Simplification of the Dirac Delta in xδ (x)

Question

I cannot get sympyto simplify xδ(x)to 0, where δis DiracDelta.

In : simplify(x*DiracDelta(x))
Out: x⋅δ(x)

Is there another simplification procedure that will evaluate the terms in the coefficient of the Dirac function at the zeros of its argument and check if they disappear?

This would be useful in constructing piecewise functions, such as f(x)= x H(x)(where H is the Heaviside function), the derivative of which should be H(x), but x⋅δ(x) + Heaviside(x)in sympy. Mathematica simplifies xδ(x)to 0.

Answer 1

You can massage x*DiracDelta(x)by 0, integrating, and then differentiating, because you integrateunderstand what is happening and returns 0.

>>> (x*DiracDelta(x)).integrate(x).diff(x)
0

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