Waldek Hebisch schrieb: > > Using delta functions can lead to problems with zero divisors. > For example in Maple I get: > > > (x - 4)*Dirac(x - 4); > (x - 4) Dirac(x - 4) > > > simplify((x - 4)*Dirac(x - 4)); > 0 > > > (x - 4)*Dirac(x - 4)/(x-4); > Dirac(x - 4) > > 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? >
MAple's evaluations are consistent applications of the rule
f(x)*delta(x-a) -> f(a)
which defines the meaning of a Dirac delta times a function that is differentiable infinitely often. So the cofactor must not be split it subfactors here.
The Dirac delta is a so-called "distribution"; these object are defined via their action on certain spaces of "test functions". You may for example refer to Costantinescu (1974), "Distributionen und ihre Anwendungen in der Physik", but any other text on "distributions" should do as well.