Computation tool for the q -deformed quasi-shuffle algebras and representations of structure of MZVs

Abstract

We would like to introduce our package using Maple to compute within the q -deformed 1 quasi-shuffle algebras and to represent structure of multiple zeta values (MZVs). For this package, we can define an arbitrary alphabet from which the letters associated with indices totally ordered and then carry out computations on words, that will complement functions for the package StringTools in Maple. In the vector space of (noncommutative) polynomials which is equipped q -deformed quasi-shuffle products and concatenation product [1, 2], we compute the bases in duality and express an arbitrary homogeneous polynomial in terms of these bases. Moreover, due to our algorithms, we can represent structure of MZVs on the transcendence bases in terms of irreducible elements [4]. We used this package to compute all examples and verify the results in the paper [4] which was present at the conference ISSAC 2015.