In the software [Regina][1] what I do is apply [Descartes Rule of Signs][2] on the characteristic polynomial.  The algorithm for computing the determinant we use has complexity of the order of $n^4$, but it seems to work quite effectively for the signature computations we've been doing so far. 

The primary reason we use these techniques is they're fairly easy to implement.  Also, we're worried about rigour so we want to avoid floating-point data types that could have round-off errors.  We use arbitrary precision integers for the computations, via the GNU Multi-Precision libraries. 


  [1]: http://regina.sourceforge.net/
  [2]: http://en.wikipedia.org/wiki/Descartes%27_rule_of_signs