{ "info": { "author": "Oleksandr Gituliar, Vitaly Magerya", "author_email": "oleksandr@gituliar.net", "bugtrack_url": null, "classifiers": [ "Development Status :: 4 - Beta", "Intended Audience :: Science/Research", "License :: OSI Approved :: ISC License (ISCL)", "Operating System :: POSIX :: Linux", "Programming Language :: Python :: 2.7", "Topic :: Scientific/Engineering :: Mathematics", "Topic :: Scientific/Engineering :: Physics" ], "description": "*Fuchsia* reduces differential equations for Feynman master integrals to canonical form.\n\nIn concrete terms, let us say we have a system of differential equations of this form:\n\n \u2202f(x,\u03f5)/\u2202x = \ud835\udd44(x,\u03f5) f(x,\u03f5)\n\nwhere `\ud835\udd44(x,\u03f5)` is a given matrix of rational functions in `x` and `\u03f5`, i.e, a free variable and an infinitesimal parameter.\nOur ultimately goal is to find a column vector of unknown functions `f(x,\u03f5)` as a Laurent series in `\u03f5`, which satisfies our equations.\n\nWith the help of *Fuchsia* we can find a transformation matrix `\ud835\udd4b(x,\u03f5)` which turns our system to the equivalent Fuchsian system of this form:\n\n \u2202g(x,\u03f5)/\u2202x = \u03f5 \ud835\udd4a(x) g(x,\u03f5)\n\nwhere `\ud835\udd4a(x) = \u2211\u1d62 \ud835\udd4a\u1d62/(x-x\u1d62)` and `f(x,\u03f5) = \ud835\udd4b(x,\u03f5) g(x,\u03f5)`.\n\nSuch a transformation is useful, because we can easily solve the equivalent system for `g(x,\u03f5)` (see [1]) and then, multiplying it by `\ud835\udd4b(x,\u03f5)`, find `f(x,\u03f5)`.\n\nYou can learn about the algorithm used in *Fuchsia* to find such transformations from Roman Lee's paper [2].\n\n*Fuchsia* is available both as a command line utility and as a (Python) library for SageMath [3].\nIt will run on most Unix-like operating systems.\n\nDocumentation with more information, installation and usage details is here [4].\n\n * [1] https://arxiv.org/abs/1304.1806\n * [2] https://arxiv.org/abs/1411.0911\n * [3] http://www.sagemath.org/\n * [4] http://www.gituliar.net/fuchsia/fuchsia.pdf", "description_content_type": null, "docs_url": null, "download_url": "http://gituliar.net/fuchsia/fuchsia-16.7.25.tar.gz", "downloads": { "last_day": -1, "last_month": -1, "last_week": -1 }, "home_page": "http://www.gituliar.net/fuchsia/", "keywords": "differential equations,Feynman integrals", "license": "ISC License", "maintainer": null, "maintainer_email": null, "name": "fuchsia", "package_url": "https://pypi.org/project/fuchsia/", "platform": "any", "project_url": "https://pypi.org/project/fuchsia/", "project_urls": { "Download": "http://gituliar.net/fuchsia/fuchsia-16.7.25.tar.gz", "Homepage": "http://www.gituliar.net/fuchsia/" }, "release_url": "https://pypi.org/project/fuchsia/16.7.25/", "requires_dist": null, "requires_python": null, "summary": "Fuchsia reduces differential equations for Feynman master integrals to canonical form", "version": "16.7.25" }, "last_serial": 2259916, "releases": { 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