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.

翻译：本文描述了一种计算实代数簇与复代数簇Whitney分层的新算法。该算法是对Helmer与Nanda算法（HN算法）的改进，其关键改进在于：在HN算法的关键步骤中，我们采用等维分解技术替代了计算多项式理想伴随素理想集的操作，从而提升了计算效率。需要指出的是，即使原HN算法能生成极小Whitney分层，本改进算法在某些情况下可能无法保证分层的极小性。此外，我们提出了一种将复代数簇的任意Whitney分层粗化为极小Whitney分层的算法；该算法的理论基础源于Teissier的经典结果。