Trait/Object

cats.kernel

CommutativeGroup

Related Docs: object CommutativeGroup | package kernel

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trait CommutativeGroup[A] extends Group[A] with CommutativeMonoid[A]

An commutative group (also known as an abelian group) is a group whose combine operation is commutative.

Linear Supertypes
CommutativeMonoid[A], CommutativeSemigroup[A], Group[A], Monoid[A], Semigroup[A], Serializable, Serializable, Any
Known Subclasses
BigDecimalGroup, BigIntGroup, ByteGroup, DoubleGroup, DurationGroup, FloatGroup, IntGroup, LongGroup, ShortGroup, UnitAlgebra
Ordering
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  2. By Inheritance
Inherited
  1. CommutativeGroup
  2. CommutativeMonoid
  3. CommutativeSemigroup
  4. Group
  5. Monoid
  6. Semigroup
  7. Serializable
  8. Serializable
  9. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

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

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    Associative operation which combines two values.

    Associative operation which combines two values.

    Definition Classes
    Semigroup

  2. abstract def empty: A

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    Return the identity element for this monoid.

    Return the identity element for this monoid.

    Definition Classes
    Monoid

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

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    Definition Classes
    Any

  4. abstract def inverse(a: A): A

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    Find the inverse of a.

    Find the inverse of a.

    combine(a, inverse(a)) = combine(inverse(a), a) = empty.

    Definition Classes
    Group

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. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any

  5. def combineAll(as: TraversableOnce[A]): A

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    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes
    Monoid

  6. def combineAllOption(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
    Monoid → Semigroup

  7. def combineN(a: A, n: Int): A

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    Return a appended to itself n times.

    Return a appended to itself n times. If n is negative, then this returns inverse(a) appended to itself n times.

    Definition Classes
    Group → Monoid → Semigroup

  8. def equals(arg0: Any): Boolean

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    Definition Classes
    Any

  9. def hashCode(): Int

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    Definition Classes
    Any

  10. def isEmpty(a: A)(implicit ev: Eq[A]): Boolean

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    Tests if a is the identity.

    Tests if a is the identity.

    Definition Classes
    Monoid

  11. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  12. def remove(a: A, b: A): A

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    Remove the element b from a.

    Remove the element b from a.

    Equivalent to combine(a, inverse(b))

    Definition Classes
    Group

  13. def repeatedCombineN(a: A, n: Int): A

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    Return a combined with itself more than once.

    Return a combined with itself more than once.

    Attributes
    protected[this]
    Definition Classes
    Semigroup

  14. def toString(): String

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    Definition Classes
    Any

Inherited from CommutativeMonoid[A]

Inherited from CommutativeSemigroup[A]

Inherited from Group[A]

Inherited from Monoid[A]

Inherited from Semigroup[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped