"Source: Text/Module/Multilinear.text";
"Line: 3442";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Module/Multilinear.text, line: 3442
// Example: H63E45 ()
print "Example: H63E45";
ei := GetEchoInput();
SetEchoInput(true);
t := KTensorSpace(GF(5), [5, 5, 4])!0;
for i in [1..4] do
  Assign(~t, [i, i+1, i], 1);   // 1s above diag
  Assign(~t, [i+1, i, i], -1);  // 4s below diag
end for;
t;
IsAlternating(t);
SystemOfForms(t);
IsFullyNondegenerate(t);
H := HeisenbergGroup(t);
LMGOrder(LMGCenter(H)) eq 5^4;
s := pCentralTensor(H, 5, 1, 1);
s;
PgrpCat := TensorCategory([1, 1, 1], {{2,1},{0}});
PgrpCat;
ChangeTensorCategory(~t, PgrpCat);
H := HeisenbergGroup(t);
LMGOrder(LMGCenter(H)) eq 5^4;
s := pCentralTensor(H, 5, 1, 1);
s;
SystemOfForms(s);
SetEchoInput(ei);
