BeginPackage["HyperGroupTest`"];
Clear["HyperGroupTest`*"];

HyperGroupTest::usage = "HyperGroupTest[LookUpTable] tests if hypergroupoid \
operation given LookUpTable forms a HyperGroup"

Begin["`Private`"];
Clear["HyperGroupTest`Private`*"];

HyperGroupTest[LookUpTable_List] := 
    Table[If[ReproductivityTest[LookUpTable[[j]]], 
        If[AssociativityTest[LookUpTable[[j]]], True, False], False], {j, 1, 
        Length[LookUpTable]}];

AssociativityTest[LookUpTable1_List] := 
    Module[{i,j,k,len,test},
           i = 1; j = 1; k = 1; test = True; len = Length[LookUpTable1];
           While[test && i<=len, 
                      test = Union[Flatten[Union[Extract[LookUpTable1,Distribute[{LookUpTable1[[i, j]], {k}}, List]]]]] == 
                             Union[Flatten[Union[Extract[LookUpTable1,Distribute[{{i}, LookUpTable1[[j, k]]}, List]]]]]; 
                      k = k + 1;  If[k > len, 
                                     k = 1; j = j + 1; 
                                     If[j > len, i = i + 1; j = 1];
                                    ];
                ];
           Return[test]
          ];

ReproductivityTest[LookUpTable1_List] :=
Union[Apply[Union, LookUpTable1 , 1]] == {Range[1, Length[LookUpTable1]]} &&
Union[Apply[Union,Transpose[LookUpTable1], 1]] == {Range[1, Length[LookUpTable1]]};

End[];
EndPackage[];