  We describe a new algorithm to compute Whitney stratifications of real and
complex algebraic varieties. This algorithm is a modification of the algorithm
of Helmer and Nanda (HN), but is made more efficient by using techniques for
equidimensional decomposition rather than computing the set of associated
primes of a polynomial ideal at a key step in the HN algorithm. We note that
this modified algorithm may fail to produce a minimal Whitney stratification
even when the HN algorithm would produce a minimal stratification. We,
additionally, present an algorithm to coarsen any Whitney stratification of a
complex variety to a minimal Whitney stratification; the theoretical basis for
our approach is a classical result of Teissier.
