"Source: Text/Algebra/AlgLieKM.text";
"Line: 351";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgLieKM.text, line: 351
// Example: H111E4 ()
print "Example: H111E4";
ei := GetEchoInput();
SetEchoInput(true);
L<t> := AffineLieAlgebra("B~3", Rationals());
Lf := FiniteLieAlgebra(L);
e,f,h := StandardGenerators(L);
E,F,H := StandardBasis(Lf);
e[1] eq L!E[1];
assert $1;
x := e[4];
x;
EltTup(x);
elt<L | EltTup(x) > eq x;
assert $1;
y := elt<L | <[<t^2-t^-2, F[1]>,<-2,Lf.3>], -1/3, 1> >;
y;
z := t^3*L.2 - 1/5*h[1] + 1/7*L`c-L`d;
z;
x*(y*z) + y*(z*x) + z*(x*y);
assert IsZero($1);
SetEchoInput(ei);
