"Source: Text/Module/Multilinear.text";
"Line: 336";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Module/Multilinear.text, line: 336
// Example: H63E5 ()
print "Example: H63E5";
ei := GetEchoInput();
SetEchoInput(true);
K := GF(541);
U := KMatrixSpace(K,2,3);
my_prod := func< x | x[1]*Transpose(x[2])*x[3] >;
t := Tensor([U,U,U,U], my_prod );
t;
A := U![1,0,0,0,0,0];
A;
<A,A,A>@t;  // A is a generalized idempotent
X := [Random(U) : i  in [1..5]];
X;
A := <X[1],X[2],X[3]> @ t;
B := <X[4],X[3],X[2]> @ t;
A, B;
<A, X[4], X[5]> @ t eq <X[1], B, X[5]> @ t;
l_asct := func< X | Eltseq(<<X[1], X[2], X[3]> @ t, X[4], X[5]> @ t 
    - <X[1], <X[4], X[3], X[2]> @ t, X[5]> @ t) >;
Lt := Tensor([* U : i in [0..5] *], l_asct);
Lt;
I := Image(Lt);
I;
Dimension(I);
SetEchoInput(ei);
