RationalAlgebra

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

   

   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

    

    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 isWhole(a: Rational): Boolean

    

    Definition Classes

    RationalIsReal → IsReal

26. def isZero(a: Rational): Boolean

    

    Definition Classes

    Signed

27. def lcm(a: Rational, b: Rational): Rational

    

    Definition Classes

    EuclideanRing

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

    

    Definition Classes

    RationalIsReal → Order → PartialOrder

29. def lteqv(x: Rational, y: Rational): Boolean

    

    Definition Classes

    RationalIsReal → Order → PartialOrder

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

    

    Definition Classes

    Order

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

    

    Definition Classes

    Order

32. def minus(a: Rational, b: Rational): Rational

    

    Definition Classes

    RationalIsField → AdditiveGroup

33. def mod(a: Rational, b: Rational): Rational

    

    Definition Classes

    RationalIsField → EuclideanRing

34. def multiplicative: AbGroup[Rational]

    

    Definition Classes

    MultiplicativeAbGroup → MultiplicativeCMonoid → MultiplicativeCSemigroup → MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup

35. final def ne(arg0: AnyRef): Boolean

    

    Definition Classes

    AnyRef

36. def negate(a: Rational): Rational

    

    Definition Classes

    RationalIsField → AdditiveGroup

37. 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

38. final def notify(): Unit

    

    Definition Classes

    AnyRef

39. final def notifyAll(): Unit

    

    Definition Classes

    AnyRef

40. 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

41. def one: Rational

    

    Definition Classes

    RationalIsField → MultiplicativeMonoid

42. 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

43. def plus(a: Rational, b: Rational): Rational

    

    Definition Classes

    RationalIsField → AdditiveSemigroup

44. 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

45. 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

46. 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

47. def quot(a: Rational, b: Rational): Rational

    

    Definition Classes

    RationalIsField → EuclideanRing

48. def quotmod(a: Rational, b: Rational): (Rational, Rational)

    

    Definition Classes

    RationalIsField → EuclideanRing

49. def reciprocal(x: Rational): Rational

    

    Definition Classes

    MultiplicativeGroup

50. 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

51. def round(a: Rational): Rational

    

    Definition Classes

    RationalIsReal → IsReal

52. 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

53. 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

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

    

    Definition Classes

    AnyRef

55. def times(a: Rational, b: Rational): Rational

    

    Definition Classes

    RationalIsField → MultiplicativeSemigroup

56. def toDouble(r: Rational): Double

    

    Definition Classes

    RationalIsReal → IsReal

57. def toString(): String

    

    Definition Classes

    AnyRef → Any

58. 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

59. def tryGt(x: Rational, y: Rational): Option[Boolean]

    

    Definition Classes

    PartialOrder

60. def tryGteqv(x: Rational, y: Rational): Option[Boolean]

    

    Definition Classes

    PartialOrder

61. def tryLt(x: Rational, y: Rational): Option[Boolean]

    

    Definition Classes

    PartialOrder

62. def tryLteqv(x: Rational, y: Rational): Option[Boolean]

    

    Definition Classes

    PartialOrder

63. final def wait(): Unit

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

65. final def wait(arg0: Long): Unit

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

66. def zero: Rational

    

    Definition Classes

    RationalIsField → AdditiveMonoid