Faster computation of Whitney stratifications and their minimization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912732898394112 |
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| author | Helmer, Martin Mohr, Rafael |
| author_facet | Helmer, Martin Mohr, Rafael |
| contents | We describe two new algorithms for the computation of Whitney stratifications of real and complex algebraic varieties. The first 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.
The second algorithm coarsens a given Whitney stratification of a complex variety to the unique minimal Whitney stratification; we refer to this as the minimization of a stratification. The theoretical basis for our approach is a classical result of Teissier. To our knowledge this yields the first algorithm for computing a minimal Whitney stratification. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_17122 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Faster computation of Whitney stratifications and their minimization Helmer, Martin Mohr, Rafael Algebraic Geometry Symbolic Computation Commutative Algebra Algebraic Topology 14B05, 14Q20, 32S60, 32S15 We describe two new algorithms for the computation of Whitney stratifications of real and complex algebraic varieties. The first 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. The second algorithm coarsens a given Whitney stratification of a complex variety to the unique minimal Whitney stratification; we refer to this as the minimization of a stratification. The theoretical basis for our approach is a classical result of Teissier. To our knowledge this yields the first algorithm for computing a minimal Whitney stratification. |
| title | Faster computation of Whitney stratifications and their minimization |
| topic | Algebraic Geometry Symbolic Computation Commutative Algebra Algebraic Topology 14B05, 14Q20, 32S60, 32S15 |
| url | https://arxiv.org/abs/2406.17122 |