Suppose $I = \langle f_1, ... , f_l \rangle$ is an ideal generated by polynomials $f \in k[x_1,\dots,x_n]$, where $k$ is a field of rational functions in some parameters $s_1,\dots,s_m$.

What are the techniques to study the dependence of the grobner basis of $I$ (with respect to some order) on the parameters $s$? Is it possible to find "regions" in the parameter space where the basis is doesn't change?


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