Computing a holonomic submodule of the partial Weyl closure
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917460014268416 |
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| author | Brochet, Hadrien |
| author_facet | Brochet, Hadrien |
| contents | The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the singularities of the system, it serves as a preparatory step for many algorithms in symbolic integration. A new algorithm is introduced to compute a holonomic submodule of the partial Weyl closure of a finite-rank module, where the closure is taken with respect to a subset of the variables. The method relies on a non-commutative analogue of Rabinowitsch's trick. The algorithm is implemented in the Julia package MultivariateCreativeTelescoping.jl and shows substantial speedups over existing exact Weyl closure algorithms in Singular and Macaulay2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing a holonomic submodule of the partial Weyl closure Brochet, Hadrien Symbolic Computation The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the singularities of the system, it serves as a preparatory step for many algorithms in symbolic integration. A new algorithm is introduced to compute a holonomic submodule of the partial Weyl closure of a finite-rank module, where the closure is taken with respect to a subset of the variables. The method relies on a non-commutative analogue of Rabinowitsch's trick. The algorithm is implemented in the Julia package MultivariateCreativeTelescoping.jl and shows substantial speedups over existing exact Weyl closure algorithms in Singular and Macaulay2. |
| title | Computing a holonomic submodule of the partial Weyl closure |
| topic | Symbolic Computation |
| url | https://arxiv.org/abs/2602.06209 |