Trait

spire.laws.shadows

ShadowEuclideanRing

Related Doc: package shadows

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trait ShadowEuclideanRing[A, S] extends EuclideanRing[Shadow[A, S]] with ShadowGCDRing[A, S]

Linear Supertypes
ShadowGCDRing[A, S], ShadowCRing[A, S], ShadowCRng[A, S], ShadowAdditiveAbGroup[A, S], ShadowCRig[A, S], ShadowMultiplicativeCMonoid[A, S], ShadowCSemiring[A, S], ShadowMultiplicativeCSemigroup[A, S], ShadowAdditiveCMonoid[A, S], ShadowAdditiveCSemigroup[A, S], EuclideanRing[Shadow[A, S]], GCDRing[Shadow[A, S]], CommutativeRing[Shadow[A, S]], CommutativeRng[Shadow[A, S]], CommutativeRig[Shadow[A, S]], MultiplicativeCommutativeMonoid[Shadow[A, S]], CommutativeSemiring[Shadow[A, S]], MultiplicativeCommutativeSemigroup[Shadow[A, S]], Ring[Shadow[A, S]], Rng[Shadow[A, S]], AdditiveCommutativeGroup[Shadow[A, S]], AdditiveGroup[Shadow[A, S]], Rig[Shadow[A, S]], MultiplicativeMonoid[Shadow[A, S]], Semiring[Shadow[A, S]], MultiplicativeSemigroup[Shadow[A, S]], AdditiveCommutativeMonoid[Shadow[A, S]], AdditiveCommutativeSemigroup[Shadow[A, S]], AdditiveMonoid[Shadow[A, S]], AdditiveSemigroup[Shadow[A, S]], Serializable, Serializable, AnyRef, Any
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Inherited
  1. ShadowEuclideanRing
  2. ShadowGCDRing
  3. ShadowCRing
  4. ShadowCRng
  5. ShadowAdditiveAbGroup
  6. ShadowCRig
  7. ShadowMultiplicativeCMonoid
  8. ShadowCSemiring
  9. ShadowMultiplicativeCSemigroup
  10. ShadowAdditiveCMonoid
  11. ShadowAdditiveCSemigroup
  12. EuclideanRing
  13. GCDRing
  14. CommutativeRing
  15. CommutativeRng
  16. CommutativeRig
  17. MultiplicativeCommutativeMonoid
  18. CommutativeSemiring
  19. MultiplicativeCommutativeSemigroup
  20. Ring
  21. Rng
  22. AdditiveCommutativeGroup
  23. AdditiveGroup
  24. Rig
  25. MultiplicativeMonoid
  26. Semiring
  27. MultiplicativeSemigroup
  28. AdditiveCommutativeMonoid
  29. AdditiveCommutativeSemigroup
  30. AdditiveMonoid
  31. AdditiveSemigroup
  32. Serializable
  33. Serializable
  34. AnyRef
  35. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. implicit abstract def A: EuclideanRing[A]

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    Definition Classes
    ShadowEuclideanRing → ShadowGCDRing → ShadowCRing → ShadowCRng → ShadowAdditiveAbGroup → ShadowCRig → ShadowMultiplicativeCMonoid → ShadowCSemiring → ShadowMultiplicativeCSemigroup → ShadowAdditiveCMonoid → ShadowAdditiveCSemigroup

  2. implicit abstract def S: EuclideanRing[S]

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    Definition Classes
    ShadowEuclideanRing → ShadowGCDRing → ShadowCRing → ShadowCRng → ShadowAdditiveAbGroup → ShadowCRig → ShadowMultiplicativeCMonoid → ShadowCSemiring → ShadowMultiplicativeCSemigroup → ShadowAdditiveCMonoid → ShadowAdditiveCSemigroup

  3. implicit abstract def eqA: Eq[A]

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    Definition Classes
    ShadowMultiplicativeCMonoid

  4. implicit abstract def eqS: Eq[S]

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    Definition Classes
    ShadowMultiplicativeCMonoid

  5. implicit abstract val shadowing: Shadowing[A, S]

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    Definition Classes
    ShadowMultiplicativeCSemigroup

Concrete Value Members

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

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    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any

  3. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  4. def additive: CommutativeGroup[Shadow[A, S]]

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    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any

  6. def clone(): AnyRef

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

  7. def emod(x: Shadow[A, S], y: Shadow[A, S]): Shadow[A, S]

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    Definition Classes
    ShadowEuclideanRing → EuclideanRing

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

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    Definition Classes
    AnyRef

  9. def equals(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  10. def equot(x: Shadow[A, S], y: Shadow[A, S]): Shadow[A, S]

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    Definition Classes
    ShadowEuclideanRing → EuclideanRing

  11. def equotmod(x: Shadow[A, S], y: Shadow[A, S]): (Shadow[A, S], Shadow[A, S])

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    Definition Classes
    ShadowEuclideanRing → EuclideanRing

  12. def euclideanFunction(x: Shadow[A, S]): BigInt

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    Definition Classes
    ShadowEuclideanRing → EuclideanRing

  13. def finalize(): Unit

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

  14. def fromBigInt(n: BigInt): Shadow[A, S]

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    Definition Classes
    ShadowCRing → Ring

  15. def fromInt(n: Int): Shadow[A, S]

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    Definition Classes
    ShadowCRing → Ring

  16. def gcd(x: Shadow[A, S], y: Shadow[A, S])(implicit ev: Eq[Shadow[A, S]]): Shadow[A, S]

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    Definition Classes
    ShadowGCDRing → GCDRing

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

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    Definition Classes
    AnyRef → Any

  18. def hashCode(): Int

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    Definition Classes
    AnyRef → Any

  19. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  20. def isOne(x: Shadow[A, S])(implicit ev: Eq[Shadow[A, S]]): Boolean

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    Definition Classes
    ShadowMultiplicativeCMonoid → MultiplicativeMonoid

  21. def isZero(x: Shadow[A, S])(implicit ev: Eq[Shadow[A, S]]): Boolean

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    Definition Classes
    ShadowAdditiveCMonoid → AdditiveMonoid

  22. def lcm(x: Shadow[A, S], y: Shadow[A, S])(implicit ev: Eq[Shadow[A, S]]): Shadow[A, S]

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    Definition Classes
    ShadowGCDRing → GCDRing

  23. def minus(x: Shadow[A, S], y: Shadow[A, S]): Shadow[A, S]

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    Definition Classes
    ShadowAdditiveAbGroup → AdditiveGroup

  24. def multiplicative: CommutativeMonoid[Shadow[A, S]]

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    Definition Classes
    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

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    Definition Classes
    AnyRef

  26. def negate(x: Shadow[A, S]): Shadow[A, S]

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    Definition Classes
    ShadowAdditiveAbGroup → AdditiveGroup

  27. final def notify(): Unit

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    Definition Classes
    AnyRef

  28. final def notifyAll(): Unit

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    Definition Classes
    AnyRef

  29. def one: Shadow[A, S]

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    Definition Classes
    ShadowMultiplicativeCMonoid → MultiplicativeMonoid

  30. def plus(x: Shadow[A, S], y: Shadow[A, S]): Shadow[A, S]

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    Definition Classes
    ShadowAdditiveCSemigroup → AdditiveSemigroup

  31. def positivePow(a: Shadow[A, S], n: Int): Shadow[A, S]

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    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

  32. def positiveSumN(a: Shadow[A, S], n: Int): Shadow[A, S]

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

  33. def pow(x: Shadow[A, S], n: Int): Shadow[A, S]

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    Definition Classes
    ShadowMultiplicativeCSemigroup → MultiplicativeSemigroup

  34. def product(xs: TraversableOnce[Shadow[A, S]]): Shadow[A, S]

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    Definition Classes
    ShadowMultiplicativeCMonoid → MultiplicativeMonoid

  35. def sum(xs: TraversableOnce[Shadow[A, S]]): Shadow[A, S]

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    Definition Classes
    ShadowAdditiveCMonoid → AdditiveMonoid

  36. def sumN(x: Shadow[A, S], n: Int): Shadow[A, S]

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    Definition Classes
    ShadowAdditiveCSemigroup → AdditiveSemigroup

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

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    Definition Classes
    AnyRef

  38. def times(x: Shadow[A, S], y: Shadow[A, S]): Shadow[A, S]

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    Definition Classes
    ShadowMultiplicativeCSemigroup → MultiplicativeSemigroup

  39. def toString(): String

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    Definition Classes
    AnyRef → Any

  40. def tryProduct(xs: TraversableOnce[Shadow[A, S]]): Option[Shadow[A, S]]

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    Definition Classes
    ShadowMultiplicativeCSemigroup → MultiplicativeSemigroup

  41. def trySum(xs: TraversableOnce[Shadow[A, S]]): Option[Shadow[A, S]]

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    Definition Classes
    ShadowAdditiveCSemigroup → AdditiveSemigroup

  42. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  45. def zero: Shadow[A, S]

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    Definition Classes
    ShadowAdditiveCMonoid → AdditiveMonoid

Inherited from ShadowGCDRing[A, S]

Inherited from ShadowCRing[A, S]

Inherited from ShadowCRng[A, S]

Inherited from ShadowAdditiveAbGroup[A, S]

Inherited from ShadowCRig[A, S]

Inherited from ShadowMultiplicativeCMonoid[A, S]

Inherited from ShadowCSemiring[A, S]

Inherited from ShadowMultiplicativeCSemigroup[A, S]

Inherited from ShadowAdditiveCMonoid[A, S]

Inherited from ShadowAdditiveCSemigroup[A, S]

Inherited from EuclideanRing[Shadow[A, S]]

Inherited from GCDRing[Shadow[A, S]]

Inherited from CommutativeRing[Shadow[A, S]]

Inherited from CommutativeRng[Shadow[A, S]]

Inherited from CommutativeRig[Shadow[A, S]]

Inherited from MultiplicativeCommutativeMonoid[Shadow[A, S]]

Inherited from CommutativeSemiring[Shadow[A, S]]

Inherited from MultiplicativeCommutativeSemigroup[Shadow[A, S]]

Inherited from Ring[Shadow[A, S]]

Inherited from Rng[Shadow[A, S]]

Inherited from AdditiveCommutativeGroup[Shadow[A, S]]

Inherited from AdditiveGroup[Shadow[A, S]]

Inherited from Rig[Shadow[A, S]]

Inherited from MultiplicativeMonoid[Shadow[A, S]]

Inherited from Semiring[Shadow[A, S]]

Inherited from MultiplicativeSemigroup[Shadow[A, S]]

Inherited from AdditiveCommutativeMonoid[Shadow[A, S]]

Inherited from AdditiveCommutativeSemigroup[Shadow[A, S]]

Inherited from AdditiveMonoid[Shadow[A, S]]

Inherited from AdditiveSemigroup[Shadow[A, S]]

Inherited from Serializable

Inherited from Serializable

Inherited from AnyRef

Inherited from Any

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