A zero-test for D-algebraic transseries
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917239561650176 |
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| author | Chen, Shaoshi Fang, Hanqian van der Hoeven, Joris |
| author_facet | Chen, Shaoshi Fang, Hanqian van der Hoeven, Joris |
| contents | Consider formal power series $f_1,\ldots, f_k\in\mathbb{Q}[[z]]$ that are defined as the solutions of a system of polynomial differential equations together with a sufficient number of initial conditions. Given $P\in \mathbb{Q}[F_1,\ldots,F_k]$, several algorithms have been proposed in order to test whether $P(f_1,\ldots,f_k)=0$. In this paper, we present such an algorithm for the case where $f_1,\ldots,f_k$ are so-called transseries instead of power series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A zero-test for D-algebraic transseries Chen, Shaoshi Fang, Hanqian van der Hoeven, Joris Symbolic Computation 68W30, 34A09, 34A12 Consider formal power series $f_1,\ldots, f_k\in\mathbb{Q}[[z]]$ that are defined as the solutions of a system of polynomial differential equations together with a sufficient number of initial conditions. Given $P\in \mathbb{Q}[F_1,\ldots,F_k]$, several algorithms have been proposed in order to test whether $P(f_1,\ldots,f_k)=0$. In this paper, we present such an algorithm for the case where $f_1,\ldots,f_k$ are so-called transseries instead of power series. |
| title | A zero-test for D-algebraic transseries |
| topic | Symbolic Computation 68W30, 34A09, 34A12 |
| url | https://arxiv.org/abs/2602.01188 |