spire.algebra

Field

trait Field[A] extends EuclideanRing[A] with MultiplicativeAbGroup[A]

Linear Supertypes
MultiplicativeAbGroup[A], MultiplicativeGroup[A], EuclideanRing[A], CRing[A], MultiplicativeCMonoid[A], MultiplicativeCSemigroup[A], Ring[A], Rng[A], AdditiveAbGroup[A], AdditiveCMonoid[A], AdditiveCSemigroup[A], AdditiveGroup[A], Rig[A], MultiplicativeMonoid[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Any
Known Subclasses
BigDecimalAlgebra, BigDecimalIsField, DistField, DoubleAlgebra, DoubleIsField, FloatAlgebra, FloatIsField, Fractional, RealAlgebra, RealIsFractional
Ordering
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Inherited
  1. Field
  2. MultiplicativeAbGroup
  3. MultiplicativeGroup
  4. EuclideanRing
  5. CRing
  6. MultiplicativeCMonoid
  7. MultiplicativeCSemigroup
  8. Ring
  9. Rng
  10. AdditiveAbGroup
  11. AdditiveCMonoid
  12. AdditiveCSemigroup
  13. AdditiveGroup
  14. Rig
  15. MultiplicativeMonoid
  16. Semiring
  17. MultiplicativeSemigroup
  18. AdditiveMonoid
  19. AdditiveSemigroup
  20. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def div(x: A, y: A): A

    Definition Classes
    MultiplicativeGroup

  2. abstract def gcd(a: A, b: A): A

    Definition Classes
    EuclideanRing

  3. abstract def getClass(): Class[_]

    Definition Classes
    Any

  4. abstract def mod(a: A, b: A): A

    Definition Classes
    EuclideanRing

  5. abstract def negate(x: A): A

    Definition Classes
    AdditiveGroup

  6. abstract def one: A

    Definition Classes
    MultiplicativeMonoid

  7. abstract def plus(x: A, y: A): A

    Definition Classes
    AdditiveSemigroup

  8. abstract def quot(a: A, b: A): A

    Definition Classes
    EuclideanRing

  9. abstract def times(x: A, y: A): A

    Definition Classes
    MultiplicativeSemigroup

  10. 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: AbGroup[A]

    Definition Classes
    AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  6. def equals(arg0: Any): Boolean

    Definition Classes
    Any

  7. final def euclid(a: A, b: A)(implicit eq: Eq[A]): A

    Attributes
    protected[this]
    Definition Classes
    EuclideanRing
    Annotations
    @tailrec()

  8. def fromDouble(a: Double): A

    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.

  9. def fromInt(n: Int): A

    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
    Ring

  10. def hashCode(): Int

    Definition Classes
    Any

  11. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  12. def isOne(a: A)(implicit ev: Eq[A]): Boolean

    Definition Classes
    MultiplicativeMonoid

  13. def isZero(a: A)(implicit ev: Eq[A]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid

  14. def lcm(a: A, b: A): A

    Definition Classes
    EuclideanRing

  15. def minus(x: A, y: A): A

    Definition Classes
    AdditiveGroup

  16. def multiplicative: AbGroup[A]

    Definition Classes
    MultiplicativeAbGroup → MultiplicativeCMonoid → MultiplicativeCSemigroup → MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup

  17. def pow(a: A, n: Int): A

    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
    Rig → Semiring

  18. def prod(as: TraversableOnce[A]): A

    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

  19. def prodOption(as: TraversableOnce[A]): Option[A]

    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

  20. def prodn(a: A, n: Int): A

    Return a multiplicated with itself n times.

    Return a multiplicated with itself n times.

    Definition Classes
    MultiplicativeGroup → MultiplicativeMonoid → MultiplicativeSemigroup

  21. def prodnAboveOne(a: A, n: Int): A

    Attributes
    protected
    Definition Classes
    MultiplicativeSemigroup

  22. def quotmod(a: A, b: A): (A, A)

    Definition Classes
    EuclideanRing

  23. def reciprocal(x: A): A

    Definition Classes
    MultiplicativeGroup

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

    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

  25. def sumOption(as: TraversableOnce[A]): Option[A]

    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

  26. def sumn(a: A, n: Int): A

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  27. def sumnAboveOne(a: A, n: Int): A

    Attributes
    protected
    Definition Classes
    AdditiveSemigroup

  28. def toString(): String

    Definition Classes
    Any

Inherited from MultiplicativeAbGroup[A]

Inherited from MultiplicativeGroup[A]

Inherited from EuclideanRing[A]

Inherited from CRing[A]

Inherited from MultiplicativeCMonoid[A]

Inherited from MultiplicativeCSemigroup[A]

Inherited from Ring[A]

Inherited from Rng[A]

Inherited from AdditiveAbGroup[A]

Inherited from AdditiveCMonoid[A]

Inherited from AdditiveCSemigroup[A]

Inherited from AdditiveGroup[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Any

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