We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal spaces and maps, and (b) a new interpretation of this conormal criterion via ideal saturations, which can be practically implemented on a computer. We show that this algorithm improves upon the existing state of the art by several orders of magnitude, even for relatively small input varieties. En route, we introduce related algorithms for efficiently stratifying affine varieties, flags on a given variety, and algebraic maps.

中文翻译：

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共常空间和惠特尼分层

我们描述了一种用于计算复杂射影变体的惠特尼分层的新算法。主要成分是 (a) 代数准则，由于 L\^e 和 Teissier，它根据共正规空间和映射重新制定了惠特尼正则性，以及 (b) 通过理想饱和度对该共正规标准的新解释，它可以是在计算机上实际实现。我们表明，即使对于相对较小的输入品种，该算法也将现有技术提高了几个数量级。在此过程中，我们介绍了相关算法，以有效地对仿射变体、给定变体上的标志和代数图进行分层。