"Source: Text/LieTheory/RootDtm.text";
"Line: 2322";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/RootDtm.text, line: 2322
// Example: H107E22 ()
print "Example: H107E22";
ei := GetEchoInput();
SetEchoInput(true);
R := RootDatum("G2");
RootHeight(R, 5);
assert $1 eq 4;
F := CoxeterForm(R);
v := VectorSpace(Rationals(),2) ! Root(R, 5);
(v*F, v) eq RootNorm(R, 5);
assert $1;
IsLongRoot(R, 5);
assert $1;
LeftString(R, 1, 5);
roots := Roots(R);
for i in [1..3] do
  RootPosition(R, roots[5]-i*roots[1]);
end for;
SetEchoInput(ei);
