Skip to main content

Fuchsia reduces differential equations for Feynman master integrals to canonical form

Project 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].

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

fuchsia-16.7.25.tar.gz (17.5 kB view hashes)

Uploaded Source

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page