/*  BigattiLascalaRobbiano99.cocoa
 
  last update: 25 October 2001
 
  CoCoA default algorithm for Toric is "Elim".
  If you want to change the algorithm, type

    Toric.UseAlgorithm("Elim");      -- or
    Toric.UseAlgorithm("Parallel");  -- or
    Toric.UseAlgorithm("Sequential");

 To run all the tests type

    All(Tests);
*/

Define Go(Ex)
  PrintLn Sprint(Ex.Name);
  M := Transposed(Ex.Matrix);
  S ::= Q[x[1..Len(Ex.Matrix)]];
  Using S Do 
    PrintLn Time T := Toric(M);
    PrintLn "Len(Toric(M)) = ", Len(T);
    PrintLn Dashes();
  End;
End;

Define All(Tests)
  Foreach Ex In Tests Do Go(Ex) End;
End;

Tests := [];

Append( Tests, Record[
Name   := "Rnd6_12_0_3",
Matrix := Mat([
[  0,  1,  3,  2,  3,  1],
[  1,  3,  1,  3,  0,  0],
[  2,  3,  1,  2,  0,  3],
[  3,  0,  2,  1,  1,  1],
[  1,  0,  2,  2,  2,  0],
[  0,  1,  0,  2,  0,  3],
[  1,  0,  1,  1,  3,  0],
[  0,  3,  3,  2,  0,  1],
[  0,  1,  2,  0,  0,  2],
[  1,  3,  2,  0,  3,  2],
[  2,  0,  0,  1,  2,  0],
[  1,  0,  3,  1,  1,  2]
]) ]);

Append( Tests, Record[
Name   := "Rnd6_12_0_3b",
Matrix := Mat([
[  3,  2,  0,  3,  0,  0],
[  1,  1,  3,  2,  2,  3],
[  1,  3,  3,  0,  1,  2],
[  1,  0,  1,  0,  2,  3],
[  0,  2,  0,  3,  3,  3],
[  2,  3,  2,  0,  0,  1],
[  1,  2,  0,  0,  2,  2],
[  3,  1,  2,  1,  2,  1],
[  2,  3,  3,  2,  3,  2],
[  2,  3,  1,  3,  2,  2],
[  2,  0,  3,  0,  0,  2],
[  1,  3,  1,  2,  3,  1]
]) ]);

Append( Tests, Record[
Name   := "Rnd6_12_0_3c",
Matrix := Mat([
[  0,  1,  2,  3,  1,  2],
[  1,  1,  2,  1,  0,  1],
[  0,  2,  2,  1,  3,  0],
[  2,  1,  1,  0,  1,  0],
[  3,  3,  1,  1,  1,  3],
[  0,  1,  0,  3,  3,  1],
[  1,  3,  3,  1,  2,  1],
[  1,  3,  1,  2,  1,  2],
[  1,  3,  1,  1,  1,  0],
[  2,  0,  1,  0,  2,  1],
[  3,  0,  2,  2,  3,  3],
[  3,  1,  3,  0,  1,  3]
]) ]);

Append( Tests, Record[
Name   := "Rnd5_10_0_9",
Matrix := Mat([
[  1,   1,   4,   3,   9],
[  4,   6,   3,   1,   7],
[  9,   2,   4,   9,   0],
[  5,   4,   4,   6,   6],
[  8,   4,   3,   9,   3],
[  7,   1,   6,   7,   9],
[  3,   2,   6,   1,   2],
[  3,   4,   5,   9,   0],
[  6,   0,   2,   2,   8],
[  7,   4,   9,   9,   4]
]) ]);

Append( Tests, Record[
Name   := "Rnd5_11_0_9",
Matrix := Mat([
[  6,   8,   4,   0,   0],
[  5,   6,   3,   3,   4],
[  8,   1,   4,   0,   3],
[  1,   3,   4,   5,   6],
[  3,   2,   4,   8,   1],
[  5,   9,   8,   8,   8],
[  9,   1,   2,   0,   7],
[  8,   8,   4,   7,   8],
[  4,   1,   6,   2,   0],
[  7,   9,   5,   2,   9],
[  6,   7,   9,   4,   9]
]) ]);

Append( Tests, Record[
Name   := "Trans3_3_3",
Matrix := Mat([
[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1]
]) ]);

Append( Tests, Record[
Name   := "PM4",
Matrix := Mat([
[0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0],
[0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0],
[0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0],
[0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0],
[0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0],
[0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],
[0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1],
[0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]
]) ]);

Append( Tests, Record[
Name   := "CG10",
Matrix := Mat([
[1,  1,  0,  0,  0,  0,  0,  0,  0,  0],
[1,  0,  1,  0,  0,  0,  0,  0,  0,  0],
[1,  0,  0,  1,  0,  0,  0,  0,  0,  0],
[1,  0,  0,  0,  1,  0,  0,  0,  0,  0],
[1,  0,  0,  0,  0,  1,  0,  0,  0,  0],
[1,  0,  0,  0,  0,  0,  1,  0,  0,  0],
[1,  0,  0,  0,  0,  0,  0,  1,  0,  0],
[1,  0,  0,  0,  0,  0,  0,  0,  1,  0],
[1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
[0,  1,  1,  0,  0,  0,  0,  0,  0,  0],
[0,  1,  0,  1,  0,  0,  0,  0,  0,  0],
[0,  1,  0,  0,  1,  0,  0,  0,  0,  0],
[0,  1,  0,  0,  0,  1,  0,  0,  0,  0],
[0,  1,  0,  0,  0,  0,  1,  0,  0,  0],
[0,  1,  0,  0,  0,  0,  0,  1,  0,  0],
[0,  1,  0,  0,  0,  0,  0,  0,  1,  0],
[0,  1,  0,  0,  0,  0,  0,  0,  0,  1],
[0,  0,  1,  1,  0,  0,  0,  0,  0,  0],
[0,  0,  1,  0,  1,  0,  0,  0,  0,  0],
[0,  0,  1,  0,  0,  1,  0,  0,  0,  0],
[0,  0,  1,  0,  0,  0,  1,  0,  0,  0],
[0,  0,  1,  0,  0,  0,  0,  1,  0,  0],
[0,  0,  1,  0,  0,  0,  0,  0,  1,  0],
[0,  0,  1,  0,  0,  0,  0,  0,  0,  1],
[0,  0,  0,  1,  1,  0,  0,  0,  0,  0],
[0,  0,  0,  1,  0,  1,  0,  0,  0,  0],
[0,  0,  0,  1,  0,  0,  1,  0,  0,  0],
[0,  0,  0,  1,  0,  0,  0,  1,  0,  0],
[0,  0,  0,  1,  0,  0,  0,  0,  1,  0],
[0,  0,  0,  1,  0,  0,  0,  0,  0,  1],
[0,  0,  0,  0,  1,  1,  0,  0,  0,  0],
[0,  0,  0,  0,  1,  0,  1,  0,  0,  0],
[0,  0,  0,  0,  1,  0,  0,  1,  0,  0],
[0,  0,  0,  0,  1,  0,  0,  0,  1,  0],
[0,  0,  0,  0,  1,  0,  0,  0,  0,  1],
[0,  0,  0,  0,  0,  1,  1,  0,  0,  0],
[0,  0,  0,  0,  0,  1,  0,  1,  0,  0],
[0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
[0,  0,  0,  0,  0,  1,  0,  0,  0,  1],
[0,  0,  0,  0,  0,  0,  1,  1,  0,  0],
[0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
[0,  0,  0,  0,  0,  0,  1,  0,  0,  1],
[0,  0,  0,  0,  0,  0,  0,  1,  1,  0],
[0,  0,  0,  0,  0,  0,  0,  1,  0,  1],
[0,  0,  0,  0,  0,  0,  0,  0,  1,  1]
]) ]);

Append( Tests, Record[
Name   := "CG11",
Matrix := Mat([
[1,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0],
[1,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0],
[1,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0],
[1,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0],
[1,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0],
[1,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0],
[1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0],
[1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  0],
[1,  0,  0,  0,  0,  0,  0,  0,  0,  1,  0],
[1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1],
[0,  1,  1,  0,  0,  0,  0,  0,  0,  0,  0],
[0,  1,  0,  1,  0,  0,  0,  0,  0,  0,  0],
[0,  1,  0,  0,  1,  0,  0,  0,  0,  0,  0],
[0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  0],
[0,  1,  0,  0,  0,  0,  1,  0,  0,  0,  0],
[0,  1,  0,  0,  0,  0,  0,  1,  0,  0,  0],
[0,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0],
[0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0],
[0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
[0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  0],
[0,  0,  1,  0,  1,  0,  0,  0,  0,  0,  0],
[0,  0,  1,  0,  0,  1,  0,  0,  0,  0,  0],
[0,  0,  1,  0,  0,  0,  1,  0,  0,  0,  0],
[0,  0,  1,  0,  0,  0,  0,  1,  0,  0,  0],
[0,  0,  1,  0,  0,  0,  0,  0,  1,  0,  0],
[0,  0,  1,  0,  0,  0,  0,  0,  0,  1,  0],
[0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1],
[0,  0,  0,  1,  1,  0,  0,  0,  0,  0,  0],
[0,  0,  0,  1,  0,  1,  0,  0,  0,  0,  0],
[0,  0,  0,  1,  0,  0,  1,  0,  0,  0,  0],
[0,  0,  0,  1,  0,  0,  0,  1,  0,  0,  0],
[0,  0,  0,  1,  0,  0,  0,  0,  1,  0,  0],
[0,  0,  0,  1,  0,  0,  0,  0,  0,  1,  0],
[0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  1],
[0,  0,  0,  0,  1,  1,  0,  0,  0,  0,  0],
[0,  0,  0,  0,  1,  0,  1,  0,  0,  0,  0],
[0,  0,  0,  0,  1,  0,  0,  1,  0,  0,  0],
[0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  0],
[0,  0,  0,  0,  1,  0,  0,  0,  0,  1,  0],
[0,  0,  0,  0,  1,  0,  0,  0,  0,  0,  1],
[0,  0,  0,  0,  0,  1,  1,  0,  0,  0,  0],
[0,  0,  0,  0,  0,  1,  0,  1,  0,  0,  0],
[0,  0,  0,  0,  0,  1,  0,  0,  1,  0,  0],
[0,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0],
[0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  1],
[0,  0,  0,  0,  0,  0,  1,  1,  0,  0,  0],
[0,  0,  0,  0,  0,  0,  1,  0,  1,  0,  0],
[0,  0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
[0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  1],
[0,  0,  0,  0,  0,  0,  0,  1,  1,  0,  0],
[0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
[0,  0,  0,  0,  0,  0,  0,  1,  0,  0,  1],
[0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  0],
[0,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1],
[0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1]
]) ]);

Append( Tests, Record[
Name   := "VT5_4_2",
Matrix := Mat([
[2,   2,   0,   0,   0],
[2,   1,   1,   0,   0],
[2,   1,   0,   1,   0],
[2,   1,   0,   0,   1],
[2,   0,   2,   0,   0],
[2,   0,   1,   1,   0],
[2,   0,   1,   0,   1],
[2,   0,   0,   2,   0],
[2,   0,   0,   1,   1],
[2,   0,   0,   0,   2],
[1,   2,   1,   0,   0],
[1,   2,   0,   1,   0],
[1,   2,   0,   0,   1],
[1,   1,   2,   0,   0],
[1,   1,   1,   1,   0],
[1,   1,   1,   0,   1],
[1,   1,   0,   2,   0],
[1,   1,   0,   1,   1],
[1,   1,   0,   0,   2],
[1,   0,   2,   1,   0],
[1,   0,   2,   0,   1],
[1,   0,   1,   2,   0],
[1,   0,   1,   1,   1],
[1,   0,   1,   0,   2],
[1,   0,   0,   2,   1],
[1,   0,   0,   1,   2],
[0,   2,   2,   0,   0],
[0,   2,   1,   1,   0],
[0,   2,   1,   0,   1],
[0,   2,   0,   2,   0],
[0,   2,   0,   1,   1],
[0,   2,   0,   0,   2],
[0,   1,   2,   1,   0],
[0,   1,   2,   0,   1],
[0,   1,   1,   2,   0],
[0,   1,   1,   1,   1],
[0,   1,   1,   0,   2],
[0,   1,   0,   2,   1],
[0,   1,   0,   1,   2],
[0,   0,   2,   2,   0],
[0,   0,   2,   1,   1],
[0,   0,   2,   0,   2],
[0,   0,   1,   2,   1],
[0,   0,   1,   1,   2],
[0,   0,   0,   2,   2]
]) ]);

Append( Tests, Record[
Name   := "VT7_4_1",
Matrix := Mat([
[1,   1,   1,   1,   0,   0,   0],
[1,   1,   1,   0,   1,   0,   0],
[1,   1,   1,   0,   0,   1,   0],
[1,   1,   1,   0,   0,   0,   1],
[1,   1,   0,   1,   1,   0,   0],
[1,   1,   0,   1,   0,   1,   0],
[1,   1,   0,   1,   0,   0,   1],
[1,   1,   0,   0,   1,   1,   0],
[1,   1,   0,   0,   1,   0,   1],
[1,   1,   0,   0,   0,   1,   1],
[1,   0,   1,   1,   1,   0,   0],
[1,   0,   1,   1,   0,   1,   0],
[1,   0,   1,   1,   0,   0,   1],
[1,   0,   1,   0,   1,   1,   0],
[1,   0,   1,   0,   1,   0,   1],
[1,   0,   1,   0,   0,   1,   1],
[1,   0,   0,   1,   1,   1,   0],
[1,   0,   0,   1,   1,   0,   1],
[1,   0,   0,   1,   0,   1,   1],
[1,   0,   0,   0,   1,   1,   1],
[0,   1,   1,   1,   1,   0,   0],
[0,   1,   1,   1,   0,   1,   0],
[0,   1,   1,   1,   0,   0,   1],
[0,   1,   1,   0,   1,   1,   0],
[0,   1,   1,   0,   1,   0,   1],
[0,   1,   1,   0,   0,   1,   1],
[0,   1,   0,   1,   1,   1,   0],
[0,   1,   0,   1,   1,   0,   1],
[0,   1,   0,   1,   0,   1,   1],
[0,   1,   0,   0,   1,   1,   1],
[0,   0,   1,   1,   1,   1,   0],
[0,   0,   1,   1,   1,   0,   1],
[0,   0,   1,   1,   0,   1,   1],
[0,   0,   1,   0,   1,   1,   1],
[0,   0,   0,   1,   1,   1,   1]
]) ]);

Append( Tests, Record[
Name   := "VT4_4_4",
Matrix := Mat([
[4,   0,   0,   0],
[3,   1,   0,   0],
[3,   0,   1,   0],
[3,   0,   0,   1],
[2,   2,   0,   0],
[2,   1,   1,   0],
[2,   1,   0,   1],
[2,   0,   2,   0],
[2,   0,   1,   1],
[2,   0,   0,   2],
[1,   3,   0,   0],
[1,   2,   1,   0],
[1,   2,   0,   1],
[1,   1,   2,   0],
[1,   1,   1,   1],
[1,   1,   0,   2],
[1,   0,   3,   0],
[1,   0,   2,   1],
[1,   0,   1,   2],
[1,   0,   0,   3],
[0,   4,   0,   0],
[0,   3,   1,   0],
[0,   3,   0,   1],
[0,   2,   2,   0],
[0,   2,   1,   1],
[0,   2,   0,   2],
[0,   1,   3,   0],
[0,   1,   2,   1],
[0,   1,   1,   2],
[0,   1,   0,   3],
[0,   0,   4,   0],
[0,   0,   3,   1],
[0,   0,   2,   2],
[0,   0,   1,   3],
[0,   0,   0,   4]
]) ]);

Append( Tests, Record[
Name   := "HS2_10",
Matrix := Mat([
[1,  1,  0,  0,  0,  0,  0,  0,  0,  0],
[1,  0,  1,  0,  0,  0,  0,  0,  0,  0],
[1,  0,  0,  1,  0,  0,  0,  0,  0,  0],
[1,  0,  0,  0,  1,  0,  0,  0,  0,  0],
[1,  0,  0,  0,  0,  1,  0,  0,  0,  0],
[1,  0,  0,  0,  0,  0,  1,  0,  0,  0],
[1,  0,  0,  0,  0,  0,  0,  1,  0,  0],
[1,  0,  0,  0,  0,  0,  0,  0,  1,  0],
[1,  0,  0,  0,  0,  0,  0,  0,  0,  1],
[0,  1,  1,  0,  0,  0,  0,  0,  0,  0],
[0,  1,  0,  1,  0,  0,  0,  0,  0,  0],
[0,  1,  0,  0,  1,  0,  0,  0,  0,  0],
[0,  1,  0,  0,  0,  1,  0,  0,  0,  0],
[0,  1,  0,  0,  0,  0,  1,  0,  0,  0],
[0,  1,  0,  0,  0,  0,  0,  1,  0,  0],
[0,  1,  0,  0,  0,  0,  0,  0,  1,  0],
[0,  1,  0,  0,  0,  0,  0,  0,  0,  1],
[0,  0,  1,  1,  0,  0,  0,  0,  0,  0],
[0,  0,  1,  0,  1,  0,  0,  0,  0,  0],
[0,  0,  1,  0,  0,  1,  0,  0,  0,  0],
[0,  0,  1,  0,  0,  0,  1,  0,  0,  0],
[0,  0,  1,  0,  0,  0,  0,  1,  0,  0],
[0,  0,  1,  0,  0,  0,  0,  0,  1,  0],
[0,  0,  1,  0,  0,  0,  0,  0,  0,  1],
[0,  0,  0,  1,  1,  0,  0,  0,  0,  0],
[0,  0,  0,  1,  0,  1,  0,  0,  0,  0],
[0,  0,  0,  1,  0,  0,  1,  0,  0,  0],
[0,  0,  0,  1,  0,  0,  0,  1,  0,  0],
[0,  0,  0,  1,  0,  0,  0,  0,  1,  0],
[0,  0,  0,  1,  0,  0,  0,  0,  0,  1],
[0,  0,  0,  0,  1,  1,  0,  0,  0,  0],
[0,  0,  0,  0,  1,  0,  1,  0,  0,  0],
[0,  0,  0,  0,  1,  0,  0,  1,  0,  0],
[0,  0,  0,  0,  1,  0,  0,  0,  1,  0],
[0,  0,  0,  0,  1,  0,  0,  0,  0,  1],
[0,  0,  0,  0,  0,  1,  1,  0,  0,  0],
[0,  0,  0,  0,  0,  1,  0,  1,  0,  0],
[0,  0,  0,  0,  0,  1,  0,  0,  1,  0],
[0,  0,  0,  0,  0,  1,  0,  0,  0,  1],
[0,  0,  0,  0,  0,  0,  1,  1,  0,  0],
[0,  0,  0,  0,  0,  0,  1,  0,  1,  0],
[0,  0,  0,  0,  0,  0,  1,  0,  0,  1],
[0,  0,  0,  0,  0,  0,  0,  1,  1,  0],
[0,  0,  0,  0,  0,  0,  0,  1,  0,  1],
[0,  0,  0,  0,  0,  0,  0,  0,  1,  1]
]) ]);

Append( Tests, Record[
Name   := "HS3_8",
Matrix := Mat([
[1,  1,  1,  0,  0,  0,  0,  0],
[1,  1,  0,  1,  0,  0,  0,  0],
[1,  1,  0,  0,  1,  0,  0,  0],
[1,  1,  0,  0,  0,  1,  0,  0],
[1,  1,  0,  0,  0,  0,  1,  0],
[1,  1,  0,  0,  0,  0,  0,  1],
[1,  0,  1,  1,  0,  0,  0,  0],
[1,  0,  1,  0,  1,  0,  0,  0],
[1,  0,  1,  0,  0,  1,  0,  0],
[1,  0,  1,  0,  0,  0,  1,  0],
[1,  0,  1,  0,  0,  0,  0,  1],
[1,  0,  0,  1,  1,  0,  0,  0],
[1,  0,  0,  1,  0,  1,  0,  0],
[1,  0,  0,  1,  0,  0,  1,  0],
[1,  0,  0,  1,  0,  0,  0,  1],
[1,  0,  0,  0,  1,  1,  0,  0],
[1,  0,  0,  0,  1,  0,  1,  0],
[1,  0,  0,  0,  1,  0,  0,  1],
[1,  0,  0,  0,  0,  1,  1,  0],
[1,  0,  0,  0,  0,  1,  0,  1],
[1,  0,  0,  0,  0,  0,  1,  1],
[0,  1,  1,  1,  0,  0,  0,  0],
[0,  1,  1,  0,  1,  0,  0,  0],
[0,  1,  1,  0,  0,  1,  0,  0],
[0,  1,  1,  0,  0,  0,  1,  0],
[0,  1,  1,  0,  0,  0,  0,  1],
[0,  1,  0,  1,  1,  0,  0,  0],
[0,  1,  0,  1,  0,  1,  0,  0],
[0,  1,  0,  1,  0,  0,  1,  0],
[0,  1,  0,  1,  0,  0,  0,  1],
[0,  1,  0,  0,  1,  1,  0,  0],
[0,  1,  0,  0,  1,  0,  1,  0],
[0,  1,  0,  0,  1,  0,  0,  1],
[0,  1,  0,  0,  0,  1,  1,  0],
[0,  1,  0,  0,  0,  1,  0,  1],
[0,  1,  0,  0,  0,  0,  1,  1],
[0,  0,  1,  1,  1,  0,  0,  0],
[0,  0,  1,  1,  0,  1,  0,  0],
[0,  0,  1,  1,  0,  0,  1,  0],
[0,  0,  1,  1,  0,  0,  0,  1],
[0,  0,  1,  0,  1,  1,  0,  0],
[0,  0,  1,  0,  1,  0,  1,  0],
[0,  0,  1,  0,  1,  0,  0,  1],
[0,  0,  1,  0,  0,  1,  1,  0],
[0,  0,  1,  0,  0,  1,  0,  1],
[0,  0,  1,  0,  0,  0,  1,  1],
[0,  0,  0,  1,  1,  1,  0,  0],
[0,  0,  0,  1,  1,  0,  1,  0],
[0,  0,  0,  1,  1,  0,  0,  1],
[0,  0,  0,  1,  0,  1,  1,  0],
[0,  0,  0,  1,  0,  1,  0,  1],
[0,  0,  0,  1,  0,  0,  1,  1],
[0,  0,  0,  0,  1,  1,  1,  0],
[0,  0,  0,  0,  1,  1,  0,  1],
[0,  0,  0,  0,  1,  0,  1,  1],
[0,  0,  0,  0,  0,  1,  1,  1]
]) ]);

Append( Tests, Record[
Name   := "DiagG4_5_3",
Matrix := Mat([
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]
]) ]);

Append( Tests, Record[
Name   := "DiagS5_5_3",
Matrix := Mat([
[1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 ],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 ],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0 ],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 ],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 ],
[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 ],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0 ],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0 ],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 ],
[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0 ],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ],
[0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0 ],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0 ],
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