Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914952244101120 |
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| author | Berthomieu, Jérémy Mohr, Rafael |
| author_facet | Berthomieu, Jérémy Mohr, Rafael |
| contents | We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that this algorithm has a complexity quasi-linear in the number of terms of certain $\mathfrak{m}$-adic expansions we compute. Some provided experimental data also demonstrates the practical efficacy of our algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting Berthomieu, Jérémy Mohr, Rafael Symbolic Computation Commutative Algebra We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that this algorithm has a complexity quasi-linear in the number of terms of certain $\mathfrak{m}$-adic expansions we compute. Some provided experimental data also demonstrates the practical efficacy of our algorithm. |
| title | Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting |
| topic | Symbolic Computation Commutative Algebra |
| url | https://arxiv.org/abs/2402.03144 |