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

Functions
template<typename Element, typename Point, typename Func, typename Traits, side LeftOrRight>
std::string	to_human_readable_repr (Action< Element, Point, Func, Traits, LeftOrRight > const &action)
	Return a human readable representation of an Action object.

Typedef Documentation

LeftAction

template<typename Element, typename Point, typename Func = ImageLeftAction<Element, Point>, 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 = ImageRightAction<Element, Point>, 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.

Function Documentation

to_human_readable_repr()

template<typename Element, typename Point, typename Func, typename Traits, side LeftOrRight>

std::string to_human_readable_repr

(

Action< Element, Point, Func, Traits, LeftOrRight > const &

action

)

Defined in action.hpp.

This function returns a human readable representation of an Action object.

Parameters

action

the Action.

Returns

A std::string containing the representation.

Exceptions

This function guarantees not to throw a LibsemigroupsException.