Trait/Object

algebra.ring

BoolRing

Related Docs: object BoolRing | package ring

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trait BoolRing[A] extends BoolRng[A] with CommutativeRing[A]

A Boolean ring is a ring whose multiplication is idempotent, that is a⋅a = a for all elements a. This property also implies a+a = 0 for all a, and a⋅b = b⋅a (commutativity of multiplication).

Every Boolean ring is equivalent to a Boolean algebra. See algebra.lattice.BoolFromBoolRing for details.

Linear Supertypes
CommutativeRing[A], CommutativeRig[A], MultiplicativeCommutativeMonoid[A], Ring[A], Rig[A], MultiplicativeMonoid[A], BoolRng[A], CommutativeRng[A], CommutativeSemiring[A], MultiplicativeCommutativeSemigroup[A], Rng[A], AdditiveCommutativeGroup[A], AdditiveGroup[A], Semiring[A], MultiplicativeSemigroup[A], AdditiveCommutativeMonoid[A], AdditiveCommutativeSemigroup[A], AdditiveMonoid[A], AdditiveSemigroup[A], Serializable, Serializable, Any
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Inherited
  1. BoolRing
  2. CommutativeRing
  3. CommutativeRig
  4. MultiplicativeCommutativeMonoid
  5. Ring
  6. Rig
  7. MultiplicativeMonoid
  8. BoolRng
  9. CommutativeRng
  10. CommutativeSemiring
  11. MultiplicativeCommutativeSemigroup
  12. Rng
  13. AdditiveCommutativeGroup
  14. AdditiveGroup
  15. Semiring
  16. MultiplicativeSemigroup
  17. AdditiveCommutativeMonoid
  18. AdditiveCommutativeSemigroup
  19. AdditiveMonoid
  20. AdditiveSemigroup
  21. Serializable
  22. Serializable
  23. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def getClass(): Class[_]

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    Definition Classes
    Any

  2. abstract def one: A

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    Definition Classes
    MultiplicativeMonoid

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

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    Definition Classes
    AdditiveSemigroup

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

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    Definition Classes
    MultiplicativeSemigroup

  5. abstract def zero: A

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    Definition Classes
    AdditiveMonoid

Concrete Value Members

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

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    Definition Classes
    Any

  2. final def ##(): Int

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    Definition Classes
    Any

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

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    Definition Classes
    Any

  4. def additive: CommutativeGroup[A]

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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 equals(arg0: Any): Boolean

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    Definition Classes
    Any

  7. def fromBigInt(n: BigInt): A

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    Convert the given BigInt to an instance of A.

    Convert the given BigInt to an instance of A.

    This is equivalent to n repeated summations of this ring's one, or -n summations of -one if n is negative.

    Most type class instances should consider overriding this method for performance reasons.

    Definition Classes
    Ring

  8. def fromInt(n: Int): A

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    Convert the given integer to an instance of A.

    Convert the given integer to an instance of A.

    Defined to be equivalent to sumN(one, n).

    That is, n repeated summations of this ring's one, or -n summations of -one if n is negative.

    Most type class instances should consider overriding this method for performance reasons.

    Definition Classes
    Ring

  9. def hashCode(): Int

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    Definition Classes
    Any

  10. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  11. def isOne(a: A)(implicit ev: Eq[A]): Boolean

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    Tests if a is one.

    Tests if a is one.

    Definition Classes
    MultiplicativeMonoid

  12. def isZero(a: A)(implicit ev: Eq[A]): Boolean

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    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid

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

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    Definition Classes
    AdditiveGroup

  14. def multiplicative: CommutativeMonoid[A]

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    Definition Classes
    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

  15. final def negate(x: A): A

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    Definition Classes
    BoolRng → AdditiveGroup

  16. def positivePow(a: A, n: Int): A

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    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

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

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

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

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    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  19. def product(as: TraversableOnce[A]): A

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    Given a sequence of as, compute the product.

    Given a sequence of as, compute the product.

    Definition Classes
    MultiplicativeMonoid

  20. def sum(as: TraversableOnce[A]): A

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    Given a sequence of as, compute the sum.

    Given a sequence of as, compute the sum.

    Definition Classes
    AdditiveMonoid

  21. def sumN(a: A, n: Int): A

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    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  22. def toString(): String

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    Definition Classes
    Any

  23. def tryProduct(as: TraversableOnce[A]): Option[A]

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    Given a sequence of as, combine them and return the total.

    Given a sequence of as, combine them and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup

  24. def trySum(as: TraversableOnce[A]): Option[A]

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    Given a sequence of as, combine them and return the total.

    Given a sequence of as, combine them and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

Inherited from CommutativeRing[A]

Inherited from CommutativeRig[A]

Inherited from MultiplicativeCommutativeMonoid[A]

Inherited from Ring[A]

Inherited from Rig[A]

Inherited from MultiplicativeMonoid[A]

Inherited from BoolRng[A]

Inherited from CommutativeRng[A]

Inherited from CommutativeSemiring[A]

Inherited from MultiplicativeCommutativeSemigroup[A]

Inherited from Rng[A]

Inherited from AdditiveCommutativeGroup[A]

Inherited from AdditiveGroup[A]

Inherited from Semiring[A]

Inherited from MultiplicativeSemigroup[A]

Inherited from AdditiveCommutativeMonoid[A]

Inherited from AdditiveCommutativeSemigroup[A]

Inherited from AdditiveMonoid[A]

Inherited from AdditiveSemigroup[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped