For stating the general case, and not considering "zero at infinity" as special zeros, it is convenient to work with homogeneous polynomials, and consider zeros in a projective space. In this context, a "projective zero" of a homogeneous polynomial formula_103 is, up to a scaling, a -tuple formula_104 of elements of that is different form , and such that formula_105 Here, "up to a scaling" means that formula_104 and formula_107 are considered as the same zero for any nonzero formula_108 In other words, a zero is a set of homogeneous coordinates of a point in a projective space of dimension .