spire.math

Integral

trait Integral[A] extends EuclideanRing[A] with ConvertableFrom[A] with ConvertableTo[A] with IsReal[A]

Linear Supertypes
IsReal[A], Signed[A], Order[A], PartialOrder[A], Eq[A], ConvertableTo[A], ConvertableFrom[A], EuclideanRing[A], GCDRing[A], CommutativeRing[A], CommutativeRng[A], CommutativeRig[A], MultiplicativeCommutativeMonoid[A], CommutativeSemiring[A], MultiplicativeCommutativeSemigroup[A], Ring[A], Rng[A], AdditiveCommutativeGroup[A], AdditiveGroup[A], Rig[A], MultiplicativeMonoid[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveCommutativeMonoid[A], AdditiveCommutativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Serializable, Serializable, Any
Known Subclasses
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Inherited
  1. Integral
  2. IsReal
  3. Signed
  4. Order
  5. PartialOrder
  6. Eq
  7. ConvertableTo
  8. ConvertableFrom
  9. EuclideanRing
  10. GCDRing
  11. CommutativeRing
  12. CommutativeRng
  13. CommutativeRig
  14. MultiplicativeCommutativeMonoid
  15. CommutativeSemiring
  16. MultiplicativeCommutativeSemigroup
  17. Ring
  18. Rng
  19. AdditiveCommutativeGroup
  20. AdditiveGroup
  21. Rig
  22. MultiplicativeMonoid
  23. Semiring
  24. MultiplicativeSemigroup
  25. AdditiveCommutativeMonoid
  26. AdditiveCommutativeSemigroup
  27. AdditiveMonoid
  28. AdditiveSemigroup
  29. Serializable
  30. Serializable
  31. Any
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Abstract Value Members

  1. abstract def abs(a: A): A

    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
    Signed
  2. abstract def ceil(a: A): A

    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
    IsReal
  3. abstract def compare(x: A, y: A): Int

    Definition Classes
    Order
  4. abstract def euclideanFunction(a: A): BigInt

    Definition Classes
    EuclideanRing
  5. abstract def floor(a: A): A

    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
    IsReal
  6. abstract def fromAlgebraic(n: Algebraic): A

    Definition Classes
    ConvertableTo
  7. abstract def fromBigDecimal(n: BigDecimal): A

    Definition Classes
    ConvertableTo
  8. abstract def fromByte(n: Byte): A

    Definition Classes
    ConvertableTo
  9. abstract def fromDouble(n: Double): A

    Definition Classes
    ConvertableTo
  10. abstract def fromFloat(n: Float): A

    Definition Classes
    ConvertableTo
  11. abstract def fromLong(n: Long): A

    Definition Classes
    ConvertableTo
  12. abstract def fromRational(n: Rational): A

    Definition Classes
    ConvertableTo
  13. abstract def fromReal(n: Real): A

    Definition Classes
    ConvertableTo
  14. abstract def fromShort(n: Short): A

    Definition Classes
    ConvertableTo
  15. abstract def fromType[B](b: B)(implicit arg0: ConvertableFrom[B]): A

    Definition Classes
    ConvertableTo
  16. abstract def getClass(): Class[_]

    Definition Classes
    Any
  17. abstract def isWhole(a: A): Boolean

    Returns true iff a is a an integer.

    Returns true iff a is a an integer.

    Definition Classes
    IsReal
  18. abstract def mod(a: A, b: A): A

    Definition Classes
    EuclideanRing
  19. abstract def negate(x: A): A

    Definition Classes
    AdditiveGroup
  20. abstract def one: A

    Definition Classes
    MultiplicativeMonoid
  21. abstract def plus(x: A, y: A): A

    Definition Classes
    AdditiveSemigroup
  22. abstract def quot(a: A, b: A): A

    Definition Classes
    EuclideanRing
  23. abstract def round(a: A): A

    Rounds a to the nearest integer.

    Rounds a to the nearest integer.

    Definition Classes
    IsReal
  24. abstract def signum(a: A): 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
    Signed
  25. abstract def times(x: A, y: A): A

    Definition Classes
    MultiplicativeSemigroup
  26. abstract def toAlgebraic(a: A): Algebraic

    Definition Classes
    ConvertableFrom
  27. abstract def toBigDecimal(a: A): BigDecimal

    Definition Classes
    ConvertableFrom
  28. abstract def toBigInt(a: A): BigInt

    Definition Classes
    ConvertableFrom
  29. abstract def toByte(a: A): Byte

    Definition Classes
    ConvertableFrom
  30. abstract def toDouble(a: A): Double

    Approximates a as a Double.

    Approximates a as a Double.

    Definition Classes
    IsReal
  31. abstract def toFloat(a: A): Float

    Definition Classes
    ConvertableFrom
  32. abstract def toInt(a: A): Int

    Definition Classes
    ConvertableFrom
  33. abstract def toLong(a: A): Long

    Definition Classes
    ConvertableFrom
  34. abstract def toNumber(a: A): Number

    Definition Classes
    ConvertableFrom
  35. abstract def toRational(a: A): Rational

    Definition Classes
    ConvertableFrom
  36. abstract def toReal(a: A): Real

    Definition Classes
    IsReal
  37. abstract def toShort(a: A): Short

    Definition Classes
    ConvertableFrom
  38. abstract def toString(a: A): String

    Definition Classes
    ConvertableFrom
  39. abstract def toType[B](a: A)(implicit arg0: ConvertableTo[B]): B

    Definition Classes
    ConvertableFrom
  40. abstract def zero: A

    Definition Classes
    AdditiveMonoid

Concrete Value Members

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

    Definition Classes
    Any
  2. final def ##(): Int

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

    Definition Classes
    Any
  4. def additive: CommutativeGroup[A]

    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
  5. def and(that: Eq[A]): Eq[A]

    Definition Classes
    Eq
  6. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  7. def comparison(x: A, y: A): Comparison

    Definition Classes
    Order
  8. def equals(arg0: Any): Boolean

    Definition Classes
    Any
  9. def eqv(x: A, y: A): Boolean

    Definition Classes
    Order → PartialOrder → Eq
  10. def fromBigInt(n: BigInt): A

    Definition Classes
    Ring
  11. def fromInt(n: Int): A

    Definition Classes
    Ring
  12. def gcd(a: A, b: A)(implicit ev: Eq[A]): A

    Definition Classes
    EuclideanRingGCDRing
  13. def gt(x: A, y: A): Boolean

    Definition Classes
    Order → PartialOrder
  14. def gteqv(x: A, y: A): Boolean

    Definition Classes
    Order → PartialOrder
  15. def hashCode(): Int

    Definition Classes
    Any
  16. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  17. def isOne(a: A)(implicit ev: Eq[A]): Boolean

    Definition Classes
    MultiplicativeMonoid
  18. def isSignNegative(a: A): Boolean

    Definition Classes
    Signed
  19. def isSignNonNegative(a: A): Boolean

    Definition Classes
    Signed
  20. def isSignNonPositive(a: A): Boolean

    Definition Classes
    Signed
  21. def isSignNonZero(a: A): Boolean

    Definition Classes
    Signed
  22. def isSignPositive(a: A): Boolean

    Definition Classes
    Signed
  23. def isSignZero(a: A): Boolean

    Definition Classes
    Signed
  24. def isZero(a: A)(implicit ev: Eq[A]): Boolean

    Definition Classes
    AdditiveMonoid
  25. def lcm(a: A, b: A)(implicit ev: Eq[A]): A

    Definition Classes
    EuclideanRingGCDRing
  26. def lt(x: A, y: A): Boolean

    Definition Classes
    Order → PartialOrder
  27. def lteqv(x: A, y: A): Boolean

    Definition Classes
    Order → PartialOrder
  28. def max(x: A, y: A): A

    Definition Classes
    Order
  29. def min(x: A, y: A): A

    Definition Classes
    Order
  30. def minus(x: A, y: A): A

    Definition Classes
    AdditiveGroup
  31. def multiplicative: CommutativeMonoid[A]

    Definition Classes
    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup
  32. def neqv(x: A, y: A): Boolean

    Definition Classes
    Order → Eq
  33. def on[B](f: (B) ⇒ A): Order[B]

    Definition Classes
    Order → PartialOrder → Eq
  34. def or(that: Eq[A]): Eq[A]

    Definition Classes
    Eq
  35. def partialCompare(x: A, y: A): Double

    Definition Classes
    Order → PartialOrder
  36. def partialComparison(x: A, y: A): Option[Comparison]

    Definition Classes
    PartialOrder
  37. def pmax(x: A, y: A): Option[A]

    Definition Classes
    PartialOrder
  38. def pmin(x: A, y: A): Option[A]

    Definition Classes
    PartialOrder
  39. def positivePow(a: A, n: Int): A

    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup
  40. def positiveSumN(a: A, n: Int): A

    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup
  41. def pow(a: A, n: Int): A

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup
  42. def product(as: TraversableOnce[A]): A

    Definition Classes
    MultiplicativeMonoid
  43. def quotmod(a: A, b: A): (A, A)

    Definition Classes
    EuclideanRing
  44. def reverse: Order[A]

    Definition Classes
    Order → PartialOrder
  45. def sign(a: A): 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
  46. def sum(as: TraversableOnce[A]): A

    Definition Classes
    AdditiveMonoid
  47. def sumN(a: A, n: Int): A

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
  48. def toOrdering: Ordering[A]

    Definition Classes
    Order
  49. def toString(): String

    Definition Classes
    Any
  50. def tryCompare(x: A, y: A): Option[Int]

    Definition Classes
    PartialOrder
  51. def tryProduct(as: TraversableOnce[A]): Option[A]

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup
  52. def trySum(as: TraversableOnce[A]): Option[A]

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup
  53. def whenEqual(o: Order[A]): Order[A]

    Definition Classes
    Order

Inherited from IsReal[A]

Inherited from Signed[A]

Inherited from Order[A]

Inherited from PartialOrder[A]

Inherited from Eq[A]

Inherited from ConvertableTo[A]

Inherited from ConvertableFrom[A]

Inherited from EuclideanRing[A]

Inherited from GCDRing[A]

Inherited from CommutativeRing[A]

Inherited from CommutativeRng[A]

Inherited from CommutativeRig[A]

Inherited from MultiplicativeCommutativeMonoid[A]

Inherited from CommutativeSemiring[A]

Inherited from MultiplicativeCommutativeSemigroup[A]

Inherited from Ring[A]

Inherited from Rng[A]

Inherited from AdditiveCommutativeGroup[A]

Inherited from AdditiveGroup[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveCommutativeMonoid[A]

Inherited from AdditiveCommutativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped