高余维的光滑性检验
A smoothness test for higher codimensions
摘要：
基于Hironaka关于奇点的奇点的分解的证明思想，我们给出了代数簇光滑性的一个算法检验。该测试本质上是并行的，并且不涉及计算该品种的雅可比矩阵的余维大小的子矩阵。我们还描述了一种混合方法，它结合了新的方法与雅可比准则，从而利用这两种方法的优势。我们已经实现了所有的算法在计算机代数系统奇异的，并比较不同的方法相对于时间和内存使用。测试示例源自代数几何中的问题，由于所涉及的未成年人的数量和大小，使用雅可比准则是不切实际的。
英文摘要：
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not involve the calculation of codimension-sized minors of the Jacobian matrix of the variety. We also describe a hybrid method which combines the new method with the Jacobian criterion, thus making use of the strengths of both approaches. We have implemented all algorithms in the computer algebra system Singular, and compare the different approaches with respect to timings and memory usage. The test examples originate from questions in algebraic geometry, where the use of the Jacobian criterion is impractical due to the number and size of the minors involved.
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