  Hopf algebraic structures will replace groups and group representations as
the leading paradigm in forthcoming times. K-theory, co-homology, entanglement,
statistics, representation categories, quantized or twisted structures as well
as more geometric topics of invariant theory, e.g., the Grassmann-Cayley
bracket algebra are all covered by the Hopf algebraic framework. The new branch
of 'experimental mathematics' allows one to easily enter these fields through
direct calculations using symbolic manipulation and computer algebra system
(CAS). We discuss problems which were solved when building the BIGEBRA package
for Maple and CLIFFORD [see math-ph/0212031] to handle tensor products,
Grassmann and Clifford algebras, coalgebras and Hopf algebras. Recent results
showing the usefulness of CAS for investigating new and involved mathematics
provide us with examples. An outlook on further developments is given.
