Reducing a Set of Polynomial Equations to Minimal Variables and Equations

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I have a list of polynomial equations equal to zero, lets call it

equations = [f1 == 0, f2 == 0, ..., fn ==0]

I know that each polynomial $f_{i}$ is a function of $n^2$ variables where $n$ is determined by input from the user. Is there any way that I can reduce this system of polynomial equations in Python (or with a Sage package) to a minimal number of polynomials and variables?

I tried looking up Grobner basis (http://www.sagemath.org/doc/construct...) but it does not seem to be working for what I want as it doesn't check out correctly with the analytical math I have been doing. Thanks!