Reduze - Feynman integral reduction in C++

By C. Studerus. Computer Physics Communications, 2009

415 citations recorded by the source corpus.

Abstract Reduze is a computer program for reducing Feynman integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel. Program summary Program title: Reduze Catalogue identifier: AEGE_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:: yes No. of lines in distributed program, including test data, etc.: 55 433 No. of bytes in distributed program, including test data, etc.: 554 866 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Unix/Linux Number of processors used: The number of processors is problem dependent. More than one possible but not arbitrary many. RAM: Depends on the complexity of the system. Classification: 4.4, 5 External routines: CLN ( http://www.ginac.de/CLN/ ), GiNaC ( http://www.ginac.de/ ) Nature of problem: Solving large systems of linear equations with Feynman integrals as unknowns and rational polynomials as prefactors. Solution method: Using a Gauss/Laporta algorithm to solve the system of equations. Restrictions: Limitations depend on the complexity of the system (number of equations, number of kinematic invariants). Running time: Depends on the complexity of the system.

Subfields: Artificial Intelligence, Computer Networks and Communications, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/28aca86516f12253efa9ffa8dabbc2e8c37eb214

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Citations in the corpus

New developments in FeynCalc 9.0 (2016, methodology): “Although FeynCalc doesn’t include a general purpose tool for IBP reduction (the built-in TARCER [45] is suitable only for 2-loop self-energy type integrals), this omission can be compensated by using one of the publicly available IBP-packages (FIRE [39], LiteRED [46], Reduze [47], AIR [48]).”
The two-loop sunrise graph with arbitrary masses (2013, neutral): “Integration-by-parts identities [13, 14,32] are of the form”
LiteRed 1.4: a powerful tool for reduction of multiloop integrals (2013, background): “These advantages explain why many modern most powerful reduction programs heavily rely on this algorithm, in particular, AIR [4], FIRE [5], Reduze [6, 7], and many private versions.”
A quasi-finite basis for multi-loop Feynman integrals (2014, neutral): “reference [34].”
Presenting LiteRed: a tool for the Loop InTEgrals REDuction (2012, background): “These advantages explain why many modern most powerful reduction programs heavily rely on this algorithm, in particular, AIR [4], FIRE [5], Reduze [6, 7], and many private versions.”
Critical points and number of master integrals (2013, methodology): “In[5]:= Timing@FindMIs@8-sp@k1D, -sp@k2D, -sp@k3D, -sp@k4D, 1 - sp@k1 + pD, 1 - sp@k1 + k2 + pD, 1 - sp@k1 + k2 + k3 + pD, 1 - sp@k2 + k3 + k4 + pD, 1 - sp@k3 + k4 + pD, 1 - sp@k4 + pD<, 8k1, k2, k3, k4<DD”
Collider physics at the precision frontier (2020, methodology): “Public implementations of the Laporta algorithm are available in the programs Air [458], Reduze [459, 421], Fire [460–462], LiteRed [463, 464] and Kira [432, 465, 466].”
FIRE5: A C++ implementation of Feynman Integral REduction (2014, background): “For other public products see [6, 7, 8, 9, 10, 11] The goal of this paper is to present the C++ version of FIRE — a powerful program for Feynman integral reduction.”
Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral (2016, methodology): “2) can be very easily reduced to master integrals using, for example, Reduze 2 [31,32].”
Calculation of the quark and gluon form factors to three loops in QCD (2010, methodology): “For this reduction, we used the Mathematica-based package FIRE [52] and the C++ package Reduze [53], which was developed most recently by one of us.”