Rust implementation of polylogarithms.


Keywords
rust, special-functions
License
LGPL-3.0-only

Documentation

Polylog

Build Status Documentation

The Polylog package provides Rust implementations of real and complex polylogarithms, including the dilogarithm and trilogarithm.

The Polylog package depends on the num crate.

Example

use num::complex::Complex;
use polylog::{Li, Li0, Li1, Li2, Li3, Li4, Li5, Li6};

let x = 1.0;
let z = Complex::new(1.0, 1.0);
let n = 10;

// real polylogarithms for real arguments
println!("Li0({}) = {}", x, x.li0());      // Re[Li_0(x)]
println!("Li1({}) = {}", x, x.li1());      // Re[Li_1(x)]
println!("Li2({}) = {}", x, x.li2());      // Re[Li_2(x)] (dilogarithm)
println!("Li3({}) = {}", x, x.li3());      // Re[Li_3(x)] (trilogarithm)
println!("Li4({}) = {}", x, x.li4());      // Re[Li_4(x)]
println!("Li_{}({}) = {}", n, x, x.li(n)); // Re[Li_n(x)]

// complex polylogarithms for complex arguments
println!("Li0({}) = {}", z, z.li0());      // Li_0(z)
println!("Li1({}) = {}", z, z.li1());      // Li_1(z)
println!("Li2({}) = {}", z, z.li2());      // Li_2(z) (dilogarithm)
println!("Li3({}) = {}", z, z.li3());      // Li_3(z) (trilogarithm)
println!("Li4({}) = {}", z, z.li4());      // Li_4(z)
println!("Li5({}) = {}", z, z.li5());      // Li_5(z)
println!("Li6({}) = {}", z, z.li6());      // Li_6(z)
println!("Li_{}({}) = {}", n, z, z.li(n)); // Li_n(z)

Notes

The implementation of the real dilogarithm is an adaptation of [arXiv:2201.01678].

The implementation of the complex dilogarithm has been inspired by the implementation in SPheno and has been translated to Rust.

The implementation of the real trilogarithm is an adaptation of [arXiv:2308.11619].

The implementation of the general n-th order polylogarithm is an adaptation of [arXiv:2010.09860].

Copying

Polylog is licenced under the GNU Lesser General Public License (GNU LGPL) version 3.