"Source: Text/Algebra/AlgInv.text";
"Line: 965";
"Date: Tue Feb 25 10:14:52 2020";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgInv.text, line: 965
// Example: H96E11 ()
print "Example: H96E11";
ei := GetEchoInput();
SetEchoInput(true);
K := GF(3);
M := UpperTriangularMatrix
       (K,[0,2,1,0,1,2,1,1,1,2,0,0,1,2,1,0,1,0,1,2,2]);
F1 := M - Transpose(M);
G1 := IsometryGroup(F1);
forall{ g : g in Generators(G1) | g*F1*Transpose(g) eq F1 };
assert $1;
F2 := SymmetricMatrix 
        (K, [1,2,0,1,2,2,1,0,2,2,1,0,0,0,1,2,1,1,0,1,0]);
C := TransformForm(F2, "orthogonalminus");
G := OmegaMinus(6, 3);
G2 := G^(C^-1);
forall { g : g in Generators(G2) | g*F2*Transpose(g) eq F2 };
assert $1;
I := ClassicalIntersection([G1, G2]);
#I;
assert $1 eq 14;
SetEchoInput(ei);
