"Source: Text/Algebra/AlgLie.text";
"Line: 3198";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgLie.text, line: 3198
// Example: H110E36 ()
print "Example: H110E36";
ei := GetEchoInput();
SetEchoInput(true);
R := TwistedRootDatum(RootDatum("A2") : Twist := 2);
L := TwistedLieAlgebra(R, GF(5));
H := SplitToralSubalgebra(L);
LK, phi, ChevBas, m := TwistedBasis(L, H, R);
m;
K := CoefficientRing(LK);
simp := ChevBas`BasisPos[[1..Rank(R)]];
simp;
fr := FrobeniusMap(K);
frv := func<x | Vector([ fr(i) : i in Eltseq(x)])>;
[ Position(simp, frv(x)) : x in simp ];
p := ChevBas`BasisPos;
n := ChevBas`BasisNeg;
c := ChevBas`BasisCart;
pi := Sym(6)!(1, 2)(4, 5);
ChevBasLK := VectorSpaceWithBasis([ Vector(x) : x in p cat n cat c]);
piL := DiagramAutomorphism(LK, pi);
for i in [1..Dimension(L)] do
   b := phi(L.i);
   printf "i = %o, b =    %o\n", i, Coordinates(ChevBasLK, Vector(b));
   printf "   pi(b)^fr = %o\n", [ fr(i) : i in 
                             Coordinates(ChevBasLK, Vector(piL(b))) ];
end for;
SetEchoInput(ei);
