Reference request on the rank computation of symbolic matrices using numerical methods with arbitrary precision

Question

I need to compute the rank of matrices with symbolic entries. At some complexity level this is unreliable, so I am looking for alternatives, e.g. substituting random numbers for each symbol and then computing the rank numerically, or computing the singular values. Both ideas result in the problem of determining if an entry is zero, or just close to zero which can be solved using a numerical tool with arbitrary precision functionality. I feel like there must be literature on this topic and possibly more elaborated methods, but i fail to find anything, so help is much appreciated!