It should be remarked that it is possible to extend infinitesimal (quasi-)symmetries by including variations with δ δ x i ≠ ≠ 0 as well, i.e. the independent variables are also varied. However such symmetries can always be rewritten so that they act only on the dependent variables. Therefore, in the sequel we restrict to so-called vertical variations where δ δ x i = 0 .