ⇒ Rational): Ordering[U]

    Definition Classes
    Ordering
  57. def one: Rational

    Definition Classes
    Numeric
  58. def plus(q: Rational, l: Long): Rational

  59. def plus(q: Rational, p: Rational): Rational

    Definition Classes
    Rational → Numeric
  60. def pow(q: Rational, l: Long): Rational

  61. def pow(q: Rational, p: Rational): Rational

  62. def reduce(): Rational

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

  63. def reverse: Ordering[Rational]

    Definition Classes
    Ordering → PartialOrdering
  64. def reversed(): Comparator[Rational]

    Definition Classes
    Comparator
  65. def root(q: Rational, l: Long): Rational

  66. def signum(x: Rational): Int

    Definition Classes
    Numeric
  67. def sqrt: Rational

    Return the square root of that rational number.

  68. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  69. def thenComparing[U <: Comparable[_ >: U]](arg0: Function[_ >: Rational, _ <: U]): Comparator[Rational]

    Definition Classes
    Comparator
  70. def thenComparing[U](arg0: Function[_ >: Rational, _ <: U], arg1: Comparator[_ >: U]): Comparator[Rational]

    Definition Classes
    Comparator
  71. def thenComparing(arg0: Comparator[_ >: Rational]): Comparator[Rational]

    Definition Classes
    Comparator
  72. def thenComparingDouble(arg0: ToDoubleFunction[_ >: Rational]): Comparator[Rational]

    Definition Classes
    Comparator
  73. def thenComparingInt(arg0: ToIntFunction[_ >: Rational]): Comparator[Rational]

    Definition Classes
    Comparator
  74. def thenComparingLong(arg0: ToLongFunction[_ >: Rational]): Comparator[Rational]

    Definition Classes
    Comparator
  75. def times(q: Rational, l: Long): Rational

  76. def times(q: Rational, p: Rational): Rational

    Definition Classes
    Rational → Numeric
  77. def toBigDecimal: BigDecimal

  78. 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

  79. def toDouble: Double

  80. 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
  81. def toFloat: Float

  82. 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
  83. def toInt: Int

  84. 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
  85. def toLong: Long

  86. 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
  87. 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
  88. def toString2: String

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

  89. def tryCompare(x: Rational, y: Rational): Some[Int]

    Definition Classes
    Ordering → PartialOrdering
  90. def unary_-(): Rational

    Compute the unary minus (-).

  91. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  92. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  93. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  94. def zero: Rational

    Definition Classes
    Numeric
  95. 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

  96. 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

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