spire.algebra

Rig

trait Rig[A] extends Semiring[A] with AdditiveMonoid[A] with MultiplicativeMonoid[A]

Rig is a ring whose additive structure doesn't have an inverse (ie. it is monoid, not a group). Put another way, a Rig is a Ring without a negative.

Linear Supertypes
Known Subclasses
BigDecimalIsEuclideanRing, BigDecimalIsEuclideanRing, BigDecimalIsField, BigDecimalIsField, BigDecimalIsFractional, BigDecimalIsFractional, BigDecimalIsNumeric, BigDecimalIsNumeric, BigDecimalIsRing, BigDecimalIsRing, BigIntIsEuclideanRing, BigIntIsEuclideanRing, BigIntIsIntegral, BigIntIsIntegral, BigIntIsNumeric, BigIntIsNumeric, BigIntIsRing, BigIntIsRing, BooleanIsRig, BooleanIsRig, ByteIsRing, ByteIsRing, ComplexIsEuclideanRing, ComplexIsField, ComplexIsInnerProductSpace, ComplexIsNumeric, ComplexIsRing, DoubleIsEuclideanRing, DoubleIsEuclideanRing, DoubleIsField, DoubleIsField, DoubleIsFractional, DoubleIsFractional, DoubleIsNumeric, DoubleIsNumeric, DoubleIsRing, DoubleIsRing, EuclideanRing, EuclideanRingProduct10, EuclideanRingProduct11, EuclideanRingProduct12, EuclideanRingProduct13, EuclideanRingProduct14, EuclideanRingProduct15, EuclideanRingProduct16, EuclideanRingProduct17, EuclideanRingProduct18, EuclideanRingProduct19, EuclideanRingProduct2, EuclideanRingProduct20, EuclideanRingProduct21, EuclideanRingProduct22, EuclideanRingProduct3, EuclideanRingProduct4, EuclideanRingProduct5, EuclideanRingProduct6, EuclideanRingProduct7, EuclideanRingProduct8, EuclideanRingProduct9, FPFilterIsEuclideanRing, FPFilterIsField, FPFilterIsFractional, FPFilterIsNumeric, FPFilterIsRing, Field, FieldProduct10, FieldProduct11, FieldProduct12, FieldProduct13, FieldProduct14, FieldProduct15, FieldProduct16, FieldProduct17, FieldProduct18, FieldProduct19, FieldProduct2, FieldProduct20, FieldProduct21, FieldProduct22, FieldProduct3, FieldProduct4, FieldProduct5, FieldProduct6, FieldProduct7, FieldProduct8, FieldProduct9, FloatIsEuclideanRing, FloatIsEuclideanRing, FloatIsField, FloatIsField, FloatIsFractional, FloatIsFractional, FloatIsNumeric, FloatIsNumeric, FloatIsRing, FloatIsRing, Fractional, GaussianIsEuclideanRing, GaussianIsNumeric, GaussianIsRing, IntIsEuclideanRing, IntIsEuclideanRing, IntIsIntegral, IntIsIntegral, IntIsNumeric, IntIsNumeric, IntIsRing, IntIsRing, Integral, LongIsEuclideanRing, LongIsEuclideanRing, LongIsIntegral, LongIsIntegral, LongIsNumeric, LongIsNumeric, LongIsRing, LongIsRing, NaturalIsRig, NaturalIsRig, NumberIsEuclideanRing, NumberIsEuclideanRing, NumberIsField, NumberIsField, NumberIsFractional, NumberIsFractional, NumberIsRing, NumberIsRing, Numeric, RationalIsEuclideanRing, RationalIsEuclideanRing, RationalIsField, RationalIsField, RationalIsFractional, RationalIsNumeric, RationalIsRing, RationalIsRing, RealIsEuclideanRing, RealIsEuclideanRing, RealIsField, RealIsField, RealIsFractional, RealIsFractional, RealIsNumeric, RealIsNumeric, RealIsRing, RealIsRing, RigProduct10, RigProduct11, RigProduct12, RigProduct13, RigProduct14, RigProduct15, RigProduct16, RigProduct17, RigProduct18, RigProduct19, RigProduct2, RigProduct20, RigProduct21, RigProduct22, RigProduct3, RigProduct4, RigProduct5, RigProduct6, RigProduct7, RigProduct8, RigProduct9, Ring, RingProduct10, RingProduct11, RingProduct12, RingProduct13, RingProduct14, RingProduct15, RingProduct16, RingProduct17, RingProduct18, RingProduct19, RingProduct2, RingProduct20, RingProduct21, RingProduct22, RingProduct3, RingProduct4, RingProduct5, RingProduct6, RingProduct7, RingProduct8, RingProduct9, SafeLongIsEuclideanRing, SafeLongIsEuclideanRing, SafeLongIsIntegral, SafeLongIsRing, SafeLongIsRing, ShortIsRing, ShortIsRing, UByteIsRig, UByteIsRig, UIntIsRig, UIntIsRig, ULongIsRig, ULongIsRig, UShortIsRig, UShortIsRig, ZAlgebra
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
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  1. Rig
  2. MultiplicativeMonoid
  3. AdditiveMonoid
  4. Semiring
  5. MultiplicativeSemigroup
  6. AdditiveSemigroup
  7. AnyRef
  8. Any
Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def one: A

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

    Definition Classes
    AdditiveSemigroup
  3. abstract def times(x: A, y: A): A

    Definition Classes
    MultiplicativeSemigroup
  4. 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: Monoid[A]

    Definition Classes
    AdditiveMonoidAdditiveSemigroup
  7. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  8. def clone(): AnyRef

    Attributes
    protected[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. def finalize(): Unit

    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws()
  12. final def getClass(): java.lang.Class[_]

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

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

    Definition Classes
    Any
  15. def multiplicative: Monoid[A]

  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: A, n: Int): A

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

    Definition Classes
    AnyRef
  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 MultiplicativeMonoid[A]

Inherited from AdditiveMonoid[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveSemigroup[A]

Inherited from AnyRef

Inherited from Any