Metadata-Version: 1.1
Name: fuchsia
Version: 16.6.23
Summary: Fuchsia reduces differential equations for Feynman master integrals to canonical form
Home-page: http://www.gituliar.net/fuchsia/
Author: Oleksandr Gituliar, Vitaly Magerya
Author-email: oleksandr@gituliar.net
License: ISC License
Download-URL: http://gituliar.net/fuchsia/fuchsia-16.6.23.tar.gz
Description: *Fuchsia* reduces differential equations for Feynman master integrals to canonical form.
        
        In concrete terms, let us say we have a system of differential equations of this form:
        
            ∂f(x,ϵ)/∂x = 𝕄(x,ϵ) f(x,ϵ)
        
        where `𝕄(x,ϵ)` is a given matrix of rational functions in `x` and `ϵ`, i.e, a free variable and an infinitesimal parameter.
        Our ultimately goal is to find a column vector of unknown functions `f(x,ϵ)` as a Laurent series in `ϵ`, which satisfies our equations.
        
        With the help of *Fuchsia* we can find a transformation matrix `𝕋(x,ϵ)` which turns our system to the equivalent Fuchsian system of this form:
        
            ∂g(x,ϵ)/∂x = ϵ 𝕊(x) g(x,ϵ)
        
        where `𝕊(x) = ∑ᵢ 𝕊ᵢ/(x-xᵢ)` and `f(x,ϵ) = 𝕋(x,ϵ) g(x,ϵ)`.
        
        Such a transformation is useful, because we can easily solve the equivalent system for `g(x,ϵ)` (see [1]) and then, multiplying it by `𝕋(x,ϵ)`, find `f(x,ϵ)`.
        
        You can learn about the algorithm used in *Fuchsia* to find such transformations from Roman Lee's paper [2].
        
        *Fuchsia* is available both as a command line utility and as a (Python) library for SageMath [3].
        It will run on most Unix-like operating systems.
        
        Documentation with more information, installation and usage details is here [4].
        
          * [1] https://arxiv.org/abs/1304.1806
          * [2] https://arxiv.org/abs/1411.0911
          * [3] http://www.sagemath.org/
          * [4] http://www.gituliar.net/fuchsia/fuchsia.pdf
        
Keywords: differential equations,Feynman integrals
Platform: any
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Scientific/Engineering :: Physics
Classifier: License :: OSI Approved :: ISC License (ISCL)
Classifier: Operating System :: POSIX :: Linux
Classifier: Programming Language :: Python :: 2.7
