Indignum est excellentium virorum horas
perire quia machina adhibita
vilissimo cuique secure transcribi
Since MuPAD went commercial
Actually, the most useful fork of Axiom at the moment
(and perhaps for the next 30 years) is
but see also OpenAxiom.
Some time ago I started to write a package for combinatorial probability
theory in FriCAS.
It can handle computations with moments, cumulants and orthogonal polynomials
and is included in the FriCAS library since release 1.1.4.
Here is a short description
and example files
Here is a source code
is annotated using
and typeset here.
In the future I plan to release packages for set partitions
and algebras which will allow to handle multivariate noncommutative probability as well.
"For it is unworthy of distinguished men to waste their time with slavish calculations, which can be done safely with the use of this machine by anyone else."