# try to compute B_f for different L and f

L := SemiSl2Heisenberg;
list := [0,0,0,0,-1,1];

########################## data ###################################
# L := 6DimMetabelian;
# [0,0,0,0,0,10] - 6
# [0,0,0,0,-1,1] - 2, abelian

# L := SemiSl2Heisenberg (6-dim semidirect prod. of sl(2) and Heisenberg); p=7
# [0,0,0,0,-1,1] - 2, abelian

# L := Ap (=sl(p-1); p=5)
# [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1] - 16
# [0,0,0,0,0,0,0,0,0,0,0,3,0,2,0,0,0,0,0,0,0,0,0,1] - 10
# [0,0,0,1,0,0,2,0,-1,0,0,0,0,0,1,0,0,0,0,1,0,0,2,0] - 6
# [0,0,0,1,0,0,2,0,-1,0,0,0,0,0,1,0,0,0,0,1,0,0,2,-1] - 6
# [0,0,0,0,0,0,0,0,0,0,-1,3,0,2,0,0,0,-1,3,0,1,0,0,1] - 6
# [-1,1,0,1,0,0,2,0,-1,0,0,0,0,0,1,0,0,0,0,1,0,0,2,1] - 4, abelian
# [-1,1,0,1,0,0,2,0,-1,0,0,0,-1,0,1,0,0,0,3,1,1,1,2,1] - 4, abelian
# [-1,1,0,1,0,1,2,0,-1,0,0,0,-1,0,1,-1,1,0,3,1,1,1,2,1] - 4, abelian
# [2,1,-1,1,0,1,2,0,-1,0,1,0,-1,0,1,-1,1,-1,3,1,1,1,2,1] - 4, abelian
# [2,1,-1,1,3,1,2,0,-1,1,1,-1,-1,2,1,-1,1,-1,3,1,1,1,2,1] - 4, abelian
# [0,0,0,0,-1,1,2,3,-1,1,1,-1,-1,2,1,-1,1,-1,3,1,1,1,2,1] - 4, abelian
# [0,0,0,0,0,0,2,-1,-1,1,1,3,-1,2,0,-1,1,-1,3,0,1,1,2,1] - 4, abelian
# [0,0,0,0,0,0,0,0,0,-1,1,3,0,2,0,-1,1,-1,3,0,1,0,2,1] - 4, abelian

#L := Witt;
# minimal dimension is 1
#L := Zassenhaus (2);
#list := [0,0,0,1,0,0,2,0,-1,0,0,0,0,0,1,0,0,0,0,1,0,0,2,0,-1];
# minimal dimension is 1 

# L := ToyModularSemisimple (A1);
# dimension for Kerf:
# [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] - 12
# [1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1] - 12
# [1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1] - 6 - nonabelian
# [1,1,0,0,0,0,0,0,0,0,0,0,0,-1,1,1] - 4 - abelian
# [1,1,0,0,0,0,0,0,0,-1,0,0,1,-1,1,1] - 4 - abelian
# [0,1,1,0,0,0,0,0,0,-1,0,0,1,-1,1,1] - 4 - abelian
# [0,0,1,0,0,2,-1,0,0,-1,0,0,1,-1,1,1] - 4 - abelian
# [0,0,0,1,0,0,2,0,-1,0,0,0,0,0,1,0] - 4 - abelian
####################################################################

B := Basis (L);

func := function (x)
	local coeff, s, i;
	coeff := Coefficients (B, x);
	s := 0;
	for i in [1..Length(list)] do
		s := s + coeff[i]*list[i];
	od;
	return (s);
end;

f := MappingByFunction (L, GroundField, func);

N := LieNormalizer3 (L, Ker(f));

Print (Dimension (N), "\n");
Print (IsLieAbelian (N), "\n");