Trait/Object

spire.math

Integral

Related Docs: object Integral | package math

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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
Ordering
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  2. By Inheritance
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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Visibility
  1. Public
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Abstract Value Members

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

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    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

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    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

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

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

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    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

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

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

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

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

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

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

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

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

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

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    Definition Classes
    ConvertableTo
  16. abstract def gcd(a: A, b: A)(implicit ev: Eq[A]): A

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    Definition Classes
    GCDRing
  17. abstract def getClass(): Class[_]

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

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    Returns true iff a is a an integer.

    Returns true iff a is a an integer.

    Definition Classes
    IsReal
  19. abstract def lcm(a: A, b: A)(implicit ev: Eq[A]): A

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    Definition Classes
    GCDRing
  20. abstract def mod(a: A, b: A): A

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

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    Definition Classes
    AdditiveGroup
  22. abstract def one: A

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

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

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

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    Rounds a to the nearest integer.

    Rounds a to the nearest integer.

    Definition Classes
    IsReal
  26. abstract def signum(a: A): Int

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    Returns 0 if a is 0, 1 if a is positive, and -1 is a is negative.

    Returns 0 if a is 0, 1 if a is positive, and -1 is a is negative.

    Definition Classes
    Signed
  27. abstract def times(x: A, y: A): A

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

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

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

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

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

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    Approximates a as a Double.

    Approximates a as a Double.

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

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

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

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

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

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

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

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

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

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    Definition Classes
    ConvertableFrom
  42. abstract def zero: A

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    Definition Classes
    AdditiveMonoid

Concrete Value Members

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

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

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

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

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

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

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

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

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

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

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

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    Definition Classes
    Ring
  12. def gt(x: A, y: A): Boolean

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

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

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

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

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

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

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

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

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

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

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

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    Definition Classes
    AdditiveMonoid
  24. def lt(x: A, y: A): Boolean

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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    Definition Classes
    Order → PartialOrder
  43. def sign(a: A): Sign

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    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
  44. def sum(as: TraversableOnce[A]): A

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

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

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    Definition Classes
    Order
  47. def toString(): String

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

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

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

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

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    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