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submonoids of the monoid of all maps from one set to itself.

Sorry for my bad english.

I have all maps from {1,2,3} to {1,2,3}. So I have 27 maps. And it is monoid, with * as superposition and e as map (1->1,2->2,3->3).

  1. M = FiniteSetMaps([1, 2, 3])
  2. print(M.category())
  3. print(M.an_element())
  4. print(M.cardinality())

Output: Category of finite enumerated monoids; map: 1 -> 4, 2 -> 2, 4 -> 1; 27 How can I list all submonoids of that monoid ? (I know there are 699)