Value Members

1.  final def !=(arg0: Any): Boolean

   Definition Classes

   AnyRef → Any

2.  final def ##(): Int

   Definition Classes

   AnyRef → Any

3.  final def ==(arg0: Any): Boolean

   Definition Classes

   AnyRef → Any

4.  def abs(a: Rational): Rational

   An idempotent function that ensures an object has a non-negative sign.

   An idempotent function that ensures an object has a non-negative sign.

   Definition Classes

   RationalIsReal → Signed

5.  def additive: AbGroup[Rational]

   Definition Classes

   AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

6.  final def asInstanceOf[T0]: T0

   Definition Classes

   Any

7.  def ceil(a: Rational): Rational

   Rounds a the nearest integer that is greater than or equal to a.

   Rounds a the nearest integer that is greater than or equal to a.

   Definition Classes

   RationalIsReal → IsReal

8.  def clone(): AnyRef

   Attributes

   protected[java.lang]

   Definition Classes

   AnyRef

   Annotations

   @throws( ... )

9.  def compare(x: Rational, y: Rational): Int

   Definition Classes

   RationalIsReal → Order

10.  def div(a: Rational, b: Rational): Rational

    Definition Classes

    RationalIsField → MultiplicativeGroup

11.  final def eq(arg0: AnyRef): Boolean

    Definition Classes

    AnyRef

12.  def equals(arg0: Any): Boolean

    Definition Classes

    AnyRef → Any

13.  def eqv(x: Rational, y: Rational): Boolean

    Returns true if x and y are equivalent, false otherwise.

    Returns true if x and y are equivalent, false otherwise.

    Definition Classes

    RationalIsReal → Order → PartialOrder → Eq

14.  final def euclid(a: Rational, b: Rational)(implicit eq: Eq[Rational]): Rational

    Attributes

    protected[this]

    Definition Classes

    EuclideanRing

    Annotations

    @tailrec()

15.  def finalize(): Unit

    Attributes

    protected[java.lang]

    Definition Classes

    AnyRef

    Annotations

    @throws( classOf[java.lang.Throwable] )

16.  def floor(a: Rational): Rational

    Rounds a the nearest integer that is less than or equal to a.

    Rounds a the nearest integer that is less than or equal to a.

    Definition Classes

    RationalIsReal → IsReal

17.  def fromDouble(n: Double): Rational

    This is implemented in terms of basic Field ops.

    This is implemented in terms of basic Field ops. However, this is probably significantly less efficient than can be done with a specific type. So, it is recommended that this method is overriden.

    This is possible because a Double is a rational number.

    Definition Classes

    RationalIsField → Field

18.  def fromInt(n: Int): Rational

    Defined to be equivalent to additive.sumn(one, n).

    Defined to be equivalent to additive.sumn(one, n). That is, n repeated summations of this ring's one, or -one if n is negative.

    Definition Classes

    RationalIsField → Ring

19.  def gcd(a: Rational, b: Rational): Rational

    Definition Classes

    RationalIsField → EuclideanRing

20.  final def getClass(): Class[_]

    Definition Classes

    AnyRef → Any

21.  def gt(x: Rational, y: Rational): Boolean

    Definition Classes

    RationalIsReal → Order → PartialOrder

22.  def gteqv(x: Rational, y: Rational): Boolean

    Definition Classes

    RationalIsReal → Order → PartialOrder

23.  def hashCode(): Int

    Definition Classes

    AnyRef → Any

24.  final def isInstanceOf[T0]: Boolean

    Definition Classes

    Any

25.  def isOne(a: Rational)(implicit ev: Eq[Rational]): Boolean

    Definition Classes

    MultiplicativeMonoid

26.  def isSignNegative(a: Rational): Boolean

    Definition Classes

    Signed

27.  def isSignNonNegative(a: Rational): Boolean

    Definition Classes

    Signed

28.  def isSignNonPositive(a: Rational): Boolean

    Definition Classes

    Signed

29.  def isSignNonZero(a: Rational): Boolean

    Definition Classes

    Signed

30.  def isSignPositive(a: Rational): Boolean

    Definition Classes

    Signed

31.  def isSignZero(a: Rational): Boolean

    Definition Classes

    Signed

32.  def isWhole(a: Rational): Boolean

    Returns true iff a is a an integer.

    Returns true iff a is a an integer.

    Definition Classes

    RationalIsReal → IsReal

33.  def isZero(a: Rational)(implicit ev: Eq[Rational]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes

    AdditiveMonoid

34.  def lcm(a: Rational, b: Rational): Rational

    Definition Classes

    EuclideanRing

35.  def lt(x: Rational, y: Rational): Boolean

    Definition Classes

    RationalIsReal → Order → PartialOrder

36.  def lteqv(x: Rational, y: Rational): Boolean

    Definition Classes

    RationalIsReal → Order → PartialOrder

37.  def max(x: Rational, y: Rational): Rational

    Definition Classes

    Order

38.  def min(x: Rational, y: Rational): Rational

    Definition Classes

    Order

39.  def minus(a: Rational, b: Rational): Rational

    Definition Classes

    RationalIsField → AdditiveGroup

40.  def mod(a: Rational, b: Rational): Rational

    Definition Classes

    RationalIsField → EuclideanRing

41.  def multiplicative: AbGroup[Rational]

    Definition Classes

    MultiplicativeAbGroup → MultiplicativeCMonoid → MultiplicativeCSemigroup → MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup

42.  final def ne(arg0: AnyRef): Boolean

    Definition Classes

    AnyRef

43.  def negate(a: Rational): Rational

    Definition Classes

    RationalIsField → AdditiveGroup

44.  def neqv(x: Rational, y: Rational): Boolean

    Returns false if x and y are equivalent, true otherwise.

    Returns false if x and y are equivalent, true otherwise.

    Definition Classes

    RationalIsReal → Eq

45.  final def notify(): Unit

    Definition Classes

    AnyRef

46.  final def notifyAll(): Unit

    Definition Classes

    AnyRef

47.  def on[B](f: (B) ⇒ Rational): Order[B]

    Defines an order on B by mapping B to A using f and using As order to order B.

    Defines an order on B by mapping B to A using f and using As order to order B.

    Definition Classes

    Order → PartialOrder → Eq

48.  def one: Rational

    Definition Classes

    RationalIsField → MultiplicativeMonoid

49.  def partialCompare(x: Rational, y: Rational): Double

    Result of comparing x with y.

    Result of comparing x with y. Returns NaN if operands are not comparable. If operands are comparable, returns a Double whose sign is: - negative iff x < y - zero iff x === y - positive iff x > y

    Definition Classes

    Order → PartialOrder

50.  def plus(a: Rational, b: Rational): Rational

    Definition Classes

    RationalIsField → AdditiveSemigroup

51.  def pmax(x: Rational, y: Rational): Option[Rational]

    Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.

    Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.

    Definition Classes

    PartialOrder

52.  def pmin(x: Rational, y: Rational): Option[Rational]

    Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.

    Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.

    Definition Classes

    PartialOrder

53.  def pow(a: Rational, b: Int): Rational

    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    This is similar to Semigroup#pow, except that a pow 0 is defined to be the multiplicative identity.

    Definition Classes

    RationalIsField → Rig → Semiring

54.  def prod(as: TraversableOnce[Rational]): Rational

    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes

    MultiplicativeMonoid

55.  def prodOption(as: TraversableOnce[Rational]): Option[Rational]

    Given a sequence of as, sum them using the semigroup and return the total.

    Given a sequence of as, sum them using the semigroup and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes

    MultiplicativeSemigroup

56.  def prodn(a: Rational, n: Int): Rational

    Return a multiplicated with itself n times.

    Return a multiplicated with itself n times.

    Definition Classes

    MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup

57.  def prodnAboveOne(a: Rational, n: Int): Rational

    Attributes

    protected

    Definition Classes

    MultiplicativeSemigroup

58.  def quot(a: Rational, b: Rational): Rational

    Definition Classes

    RationalIsField → EuclideanRing

59.  def quotmod(a: Rational, b: Rational): (Rational, Rational)

    Definition Classes

    RationalIsField → EuclideanRing

60.  def reciprocal(x: Rational): Rational

    Definition Classes

    MultiplicativeGroup

61.  def reverse: Order[Rational]

    Defines an ordering on A where all arrows switch direction.

    Defines an ordering on A where all arrows switch direction.

    Definition Classes

    Order → PartialOrder

62.  def round(a: Rational): Rational

    Rounds a to the nearest integer.

    Rounds a to the nearest integer.

    Definition Classes

    RationalIsReal → IsReal

63.  def sign(a: Rational): Sign

    Returns Zero if a is 0, Positive if a is positive, and Negative is a is negative.

    Returns Zero if a is 0, Positive if a is positive, and Negative is a is negative.

    Definition Classes

    RationalIsReal → Signed

64.  def signum(a: Rational): Int

    Returns 0 if a is 0, > 0 if a is positive, and < 0 is a is negative.

    Returns 0 if a is 0, > 0 if a is positive, and < 0 is a is negative.

    Definition Classes

    RationalIsReal → Signed

65.  def sum(as: TraversableOnce[Rational]): Rational

    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes

    AdditiveMonoid

66.  def sumOption(as: TraversableOnce[Rational]): Option[Rational]

    Given a sequence of as, sum them using the semigroup and return the total.

    Given a sequence of as, sum them using the semigroup and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes

    AdditiveSemigroup

67.  def sumn(a: Rational, n: Int): Rational

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes

    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

68.  def sumnAboveOne(a: Rational, n: Int): Rational

    Attributes

    protected

    Definition Classes

    AdditiveSemigroup

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

    Definition Classes

    AnyRef

70.  def times(a: Rational, b: Rational): Rational

    Definition Classes

    RationalIsField → MultiplicativeSemigroup

71.  def toAlgebraic(a: Rational): Algebraic

    Definition Classes

    IsRational → IsAlgebraic

72.  def toDouble(r: Rational): Double

    Approximates a as a Double.

    Approximates a as a Double.

    Definition Classes

    RationalIsReal → IsReal

73.  def toRational(a: Rational): Rational

    Definition Classes

    RationalIsReal → IsRational

74.  def toReal(a: Rational): Real

    Definition Classes

    IsAlgebraic → IsReal

75.  def toString(): String

    Definition Classes

    AnyRef → Any

76.  def tryCompare(x: Rational, y: Rational): Option[Int]

    Result of comparing x with y.

    Result of comparing x with y. Returns None if operands are not comparable. If operands are comparable, returns Some[Int] where the Int sign is: - negative iff x < y - zero iff x == y - positive iff x > y

    Definition Classes

    PartialOrder

77.  final def wait(): Unit

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

78.  final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

79.  final def wait(arg0: Long): Unit

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

80.  def zero: Rational

    Definition Classes

    RationalIsField → AdditiveMonoid