Integration-by-Parts: A Survey

DOI10.1007/978-3-030-80219-6_13zbMath1484.81044OpenAlexW3216167491MaRDI QIDQ5022181

Peter Marquard

Publication date: 18 January 2022

Published in: Texts & Monographs in Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-80219-6_13

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (1)

The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Cites Work

• FIRE5: a C++ implementation of Feynman integral REduction
• FIRE4, LiteRed and accompanying tools to solve integration by parts relations
• Finding linear dependencies in integration-by-parts equations: a Monte Carlo approach
• Algorithm FIRE-Feynman integral reduction
• \texttt{Reduze} -- Feynman integral reduction in \texttt{C++}
• TARCER -- a Mathematica program for the reduction of two-loop propagator integrals
• The property of maximal transcendentality: calculation of Feynman integrals
• Kira -- a Feynman integral reduction program
• FIRE6: Feynman integral reduction with modular arithmetic
• Reconstructing rational functions with \texttt{FireFly}
• Large Scale Analytic Calculations in Quantum Field Theories
• Top-Down Decomposition: A Cut-Based Approach to Integral Reductions
• MATAD: A program package for the computation of MAssive TADpoles
• \textsc{Forcer}, a \textsc{Form} program for the parametric reduction of four-loop massless propagator diagrams
• FMFT: fully massive four-loop tadpoles

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