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 → Ordering

Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any
  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: AnyRef): Boolean

    Definition Classes
    AnyRef
  15. final def ==(arg0: Any): Boolean

    Definition Classes
    Any
  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
    @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

    the denominator (e.

    the denominator (e.g., 3)

  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 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

  34. 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

  35. 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
  36. 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

  37. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  38. def gt(x: Rational, y: Rational): Boolean

    Definition Classes
    Ordering → PartialOrdering
  39. def gteq(x: Rational, y: Rational): Boolean

    Definition Classes
    Ordering → PartialOrdering
  40. 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
  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 negate(q: Rational): Rational

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

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

    Definition Classes
    AnyRef
  57. val num: Long

    the numerator (e.

    the numerator (e.g., 2)

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

    Definition Classes
    Ordering
  59. def one: Rational

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

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

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

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

  64. def reduce(): Rational

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

  65. def reverse: Ordering[Rational]

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

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

  68. def signum(x: Rational): Int

    Definition Classes
    Numeric
  69. def sqrt: Rational

    Return the square root of that rational number.

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

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

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

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

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

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

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

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

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

    Definition Classes
    Rational → Numeric
  79. def toBigDecimal: BigDecimal

  80. 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

  81. def toDouble: Double

  82. 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
  83. def toFloat: Float

  84. 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
  85. def toInt: Int

  86. 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
  87. def toLong: Long

  88. 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
  89. 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
  90. def toString2: String

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

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

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

    Compute the unary minus (-).

  93. final def wait(): Unit

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

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

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

    Definition Classes
    Numeric
  97. 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

  98. 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