System of PDE's Satisfied by the Product
Computing a system for the product is now a simple call to Mgfun[`sys*sys`] .
Note that the routine gfun[`diffeq*diffeq`] performs a similar task, but is restricted to the univariate case, i.e., to functions described by a single ODE. Thus, it can only compute the ODE which does not involve cross-derivatives in the system above, and a similar equation with derivations with respect to . It turns out that this would induce a loss of information, precluding the following calculation of the integral. Besides, Mgfun[`sys*sys`] would also deal with systems of mixed differential-difference equations.