S is a basis for an ideal in the Lie algebra g if [x,y] in span(S) for all x in S and y in g.

Query(S, "Ideal") returns true if the subalgebra S defines an ideal.

Query(S, parm, "Ideal") returns a sequence TF, Eq, Soln, IdealList.  Here TF is true if Maple finds parameter values for which S is an ideal and false otherwise; Eq is the set of equations (with the variables parm as unknowns) which must be satisfied for S to be an ideal; Soln is the list of solutions to the equations Eq; and IdealList is the list of ideals obtained from the parameter values given by the different solutions in Soln.

The command Query is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form Query(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-Query(...).