spire.algebra

RingAlgebra

trait RingAlgebra[V, R] extends Module[V, R] with Rng[V]

A RingAlgebra is a module that is also a Rng. An example is the Gaussian numbers.

Linear Supertypes
Rng[V], Semiring[V], MultiplicativeSemigroup[V], Module[V, R], AdditiveAbGroup[V], AdditiveCMonoid[V], AdditiveCSemigroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], AnyRef, Any
Known Subclasses
FieldAlgebra, MapInnerProductSpace, MapRng, MapVectorSpace, PolynomialEuclideanRing, PolynomialRing, PolynomialRng, ZAlgebra
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. RingAlgebra
  2. Rng
  3. Semiring
  4. MultiplicativeSemigroup
  5. Module
  6. AdditiveAbGroup
  7. AdditiveCMonoid
  8. AdditiveCSemigroup
  9. AdditiveGroup
  10. AdditiveMonoid
  11. AdditiveSemigroup
  12. AnyRef
  13. Any
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Visibility
  1. Public
  2. All

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: Rng[R]

    Definition Classes
    Module

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

    Definition Classes
    MultiplicativeSemigroup

  5. abstract def timesl(r: R, 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. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  8. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  9. def finalize(): Unit

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

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

    Definition Classes
    AnyRef → Any

  11. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  12. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    AdditiveGroup

  14. def multiplicative: Semigroup[V]

    Definition Classes
    MultiplicativeSemigroup

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

    Definition Classes
    AnyRef

  16. final def notify(): Unit

    Definition Classes
    AnyRef

  17. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  18. 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

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

    Definition Classes
    AnyRef

  20. def timesr(v: V, r: R): V

    Definition Classes
    Module

  21. def toString(): String

    Definition Classes
    AnyRef → Any

  22. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Rng[V]

Inherited from Semiring[V]

Inherited from MultiplicativeSemigroup[V]

Inherited from Module[V, R]

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

Ungrouped