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We provide a C++ library and Python, Mathematica and Fortran interfaces to thermal functions, defined\f[J_{B/F}(y^2)=\Re\int_0^{\infty} dx,x^2 \ln\left(1\mp\exp\left(-\sqrt{x^2 + y^2}\right)\right).\f]

We offer Taylor expansion, numerical integration (quadrature), a Bessel functionrepresentation, an approximation, a Hurwitz zeta function representation, and an upper bound for the integrals. First and secondderivatives with respect to \f$y^2\f$ are also implemented.

The accompanying manual is1802.02720. If you use this library, please cite,

@article{Fowlie:2018eiu,    author         = "Fowlie, Andrew",    title          = "{A fast C++ implementation of thermal functions}",    doi            = "10.1016/j.cpc.2018.02.015",    year           = "2018",    eprint         = "1802.02720",    archivePrefix  = "arXiv",    primaryClass   = "hep-ph"}

The documentation is atcodedocs. To build this documentation indoxygen,

make docs

The C++ requiresgsl andgslcblas and ac++11 compiler. The Python interface requires Python 2 or 3, SWIG and aPython.h header file (which is part ofpython-dev in Ubuntu). The Mathematica interface was tested for Mathematica 11.

Build the library via

make lib

This should build./lib/thermal_funcs.so. The header file is./src/thermal_funcs.h.

There is a C example./src/example.cpp, built by

make example

This should build a program./bin/example, which when executed prints the result of evaluating a thermal function.

Build the interface via

make python

The interface

from thermal_funcs import J_B, J_FJ_F(100., method='quad')

is compatible with Python 2 and 3, though must be built for a specific version. It has no module dependencies. By default,SWIG will build for yourpython --version. To alter this, change thePYTHON variable in the makefile to compile withyour chosenPython.h header. The derivatives are called by a keyword argument e.g.,J_F(100., derivative=1).

This is slightly more involved. This may work in Linux ifmath is in yourPATH:

make mathematica

But otherwise you may have to tweak the./src/makefile variableMATH_INC for the locations of yourwscc linker andwstp.h header file. You can find this on any platform in Mathematica fromFileNameJoin[{$InstallationDirectory, "SystemFiles", "Links", "WSTP", "DeveloperKit", $SystemID, "CompilerAdditions"}].

Then within Mathematica,

Install["./src/math.exe"];Plot[{JB[ysq], JF[ysq]}, {ysq, -100, 100}]

Note well that you should use the correct (relative or absolute) path to./src/math.exe in the commandInstall["./src/math.exe"]. The interface was built and tested with Mathematica 11.1.1. The derivatives are called by a keyword argument e.g.,JB[100., derivative->1].

If the executable./src/math.exe was built butInstall fails, try installing step by step to find debugging information. First, run the created executable,

./src/math.exe

This should prompt you toCreate link:. Enter e.g.foo. Don't exit that session. In Mathematica, try

$VersionNumberlink = LinkConnect["foo"]Install[link]JB[100]

to find the step that fails.

You can also try one of the pre-built examples provided by Mathematica, e.g.,

Install["/usr/local/Wolfram/Mathematica/11.1/SystemFiles/Links/WSTP/DeveloperKit/Linux-x86-64/PrebuiltExamples/addtwo"]AddTwo[2, 2]

and re-building it locally,

MATH=/usr/local/Wolfram/Mathematica/11.1/SystemFiles/Links/WSTP/DeveloperKit/Linux-x86-64/mkdir ~/addtwocd ~/addtwocp $MATH/WSTPExamples/addtwo* ./$MATH/CompilerAdditions/wscc addtwo.tm addtwo.c -o addtwo

then in Mathematica,

Install["~/addtwo/addtwo"]AddTwo[2, 2]

This may help find the origin of any problems. You must, of course, replace the paths to the ones on your machine.

There is a basic Fortran example, built by

make fortran

and executed by

./bin/fortran_example

This requires a Fortran compiler with support foriso_c_binding, which is included in the Fortran 2003 or later standard and GNU extensions.

ThisStack Exchange answer was helpful for removing linker warnings fromwscc, andthis one was helpful for automatically locating Mathematica header files.