Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language

By Christian Bauer, A. Frink, R. Kreckel. Journal of symbolic computation, 2000

528 citations recorded by the source corpus.

The traditional split into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system that deliberately denies the need for such a distinction. It is entirely written in C++and the user can interact with it directly in that language. It was designed to provide efficient handling of multivariate polynomials, algebras and special functions that are needed for loop calculations in theoretical quantum field theory. It also bears some potential to become a more general purpose symbolic package.

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Citations in the corpus

Fully differential NNLO computations with MATRIX (2017, background): “cluster_submit_line[1-99] Lines in cluster submit file to add cluster-specific options.”
Soft triple-real radiation for Higgs production at N3LO (2013, methodology): “2 Calculation To obtain the real-emission cross-section we generate Feynman diagrams using QGRAF [83] and compute squared matrix-elements using programs based on GiNaC [84] or FORM [85] and our own C++ code for color and spin algebra.”
Feynman integrals and hyperlogarithms (2015, background): “Facilities for numeric evaluations of hyper- and polylogarithms are not included, because such are not necessary for the integration algorithms and secondly there are already established programs available for this task [14, 175].”
Integral reduction with Kira 2.0 and finite field methods (2020, background): “Dependencies Kira requires the following packages to be installed on the system: • GiNaC [73–75], which itself requires CLN [76], • zlib [77].”
Higgs boson production at hadron colliders at N3LO in QCD (2018, methodology): “Next, we perform spinor and colour algebra in a private c++ code based on GiNaC [78].”
Lectures on differential equations for Feynman integrals (2014, background): “On the positive side, there exist dedicated numerical integration routines for these functions [70, 71].”
The four-loop six-gluon NMHV ratio function (2015, methodology): “However, it is relatively straightforward to express any function with these symbol letters in terms of Goncharov polylogarithms, which in turn can be evaluated numerically with GiNaC [92, 93].”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “GiNaC (Bauer et al., 2002) is an open source C++ library for symbolic calculations.”
W±Z production at the LHC: fiducial cross sections and distributions in NNLO QCD (2016, methodology): “des we rely on a public C++ library [73] that implements the results of Ref. [48], and for the numerical evaluation of the relevant multiple polylogarithms we use the implementation [74] in the GiNaC [75] library. The contribution of the massive-quark loops is neglected in the two-loop amplitudes, b”
Reduze - Feynman integral reduction in C++ (2009, methodology): “Reduze uses the GiNaC library [8] for the algebraic manipulations.”
Single-valued harmonic polylogarithms and the multi-Regge limit (2012, methodology): “[63] C. W. Bauer, A. Frink and R. Kreckel, “Introduction to the GiNaC framework for symbolic computation within the C++ programming language,” cs/0004015 [cs-sc].”
Reduze 2 - Distributed Feynman Integral Reduction (2012, methodology): “For the displayed Fermat benchmarks, the system to be reduced was kept in RAM, while for the GiNaC benchmarks a database was used.”
W+W− production at the LHC: fiducial cross sections and distributions in NNLO QCD (2015, methodology): “[48], and for the numerical evaluation of the relevant multiple polylogarithms we use the implementation [74] in the GiNaC [75] library.”