  In this paper, the discriminant of homogeneous polynomials is studied in two
particular cases: a single homogeneous polynomial and a collection of n-1
homogeneous polynomials in n variables. In these two cases, the discriminant is
defined over a large class of coefficient rings by means of the resultant. Many
formal properties and computational rules are provided and the geometric
interpretation of the discriminant is investigated over a general coefficient
ring, typically a domain.
