https://github.com/amplitudegravity/multi-variable-residue
This program is to calculate the multi-variable residue around zero-dimension intersection point.
Science Score: 23.0%
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Last synced: 9 months ago
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This program is to calculate the multi-variable residue around zero-dimension intersection point.
Basic Info
- Host: GitHub
- Owner: AmplitudeGravity
- License: gpl-3.0
- Language: Mathematica
- Default Branch: main
- Size: 76.2 KB
Statistics
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Created about 4 years ago
· Last pushed about 4 years ago
https://github.com/AmplitudeGravity/Multi-variable-Residue/blob/main/
# Short introduction to multivariate residues(Math background and mathematica code)
This program is to calculate the multi-variable residue around zero-dimension intersection point.
The main function is called "MultiResidue" which is used to calculate $$\text{Res}_{h_1=\cdots=h_r=0} ~ {f dz_1\wedge dz_2\wedge \cdots \wedge dz_r\over h_1 h_2\cdots h_r},$$
where $h_i$ is homogeneous polynomial function and the solution of $h_1=\cdots=h_r=0$ is an isolated point $p$. The $f$ function is regular at $p$.
```
MultiResidue[f, {h1, h2,..., hr}, {z1,z2,..., zr}]
```
More examples is included in the mathematica code. A julia package is still in development. This need to use CAS in julia, e.g. [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl) and/or [SymEngine](https://github.com/symengine/SymEngine.jl).
For general in-homogeneous polynomial function, it is easy to transform to the homogeneous cases by a trick using the global residue theorem. For more details and citations, please
see and cite the origine papers [arxiv 1609.07621](https://arxiv.org/pdf/1609.07621.pdf) and [arxiv 1709.08503](https://arxiv.org/pdf/1709.08503.pdf).
# Citation
If you use **multiResidue.nb**, please cite the two papers [arxiv 1609.07621](https://arxiv.org/pdf/1609.07621.pdf) and [arxiv 1709.08503](https://arxiv.org/pdf/1709.08503.pdf) as following
```
@article{Chen:2016fgi,
author = "Chen, Gang and Cheung, Yeuk-Kwan E. and Wang, Tianheng and Xu, Feng",
title = "{A differential operator for integrating one-loop scattering equations}",
eprint = "1609.07621",
archivePrefix = "arXiv",
primaryClass = "hep-th",
doi = "10.1007/JHEP01(2017)028",
journal = "JHEP",
volume = "01",
pages = "028",
year = "2017"
}
```
```
@article{Chen:2017bug,
author = "Chen, Gang and Wang, Tianheng",
title = "{BCJ Numerators from Differential Operator of Multidimensional Residue}",
eprint = "1709.08503",
archivePrefix = "arXiv",
primaryClass = "hep-th",
doi = "10.1140/epjc/s10052-019-7604-8",
journal = "Eur. Phys. J. C",
volume = "80",
number = "1",
pages = "37",
year = "2020"
}
```
Owner
- Name: gangchern
- Login: AmplitudeGravity
- Kind: user
- Repositories: 4
- Profile: https://github.com/AmplitudeGravity
Theoretical Physics coding in Mathematica and Julia
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