Actions¶

This page contains an overview summary 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 libsemigroups::Action directly, but rather via the more convenient aliases libsemigroups::RightAction and libsemigroups::LeftAction.

To use libsemigroups::RightAction and libsemigroups::LeftAction with custom types, actions, and so on, see libsemigroups::ActionTraits.

using namespace libsemigroups;
using PPerm = PPermHelper<16>::type;
RightAction<PPerm, PPerm, ImageRightAction<PPerm, PPerm>> o;
o.add_seed(One<PPerm>()(16));
o.add_generator(
    PPerm({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({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({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({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();              // 65536
o.digraph().nr_scc();  // 17

The classes in libsemigroups for actions are: