"Source: Text/Lat/GLat.text";
"Line: 234";
"Date: Thu Apr  1 10:52:23 2021";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Lat/GLat.text, line: 234
// Example: H33E1 ()
print "Example: H33E1";
ei := GetEchoInput();
SetEchoInput(true);
L := Lattice("E", 8);
G := AutomorphismGroup(L);
#G; FactoredOrder(G);
M := MatrixRing(Rationals(), 8);
B := BasisMatrix(L);
A := MatrixGroup<8, Rationals() | [B^-1 * M!G.i * B : i in [1 .. Ngens(G)]]>;
A;
[ #Orbit(A, b) : b in Basis(L) ];
AutomorphismGroup(L: NaturalAction) eq A;
assert $1;
SetEchoInput(ei);
