The GroebnerWalk.jl package for OSCAR
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914603372380160 |
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| author | Ferry, Kamillo Nowell, Francesco |
| author_facet | Ferry, Kamillo Nowell, Francesco |
| contents | Computing Gröbner bases is known to have a very high upper bound on computation time with respect to input length. Due to the connection between polyhedral geometry and Gröbner bases through the Gröbner fan, one can attempt an incremental approach to compute Gröbner bases. First computing a Gröbner basis with respect to an `easy' term order and transforming that result to a Gröbner basis with respect to the desired term order by using information about this polyhedral fan is done by a family of algorithms termed as Gröbner walk. We implemented two variants of the Gröbner walk in the computer algebra system OSCAR and compared their performance with classical Gröbner basis methods already found in OSCAR. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The GroebnerWalk.jl package for OSCAR Ferry, Kamillo Nowell, Francesco Commutative Algebra Combinatorics 13P10, 14T10 Computing Gröbner bases is known to have a very high upper bound on computation time with respect to input length. Due to the connection between polyhedral geometry and Gröbner bases through the Gröbner fan, one can attempt an incremental approach to compute Gröbner bases. First computing a Gröbner basis with respect to an `easy' term order and transforming that result to a Gröbner basis with respect to the desired term order by using information about this polyhedral fan is done by a family of algorithms termed as Gröbner walk. We implemented two variants of the Gröbner walk in the computer algebra system OSCAR and compared their performance with classical Gröbner basis methods already found in OSCAR. |
| title | The GroebnerWalk.jl package for OSCAR |
| topic | Commutative Algebra Combinatorics 13P10, 14T10 |
| url | https://arxiv.org/abs/2503.09254 |