D Herring <firstname.lastname@example.org> wrote: > On 04/13/2013 12:02 PM, Waldek Hebisch wrote: > > Using delta functions can lead to problems with zero divisors. > ... > > which is clearly inconsistent. I wonder I there is any theory > > how to avoid such problems? I mean, what CAS can do to > > protect users from wrong results? > > The conservative approach is to disable simplifications where the CAS > is unsure of their correctness. Inside an integral, it can be > evaluated appropriately. Elsewhere, it should probably be preserved > as-is.
Beside integrals one probably should evaluate delta functions in few other contexts, like limits and explicit calls to simplify. If you globally disable other simplification due to (possible) presence of delta functions, then I am affraid that you get an unusable CAS. OTOH if you simplify other parts of expression then you get what Maple produced.
So it seems that you advocate for CAS to go on and let user worry about possible problems if his/her actions trigger evaluation at unfortunate point.