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 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

The classes in libsemigroups for actions are:

• Action
• ActionTraits
• LeftAction
• RightAction
• side