Separated Variables on Plane Algebraic Curves

Manfred Buchacher

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arXiv · 2411.08584

Separated Variables on Plane Algebraic Curves

Manfred Buchacher

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Abstract

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.

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Manfred Buchacher. 2024-11-13. Separated Variables on Plane Algebraic Curves. https://arxiv.org/abs/2411.08584

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