spire.algebra

FieldAlgebra

trait FieldAlgebra[V, F] extends RingAlgebra[V, F] with VectorSpace[V, F]

A FieldAlgebra is a vector space that is also a Ring. An example is the complex numbers.

Linear Supertypes
VectorSpace[V, F], RingAlgebra[V, F], Rng[V], Semiring[V], MultiplicativeSemigroup[V], Module[V, F], AdditiveAbGroup[V], AdditiveCMonoid[V], AdditiveCSemigroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], AnyRef, Any
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Inherited
  1. FieldAlgebra
  2. VectorSpace
  3. RingAlgebra
  4. Rng
  5. Semiring
  6. MultiplicativeSemigroup
  7. Module
  8. AdditiveAbGroup
  9. AdditiveCMonoid
  10. AdditiveCSemigroup
  11. AdditiveGroup
  12. AdditiveMonoid
  13. AdditiveSemigroup
  14. AnyRef
  15. Any
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Abstract Value Members

  1. abstract def negate(x: V): V

    Definition Classes
    AdditiveGroup

  2. abstract def plus(x: V, y: V): V

    Definition Classes
    AdditiveSemigroup

  3. implicit abstract def scalar: Field[F]

    Definition Classes
    VectorSpace → Module

  4. abstract def times(x: V, y: V): V

    Definition Classes
    MultiplicativeSemigroup

  5. abstract def timesl(r: F, v: V): V

    Definition Classes
    Module

  6. abstract def zero: V

    Definition Classes
    AdditiveMonoid

Concrete 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 additive: AbGroup[V]

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

  5. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  6. def clone(): AnyRef

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

  7. def divr(v: V, f: F): V

    Definition Classes
    VectorSpace

  8. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  9. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  10. def finalize(): Unit

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

  11. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any

  12. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  13. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  14. def minus(x: V, y: V): V

    Definition Classes
    AdditiveGroup

  15. def multiplicative: Semigroup[V]

    Definition Classes
    MultiplicativeSemigroup

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

    Definition Classes
    AnyRef

  17. final def notify(): Unit

    Definition Classes
    AnyRef

  18. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  19. def pow(a: V, n: Int): V

    Returns a multiplied with itself n times.

    Returns a multiplied with itself n times. For instance, a pow 3 === a * a * a. Since this is a semiring, there is no notion of a multiplicative identity, and so the exponent must be positive.

    Definition Classes
    Semiring

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

    Definition Classes
    AnyRef

  21. def timesr(v: V, r: F): V

    Definition Classes
    Module

  22. def toString(): String

    Definition Classes
    AnyRef → Any

  23. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from VectorSpace[V, F]

Inherited from RingAlgebra[V, F]

Inherited from Rng[V]

Inherited from Semiring[V]

Inherited from MultiplicativeSemigroup[V]

Inherited from Module[V, F]

Inherited from AdditiveAbGroup[V]

Inherited from AdditiveCMonoid[V]

Inherited from AdditiveCSemigroup[V]

Inherited from AdditiveGroup[V]

Inherited from AdditiveMonoid[V]

Inherited from AdditiveSemigroup[V]

Inherited from AnyRef

Inherited from Any

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