Actions

This page contains an overview of the functionality in libsemigroups for finding actions of semigroups, or groups, on sets. The notion of an "action" in the context of libsemigroups is analogous to the notion of an orbit of a group.

You are unlikely to want to use Action directly, but rather via the more convenient aliases RightAction and LeftAction. To use RightAction and LeftAction with custom types, actions, and so on, see ActionTraits.

See also ImageLeftAction and ImageRightAction.

using namespace libsemigroups;
RightAction<PPerm<16>, PPerm<16>, ImageRightAction<PPerm<16>, PPerm<16>>>
o;
o.add_seed(PPerm<16>::identity(16));
o.add_generator(
   PPerm<16>({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
             {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0},
             16));
o.add_generator(
   PPerm<16>({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
             {1, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
             16));
o.add_generator(
   PPerm<16>({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
             {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
             16));
o.add_generator(
   PPerm<16>({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
             {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
             16));
o.reserve(70000);
o.size();  // returns 65536

Classes
class	Action< Element, Point, Func, Traits, LeftOrRight >
	Class for generating the action of a semigroup. More...
struct	ActionTraits< Element, Point >

Typedefs
template<typename Element, typename Point, typename Func, typename Traits = ActionTraits<Element, Point>>
using	LeftAction = Action<Element, Point, Func, Traits, side::left>
template<typename Element, typename Point, typename Func, typename Traits = ActionTraits<Element, Point>>
using	RightAction = Action<Element, Point, Func, Traits, side::right>

Enumerations
enum class	side { left , right }
	Enum class indicating the handedness or side of an action. More...

Typedef Documentation

LeftAction

template<typename Element, typename Point, typename Func, typename Traits = ActionTraits<Element, Point>>

using LeftAction = Action<Element, Point, Func, Traits, side::left>

This class represents the left action of a semigroup on a set.

See also

Action for further details.

RightAction

template<typename Element, typename Point, typename Func, typename Traits = ActionTraits<Element, Point>>

using RightAction = Action<Element, Point, Func, Traits, side::right>

This class represents the right action of a semigroup on a set.

See also

Action for further details.

Enumeration Type Documentation

side

enum class side

strong

The values in this enum can be used as a template parameter for the Action class to specify whether the action of the Action is a left or right action.

Enumerator
left	This value indicates that the action in an Action instance should be a left action.
right	This value indicates that the action in an Action instance should be a right action.