Trait/Object

spire.algebra

AbGroup

Related Docs: object AbGroup | package algebra

Permalink

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
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. AbGroup
  2. CMonoid
  3. CSemigroup
  4. Group
  5. Monoid
  6. Semigroup
  7. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Abstract Value Members

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

    Permalink
    Definition Classes
    Any
  2. abstract def id: A

    Permalink

    Return the identity element for this monoid.

    Return the identity element for this monoid.

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

    Permalink

    Return the inverse of a.

    Return the inverse of a.

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

    Permalink
    Definition Classes
    Semigroup

Concrete Value Members

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

    Permalink
    Definition Classes
    Any
  2. final def ##(): Int

    Permalink
    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean

    Permalink
    Definition Classes
    Any
  4. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any
  5. def combine(as: TraversableOnce[A]): A

    Permalink

    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]

    Permalink

    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

    Permalink

    Return a combined with itself n times.

    Return a combined with itself n times.

    Definition Classes
    GroupMonoidSemigroup
  8. def combinenAboveOne(a: A, n: Int): A

    Permalink
    Attributes
    protected
    Definition Classes
    Semigroup
  9. def equals(arg0: Any): Boolean

    Permalink
    Definition Classes
    Any
  10. def hashCode(): Int

    Permalink
    Definition Classes
    Any
  11. def isId(a: A)(implicit ev: Eq[A]): Boolean

    Permalink

    Tests if a is the identity.

    Tests if a is the identity.

    Definition Classes
    Monoid
  12. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  13. def opInverse(a: A, b: A): A

    Permalink

    Combine a with the inverse of b.

    Combine a with the inverse of b.

    Definition Classes
    Group
  14. def toString(): String

    Permalink
    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