The Free Algebras Data collection contains information about systems of (noncommutative) polynomials interpreted as twosided ideals in a free algebra over the integers. We assume the user to have semantic aware tools to work with noncommutative polynomials (that supply input and computation methods). Such tools are not part of the SymbolicData Collection.
Free Algebras are given as XML sequence of noncommutative polynomials with integer coefficients in distributive normal form, complying to the syntactical restrictions of ncpoly defined in Types.xsd. The list of variables is part of the XML record.
The ncpoly syntax for variables has to be tightened within a quality assurance process to avoid characters ()[] that are interpreted as function calls – hgg, 2013-07-05