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AMFlow.cpp
A C++17 reimplementation of the auxiliary-mass-flow algorithm
introduced by Xiao Liu and Yan-Qing Ma in the Mathematica package
AMFlow:
https://gitlab.com/multiloop-pku/amflow
Liu, Ma — "AMFlow: A Mathematica package for Feynman integrals
computation via auxiliary mass flow", Comput. Phys. Commun. 283
(2023) 108565, doi:10.1016/j.cpc.2022.108565.
Copyright (C) 2022 Xiao Liu and Yan-Qing Ma (upstream MMA package)
This project (the C++ implementation) does NOT bundle any upstream
Mathematica source. All algorithmic credit belongs to the AMFlow
authors above; this repository contributes only the C++17
re-implementation, plus benchmarks comparing it numerically to the
Mathematica reference.
If you use this software in published research, please cite **both**
the AMFlow paper above (for the algorithm) and this repository (for
the implementation). See CITATION.cff for machine-readable metadata.
------------------------------------------------------------------------
Implementation provenance
------------------------------------------------------------------------
The C++17 source in this repository was developed primarily by AI
coding agents under the direction of the maintainer
(3250800970@qq.com), with every behavioural change gated by
numerical-parity verification against the upstream Mathematica
reference.
Maintainer contact: 3250800970@qq.com
------------------------------------------------------------------------
License of the AMFlow Mathematica package
------------------------------------------------------------------------
The MIT license below, reproduced in full from LICENSE.md in the AMFlow
repository (https://gitlab.com/multiloop-pku/amflow), covers the AMFlow
Mathematica package by Xiao Liu and Yan-Qing Ma (AMFlow 2.0 with Rui-Jun
Huang): the reference implementation whose Mathematica-computed values,
committed under tools/bench/ and tests/data/math_ref/, this C++
implementation is verified against, as described above. The package
itself is not bundled in this repository; this section was added in the
BootLoops fork (see README.md).
The MIT License (MIT)
Copyright (C) 2022 Xiao Liu and Yan-Qing Ma
Copyright (C) 2026 Rui-Jun Huang, Xiao Liu and Yan-Qing Ma
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.