TITLE: How to show a set of polynomials is algebraically independent?
QUESTION [17 upvotes]: Suppose that I have $n$ homogeneous polynomials $f_1, \dots, f_n \in \mathbb{C}[x_1, \dots, x_m]$ and that $n < m$.  Is there a well known method or algorithm to determine if these polynomials are algebraically independent?
As far as I know the Jacobian criterion works only for the case where $n=m$.

REPLY [5 votes]: Hi there.  A Groebner basis based algorithm that also produces an annihilating polynomial in case the polynomials are algebraically dependent can be found on the Singular site at
http://www.singular.uni-kl.de/Manual/3-0-2/sing_534.htm .