Problems with product():  It is dreadfully inefficient compared to a
good implementation of factorial.  It has the same name a new itertool
with much different functionality.  The hyper-generalization takes us
further away from the OP's dirt simple request for a piece of
functionality that is widely understood, frequently reimplemented, and
has a near zero learning curve.  If his request is accepted, it does not
preclude you from making some other module with tons of functions of
interest to encryption people, number theorists, and statisticians.