Combinatorics

Discrete mathematics

Symbol (formal)

Loop (graph theory)

Pure mathematics

Hopf algebra

Mathematics

Mathematical physics

Algorithm

Parametric statistics

Statistics

Algebra over a field

Mathematical analysis

Iterated function

Programming language

Computer science

Computation

Feynman diagram

Fibration

Homotopy

Journal of High Energy Physics

A bstract We review the Hopf algebra of the multiple polylogarithms and the symbol map, as well as the construction of single valued multiple polylogarithms and discuss an algorithm for finding fibration bases. We document how these algorithms are implemented in the M athematica package P oly L og T ools and show how it can be used to study the coproduct structure of polylogarithmic expressions and how to compute iterated parametric integrals over polylogarithmic expressions that show up in Feynman integal computations at low loop orders.

PolyLogTools — polylogs for the masses