"Source: Text/LieTheory/GrpLie.text";
"Line: 2109";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/GrpLie.text, line: 2109
// Example: H113E19 ()
print "Example: H113E19";
ei := GetEchoInput();
SetEchoInput(true);
G := GroupOfLieType("B2", GF(4));
A := AutomorphismGroup(G);
A!1 eq IdentityAutomorphism(G);
assert $1;
g := GraphAutomorphism(G, Sym(2)!(1,2));
g;
sigma := iso< GF(4) -> GF(4) | x :-> x^2, x :-> x^2 >;
h := FieldAutomorphism(G, sigma) * g;
h in A;
assert $1;
f,g,i := DecomposeAutomorphism(h);
assert f*g*i eq h;
SetEchoInput(ei);
