Simple generators of rational function fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911487983878144 |
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| author | Demin, Alexander Pogudin, Gleb |
| author_facet | Demin, Alexander Pogudin, Gleb |
| contents | Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and show that it improves upon the state of the art both in efficiency and the quality of the results. Furthermore, we demonstrate the utility of simplified generators through several case studies from different application domains, such as structural parameter identifiability. The main algorithmic novelties include performing only partial Gröbner basis computation via sparse interpolation and efficient search for polynomials of a fixed degree in a subfield of the rational function field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10878 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple generators of rational function fields Demin, Alexander Pogudin, Gleb Symbolic Computation Mathematical Software Systems and Control Commutative Algebra Dynamical Systems Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and show that it improves upon the state of the art both in efficiency and the quality of the results. Furthermore, we demonstrate the utility of simplified generators through several case studies from different application domains, such as structural parameter identifiability. The main algorithmic novelties include performing only partial Gröbner basis computation via sparse interpolation and efficient search for polynomials of a fixed degree in a subfield of the rational function field. |
| title | Simple generators of rational function fields |
| topic | Symbolic Computation Mathematical Software Systems and Control Commutative Algebra Dynamical Systems |
| url | https://arxiv.org/abs/2602.10878 |