"Source: Text/Module/Multilinear.text";
"Line: 5935";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Module/Multilinear.text, line: 5935
// Example: H63E75 ()
print "Example: H63E75";
ei := GetEchoInput();
SetEchoInput(true);
K := Rationals();
A := KMatrixSpace(K, 3, 4);
B := KMatrixSpace(K, 4, 5);
C := KMatrixSpace(K, 3, 5);
F := func< x | x[1]*x[2] >;
t := Tensor([A, B, C], F);
t;
L := LeftNucleus(t : op := true);
M := MidNucleus(t);
R := RightNucleus(t);
Dimension(L), Dimension(M), Dimension(R);
D := DerivationAlgebra(t);
Dimension(D);
Omega := KMatrixSpace(K, 47, 47);
Z1 := ZeroMatrix(K, 20, 20);
L_L2, L2 := Induce(L, 2);
L_L0, L0 := Induce(L, 0);
embedL := map< L -> Omega | x :->
    DiagonalJoin(<Transpose(x @ L_L2), Z1, Transpose(x @ L_L0)>) >;
Z0 := ZeroMatrix(K, 15, 15);
M_M2, M2 := Induce(M, 2);
M_M1, M1 := Induce(M, 1);
embedM := map< M -> Omega | x :->
    DiagonalJoin(<x @ M_M2, -Transpose(x @ M_M1), Z0>) >;
Z2 := ZeroMatrix(K, 12, 12);
R_R1, R1 := Induce(R, 1);
R_R0, R0 := Induce(R, 0);
embedR := map< R -> Omega | x :->
    DiagonalJoin(<Z2, x @ R_R1, x @ R_R0>) >;
Random(Basis(L)) @ embedL in D;
Random(Basis(M)) @ embedM in D;
Random(Basis(R)) @ embedR in D;
SetEchoInput(ei);
