NaturalAlgebra

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