trait AbGroup[A] extends Group[A] with CMonoid[A]

An abelian group is a group whose operation is commutative.

Linear Supertypes
CMonoid[A], CSemigroup[A], Group[A], Monoid[A], Semigroup[A], Any
Known Subclasses
UnitAbGroup, UnitAlgebra
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. AbGroup
  2. CMonoid
  3. CSemigroup
  4. Group
  5. Monoid
  6. Semigroup
  7. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def getClass(): Class[_]
    Definition Classes
    Any
  2. abstract def id: A

    Return the identity element for this monoid.

    Return the identity element for this monoid.

    Definition Classes
    Monoid
  3. abstract def inverse(a: A): A

    Return the inverse of a.

    Return the inverse of a.

    Definition Classes
    Group
  4. abstract def op(x: A, y: A): A
    Definition Classes
    Semigroup

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    Any
  2. final def ##(): Int
    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def combine(as: TraversableOnce[A]): A

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

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

    Definition Classes
    Monoid
  6. def combineOption(as: TraversableOnce[A]): Option[A]

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

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

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

    Definition Classes
    Semigroup
  7. def combinen(a: A, n: Int): A

    Return a combined with itself n times.

    Return a combined with itself n times.

    Definition Classes
    Group → Monoid → Semigroup
  8. def combinenAboveOne(a: A, n: Int): A
    Attributes
    protected
    Definition Classes
    Semigroup
  9. def equals(arg0: Any): Boolean
    Definition Classes
    Any
  10. def hashCode(): Int
    Definition Classes
    Any
  11. def isId(a: A)(implicit ev: Eq[A]): Boolean

    Tests if a is the identity.

    Tests if a is the identity.

    Definition Classes
    Monoid
  12. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  13. def opInverse(a: A, b: A): A

    Combine a with the inverse of b.

    Combine a with the inverse of b.

    Definition Classes
    Group
  14. def toString(): String
    Definition Classes
    Any

Inherited from CMonoid[A]

Inherited from CSemigroup[A]

Inherited from Group[A]

Inherited from Monoid[A]

Inherited from Semigroup[A]

Inherited from Any

Ungrouped