trait
Action[P, G] extends LeftAction[P, G] with RightAction[P, G]
Abstract Value Members
-
abstract
def
actl(g: G, p: P): P
-
abstract
def
actr(p: P, g: G): P
-
abstract
def
getClass(): Class[_]
Concrete Value Members
-
final
def
!=(arg0: Any): Boolean
-
final
def
##(): Int
-
final
def
==(arg0: Any): Boolean
-
final
def
asInstanceOf[T0]: T0
-
def
equals(arg0: Any): Boolean
-
def
hashCode(): Int
-
final
def
isInstanceOf[T0]: Boolean
-
def
toString(): String
A semigroup/monoid/group action of
G
onP
is the combination of compatible left and right actions, providing:actl(g, p)
, org |+|> p
, such that:1.
(g |+| h) |+|> p === g |+|> (h |+|> p)
for allg
,h
inG
andp
inP
.2.
id |+|> p === p
for allp
inP
(ifid
is defined)actr(p, g)
, orp <|+| g
, such that:3.
p <|+| (g |+| h) === (p <|+| g) <|+| h
for allg
,h
inG
andp
inP
.4.
p <|+| id === p
for allp
inP
(ifid
is defined)In addition, if
G
is a group, left and right actions are compatible:5.
g |+|> p === p <|+| g.inverse
.