x*DiracDelta(x) does not simplify to 0

[normalhuman]

Neither simplify, nor expand_func, not other methods I tried could turn x*DiracDelta(x) into 0.

Well, except for the absurd "integrate and then differentiate" trick.

Reported on Stack Overflow

[jashan498]

I would like to work on this.

[asmeurer]

As far as I know, the only thing that knows anything about DiracDelta is integrate (mathematically, DiracDelta doesn't even make sense outside of an integral, although SymPy allows that as a formalism).

I'm not sure what existing method should do it.

[jksuom]

It could probably be done by __mul__ of DiracDelta (if its priority was raised):

`f(x)*DiracDelta(x) -> f(0)*DiracDelta(x)`

It would be automatic, but I don't think any harm would follow.

[asmeurer]

Wouldn't that defeat the purpose of deltaintegrate?

[jksuom]

It seems to me that deltaintegrate aims to deal with expressions of the form δ(f(x)) (inverse image under f of δ considered as a generalized density). Straightforward multiplication could be handled in DiracDelta class with δ regarded as a distribution. It is possible to multiply δ(x) by a function but not by itself. That could be taken care of by a local __mul__ method.

[asmeurer]

I also want to note that from a technical point of view, I'm not very convinced that the current ways of doing such things are well designed (c.f. #13161).