spire.algebra

Semiring

trait Semiring[A] extends AdditiveMonoid[A] with MultiplicativeSemigroup[A]

Semiring is a ring without identities or an inverse. Thus, it has no negation, zero, or one.

A Semiring with an additive inverse (-) is a Rng. A Semiring with additive and multiplicative identities (0 and 1) is a Rig. A Semiring with all of the above is a Ring.

Linear Supertypes
MultiplicativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], AnyRef, Any
Known Subclasses
BigDecimalAlgebra, BigDecimalIsField, BigIntAlgebra, BigIntIsEuclideanRing, BooleanIsRig, BooleanStructure, ByteAlgebra, ByteIsEuclideanRing, CRig, CRing, ComplexIsNumeric, DistEuclideanRing, DistField, DistRig, DistRing, DistRng, DistSemiring, DoubleAlgebra, DoubleIsField, EuclideanRing, Field, FieldAlgebra, FloatAlgebra, FloatIsField, Fractional, IntAlgebra, IntIsEuclideanRing, Integral, LongAlgebra, LongIsEuclideanRing, MapInnerProductSpace, MapRng, MapVectorSpace, Numeric, PolynomialEuclideanRing, PolynomialRig, PolynomialRing, PolynomialRng, PolynomialSemiring, RealIsFractional, Rig, Ring, RingAlgebra, Rng, ShortAlgebra, ShortIsEuclideanRing, ZAlgebra
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Inherited
  1. Semiring
  2. MultiplicativeSemigroup
  3. AdditiveMonoid
  4. AdditiveSemigroup
  5. AnyRef
  6. Any
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Visibility
  1. Public
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Abstract Value Members

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

    Definition Classes
    AdditiveSemigroup

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

    Definition Classes
    MultiplicativeSemigroup

  3. abstract def zero: A

    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: Monoid[A]

    Definition Classes
    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 multiplicative: Semigroup[A]

    Definition Classes
    MultiplicativeSemigroup

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

    Definition Classes
    AnyRef

  15. final def notify(): Unit

    Definition Classes
    AnyRef

  16. final def notifyAll(): Unit

    Definition Classes
    AnyRef

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

    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.

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

    Definition Classes
    AnyRef

  19. def toString(): String

    Definition Classes
    AnyRef → Any

  20. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from AnyRef

Inherited from Any

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