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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2411.08584 |
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| _version_ | 1866909842774425600 |
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| author | Buchacher, Manfred |
| author_facet | Buchacher, Manfred |
| contents | We investigate the problem of deciding whether the restriction of a rational function $r\in\mathbb{K}(x,y)$ to the curve associated with an irreducible polynomial $p\in\mathbb{K}[x,y]$ is the restriction of an element of $\mathbb{K}(x)+\mathbb{K}(y)$. We present an algorithm and a conjectural semi-algorithm for finding such elements depending on whether $p$ has a non-trivial rational multiple in $\mathbb{K}(x) + \mathbb{K}(y)$ or not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Separated Variables on Plane Algebraic Curves Buchacher, Manfred Algebraic Geometry Commutative Algebra F.2.1; F.2.2 We investigate the problem of deciding whether the restriction of a rational function $r\in\mathbb{K}(x,y)$ to the curve associated with an irreducible polynomial $p\in\mathbb{K}[x,y]$ is the restriction of an element of $\mathbb{K}(x)+\mathbb{K}(y)$. We present an algorithm and a conjectural semi-algorithm for finding such elements depending on whether $p$ has a non-trivial rational multiple in $\mathbb{K}(x) + \mathbb{K}(y)$ or not. |
| title | Separated Variables on Plane Algebraic Curves |
| topic | Algebraic Geometry Commutative Algebra F.2.1; F.2.2 |
| url | https://arxiv.org/abs/2411.08584 |