spire.algebra

Field

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

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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. AnyRef
  21. Any
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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 mod(a: A, b: A): A

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

    Definition Classes
    AdditiveGroup
  5. abstract def one: A

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

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

    Definition Classes
    EuclideanRing
  8. abstract def times(x: A, y: A): A

    Definition Classes
    MultiplicativeSemigroup
  9. abstract def zero: A

    Definition Classes
    AdditiveMonoid

Concrete Value Members

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

    Definition Classes
    AnyRef
  2. final def !=(arg0: Any): Boolean

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

    Definition Classes
    AnyRef → Any
  4. final def ==(arg0: AnyRef): Boolean

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

    Definition Classes
    Any
  6. def additive: AbGroup[A]

  7. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  8. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  9. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  10. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  11. final def euclid(a: A, b: A)(implicit eq: Eq[A]): A

    Attributes
    protected[this]
    Definition Classes
    EuclideanRing
    Annotations
    @tailrec()
  12. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  13. 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.

  14. 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
  15. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  16. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  17. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  18. def lcm(a: A, b: A): A

    Definition Classes
    EuclideanRing
  19. def minus(x: A, y: A): A

    Definition Classes
    AdditiveGroup
  20. def multiplicative: AbGroup[A]

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

    Definition Classes
    AnyRef
  22. final def notify(): Unit

    Definition Classes
    AnyRef
  23. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  24. 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
    RigSemiring
  25. def quotmod(a: A, b: A): (A, A)

    Definition Classes
    EuclideanRing
  26. def reciprocal(x: A): A

    Definition Classes
    MultiplicativeGroup
  27. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  28. def toString(): String

    Definition Classes
    AnyRef → Any
  29. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  30. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  31. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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 AnyRef

Inherited from Any

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