trait Action[P, G] extends LeftAction[P, G] with RightAction[P, G]

A semigroup/monoid/group action of G on P is the combination of compatible left and right actions, providing:

  • the implementation of a method actl(g, p), or g |+|> p, such that:

1. (g |+| h) |+|> p === g |+|> (h |+|> p) for all g, h in G and p in P.

2. id |+|> p === p for all p in P (if id is defined)

  • the implementation of a method actr(p, g), or p <|+| g, such that:

3. p <|+| (g |+| h) === (p <|+| g) <|+| h for all g, h in G and p in P.

4. p <|+| id === p for all p in P (if id is defined)

In addition, if G is a group, left and right actions are compatible:

5. g |+|> p === p <|+| g.inverse.

Linear Supertypes
RightAction[P, G], LeftAction[P, G], Any
Known Subclasses
Torsor, MapIntIntIntAction
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Inherited
  1. Action
  2. RightAction
  3. LeftAction
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Abstract Value Members

  1. abstract def actl(g: G, p: P): P
    Definition Classes
    LeftAction
  2. abstract def actr(p: P, g: G): P
    Definition Classes
    RightAction
  3. abstract def getClass(): Class[_]
    Definition Classes
    Any

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 equals(arg0: Any): Boolean
    Definition Classes
    Any
  6. def hashCode(): Int
    Definition Classes
    Any
  7. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  8. def toString(): String
    Definition Classes
    Any

Inherited from RightAction[P, G]

Inherited from LeftAction[P, G]

Inherited from Any

Ungrouped