  We have reviewed some results on quantized shuffling, and in particular, the
grading and structure of this algebra. In parallel, we have summarized certain
details about classical shuffle algebras, including Lyndon words (primes) and
the construction of bases of classical shuffle algebras in terms of Lyndon
words. We have explained how to adapt this theory to the construction of bases
of quantum group algebras in terms of Lyndon words. This method has a limited
application to the specific case of the quantum group parameter being a root of
unity, with the requirement that specialization to the root of unity is
non-restricted. As an additional, applied part of this work, we have
implemented a Wolfram Mathematica package with functions for quantum shuffle
multiplication and constructions of bases in terms of Lyndon words.
