  In this paper, we consider two basic questions about presenting a homogeneous
polynomial f: how many variables are needed for presenting f? How can one find
a presentation of f involving as few variables as possible? We give a complete
answer to both questions, determining the minimal number of variables needed,
NEssVar(f), and describing these variables through their linear span,
EssVar(f). Our results give rise to effective algorithms which we implemented
in the computer algebra system CoCoA.
