On deciding transcendence of power series
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913805860077568 |
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| author | Bostan, Alin Salvy, Bruno Singer, Michael F. |
| author_facet | Bostan, Alin Salvy, Bruno Singer, Michael F. |
| contents | It is well known that algebraic power series are differentially finite (D-finite): they satisfy linear differential equations with polynomial coefficients. The converse problem, whether a given D-finite power series is algebraic or transcendental, is notoriously difficult. We prove that this problem is decidable: we give two theoretical algorithms and a transcendence test that is efficient in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On deciding transcendence of power series Bostan, Alin Salvy, Bruno Singer, Michael F. Number Theory Symbolic Computation Classical Analysis and ODEs 11J81, 16S32, 34M15 It is well known that algebraic power series are differentially finite (D-finite): they satisfy linear differential equations with polynomial coefficients. The converse problem, whether a given D-finite power series is algebraic or transcendental, is notoriously difficult. We prove that this problem is decidable: we give two theoretical algorithms and a transcendence test that is efficient in practice. |
| title | On deciding transcendence of power series |
| topic | Number Theory Symbolic Computation Classical Analysis and ODEs 11J81, 16S32, 34M15 |
| url | https://arxiv.org/abs/2504.16697 |