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: Natural): Natural

   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

   NaturalIsSigned → Signed

5.  def additive: Monoid[Natural]

   Definition Classes

   AdditiveMonoid → AdditiveSemigroup

6.  final def asInstanceOf[T0]: T0

   Definition Classes

   Any

7.  def ceil(a: Natural): Natural

   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

   IsIntegral → IsReal

8.  def clone(): AnyRef

   Attributes

   protected[java.lang]

   Definition Classes

   AnyRef

   Annotations

   @throws( ... )

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

   Definition Classes

   NaturalOrder → Order

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

    Definition Classes

    AnyRef

11.  def equals(arg0: Any): Boolean

    Definition Classes

    AnyRef → Any

12.  def eqv(x: Natural, y: Natural): Boolean

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

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

    Definition Classes

    NaturalOrder → Order → PartialOrder → Eq

13.  def finalize(): Unit

    Attributes

    protected[java.lang]

    Definition Classes

    AnyRef

    Annotations

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

14.  def floor(a: Natural): Natural

    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

    IsIntegral → IsReal

15.  final def getClass(): Class[_]

    Definition Classes

    AnyRef → Any

16.  def gt(x: Natural, y: Natural): Boolean

    Definition Classes

    NaturalOrder → Order → PartialOrder

17.  def gteqv(x: Natural, y: Natural): Boolean

    Definition Classes

    NaturalOrder → Order → PartialOrder

18.  def hashCode(): Int

    Definition Classes

    AnyRef → Any

19.  final def isInstanceOf[T0]: Boolean

    Definition Classes

    Any

20.  def isOne(a: Natural)(implicit ev: Eq[Natural]): Boolean

    Definition Classes

    MultiplicativeMonoid

21.  def isSignNegative(a: Natural): Boolean

    Definition Classes

    Signed

22.  def isSignNonNegative(a: Natural): Boolean

    Definition Classes

    Signed

23.  def isSignNonPositive(a: Natural): Boolean

    Definition Classes

    Signed

24.  def isSignNonZero(a: Natural): Boolean

    Definition Classes

    Signed

25.  def isSignPositive(a: Natural): Boolean

    Definition Classes

    Signed

26.  def isSignZero(a: Natural): Boolean

    Definition Classes

    Signed

27.  def isWhole(a: Natural): Boolean

    Returns true iff a is a an integer.

    Returns true iff a is a an integer.

    Definition Classes

    IsIntegral → IsReal

28.  def isZero(a: Natural)(implicit ev: Eq[Natural]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes

    AdditiveMonoid

29.  def lt(x: Natural, y: Natural): Boolean

    Definition Classes

    NaturalOrder → Order → PartialOrder

30.  def lteqv(x: Natural, y: Natural): Boolean

    Definition Classes

    NaturalOrder → Order → PartialOrder

31.  def max(x: Natural, y: Natural): Natural

    Definition Classes

    Order

32.  def min(x: Natural, y: Natural): Natural

    Definition Classes

    Order

33.  def multiplicative: Monoid[Natural]

    Definition Classes

    MultiplicativeMonoid → MultiplicativeSemigroup

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

    Definition Classes

    AnyRef

35.  def neqv(x: Natural, y: Natural): Boolean

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

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

    Definition Classes

    NaturalOrder → Eq

36.  final def notify(): Unit

    Definition Classes

    AnyRef

37.  final def notifyAll(): Unit

    Definition Classes

    AnyRef

38.  def on[B](f: (B) ⇒ Natural): 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

39.  def one: Natural

    Definition Classes

    NaturalIsRig → MultiplicativeMonoid

40.  def partialCompare(x: Natural, y: Natural): 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

41.  def plus(a: Natural, b: Natural): Natural

    Definition Classes

    NaturalIsRig → AdditiveSemigroup

42.  def pmax(x: Natural, y: Natural): Option[Natural]

    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

43.  def pmin(x: Natural, y: Natural): Option[Natural]

    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

44.  def pow(a: Natural, b: Int): Natural

    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

    NaturalIsRig → Rig → Semiring

45.  def prod(as: TraversableOnce[Natural]): Natural

    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

46.  def prodOption(as: TraversableOnce[Natural]): Option[Natural]

    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

47.  def prodn(a: Natural, n: Int): Natural

    Return a multiplied with itself n times.

    Return a multiplied with itself n times.

    Definition Classes

    MultiplicativeMonoid → MultiplicativeSemigroup

48.  def prodnAboveOne(a: Natural, n: Int): Natural

    Attributes

    protected

    Definition Classes

    MultiplicativeSemigroup

49.  def reverse: Order[Natural]

    Defines an ordering on A where all arrows switch direction.

    Defines an ordering on A where all arrows switch direction.

    Definition Classes

    Order → PartialOrder

50.  def round(a: Natural): Natural

    Rounds a to the nearest integer.

    Rounds a to the nearest integer.

    Definition Classes

    IsIntegral → IsReal

51.  def sign(a: Natural): 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

    Signed

52.  def signum(a: Natural): 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

    NaturalIsSigned → Signed

53.  def sum(as: TraversableOnce[Natural]): Natural

    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

54.  def sumOption(as: TraversableOnce[Natural]): Option[Natural]

    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

55.  def sumn(a: Natural, n: Int): Natural

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes

    AdditiveMonoid → AdditiveSemigroup

56.  def sumnAboveOne(a: Natural, n: Int): Natural

    Attributes

    protected

    Definition Classes

    AdditiveSemigroup

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

    Definition Classes

    AnyRef

58.  def times(a: Natural, b: Natural): Natural

    Definition Classes

    NaturalIsRig → MultiplicativeSemigroup

59.  def toAlgebraic(a: Natural): Algebraic

    Definition Classes

    IsRational → IsAlgebraic

60.  def toBigInt(n: Natural): BigInt

    Definition Classes

    NaturalIsReal → IsIntegral

61.  def toDouble(n: Natural): Double

    Approximates a as a Double.

    Approximates a as a Double.

    Definition Classes

    NaturalIsReal → IsReal

62.  def toRational(a: Natural): Rational

    Definition Classes

    IsIntegral → IsRational

63.  def toReal(a: Natural): Real

    Definition Classes

    IsAlgebraic → IsReal

64.  def toString(): String

    Definition Classes

    AnyRef → Any

65.  def tryCompare(x: Natural, y: Natural): 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

66.  final def wait(): Unit

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

69.  def zero: Natural

    Definition Classes

    NaturalIsRig → AdditiveMonoid