https://github.com/expander/polylogarithm

Implementation of polylogarithms in C/C++/Fortran
https://github.com/expander/polylogarithm

c cplusplus cpp fortran math mit-license polylogarithm special-functions

Last synced: 11 days ago
JSON representation

Implementation of polylogarithms in C/C++/Fortran

• Host: GitHub
• URL: https://github.com/expander/polylogarithm
• Owner: Expander
• License: mit
• Created: 2015-09-11T13:54:06.000Z (about 9 years ago)
• Default Branch: master
• Last Pushed: 2024-10-27T12:46:38.000Z (12 days ago)
• Last Synced: 2024-10-27T14:23:13.911Z (12 days ago)
• Topics: c, cplusplus, cpp, fortran, math, mit-license, polylogarithm, special-functions
• Language: C++
• Homepage:
• Size: 10.3 MB
• Stars: 33
• Watchers: 5
• Forks: 4
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE
  • Citation: CITATION.cff

Awesome Lists containing this project

README

        
Polylogarithm

=============

[![Build Status](https://github.com/Expander/polylogarithm/workflows/test/badge.svg)](https://github.com/Expander/polylogarithm/actions)

[![Coverage Status](https://coveralls.io/repos/github/Expander/polylogarithm/badge.svg)](https://coveralls.io/github/Expander/polylogarithm)

The Polylogarithm package provides C, C++ and Fortran implementations

of various polylogarithms, including the real and complex dilogarithm,

trilogarithm, and (Standard and Glaisher) Clausen functions.  The

implementations have been fully tested against the literature and many

other implementations and are highly optimized for fast numerical

evaluation.

The package has no external dependencies, except for the C/C++/Fortran

standard libraries.  The implementations of the individual polylogarithm

functions are distributed among different source code files, so

individual source code files can be easily extracted and incorporated

into existing projects.

Example in C++

--------------

```.cpp

#include "Li.hpp"

#include "Li2.hpp"

#include "Li3.hpp"

#include "Li4.hpp"

#include "Li5.hpp"

#include "Li6.hpp"

#include 

int main() {

   using namespace polylogarithm;

   const double x = 1.0;

   const std::complex z(1.0, 1.0);

   // real polylogarithms for real arguments

   std::cout

      << "Li_2(" << x << ") = " << Li2(x) << '\n'

      << "Li_3(" << x << ") = " << Li3(x) << '\n'

      << "Li_4(" << x << ") = " << Li4(x) << '\n';

   // complex polylogarithms for complex arguments

   std::cout

      << "Li_2(" << z << ") = " << Li2(z) << '\n'

      << "Li_3(" << z << ") = " << Li3(z) << '\n'

      << "Li_4(" << z << ") = " << Li4(z) << '\n'

      << "Li_5(" << z << ") = " << Li5(z) << '\n'

      << "Li_6(" << z << ") = " << Li6(z) << '\n'

      << "Li_10(" << z << ") = " << Li(10,z) << '\n';

}

```

Output:

```

Li_2(1) = 1.64493

Li_3(1) = 1.20206

Li_4(1) = 1.08232

Li_2((1,1)) = (0.61685,1.46036)

Li_3((1,1)) = (0.871159,1.26708)

Li_4((1,1)) = (0.959319,1.13804)

Li_5((1,1)) = (0.987467,1.06844)

Li_6((1,1)) = (0.99615,1.03355)

Li_10((1,1)) = (0.999962,1.00199)

```

Notes

-----

The implementation of the real dilogarithm is an adaptation of

[[arXiv:2201.01678](https://arxiv.org/abs/2201.01678)].

The implementation of the complex dilogarithm is inspired by the

implementation in [SPheno](https://spheno.hepforge.org/).

The implementation of the real trilogarithm is an adaptation of

[[arXiv:2308.11619](https://arxiv.org/abs/2308.11619)].

The implementation of the general n-th order complex polylogarithm an

adaptation of [[arXiv:2010.09860](https://arxiv.org/abs/2010.09860)].

Copying

-------

Polylogarithm is licenced under the MIT License.