Generalized ODE reduction algorithm with bounded degree transformation
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866909735853228032 |
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| author | Huang, Shaoxuan |
| author_facet | Huang, Shaoxuan |
| contents | As a generalization of our previous result\cite{huang2025algorithm}, this paper aims to answer the following question: Given a 2-dimensional polynomial vector field $y^{\prime}=\frac{M(x,y)}{N(x,y)}$, how to find a rational transformation $y \to \frac{A(x,y)}{B(x,y)}$ with bounded degree numerator, the inverse of which transforms this vector field into a simpler form $y^{\prime}=\sum_{i=0}^nf_i(x)y^i$. Such a structure, often known as the generalized Abel equation and has been studied in various areas, provides a deeper insight into the property of the original vector field. We have implemented an algorithm with considerable performance to tackle this problem and the code is available in \href{https://www.researchgate.net/publication/393362858_Generalized_ODE_reduction_algorithm}{Researchgate}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized ODE reduction algorithm with bounded degree transformation Huang, Shaoxuan Symbolic Computation As a generalization of our previous result\cite{huang2025algorithm}, this paper aims to answer the following question: Given a 2-dimensional polynomial vector field $y^{\prime}=\frac{M(x,y)}{N(x,y)}$, how to find a rational transformation $y \to \frac{A(x,y)}{B(x,y)}$ with bounded degree numerator, the inverse of which transforms this vector field into a simpler form $y^{\prime}=\sum_{i=0}^nf_i(x)y^i$. Such a structure, often known as the generalized Abel equation and has been studied in various areas, provides a deeper insight into the property of the original vector field. We have implemented an algorithm with considerable performance to tackle this problem and the code is available in \href{https://www.researchgate.net/publication/393362858_Generalized_ODE_reduction_algorithm}{Researchgate}. |
| title | Generalized ODE reduction algorithm with bounded degree transformation |
| topic | Symbolic Computation |
| url | https://arxiv.org/abs/2508.09754 |