Updates:
Summary: Should Heaviside raise ValueError if the argument is not real?
Comment #1 on issue 3098 by asmeu...@gmail.com: Should Heaviside raise
ValueError if the argument is not real?
http://code.google.com/p/sympy/issues/detail?id=3098
Maple gives an error:
Heaviside(1 + I);
Error, (in Heaviside) not defined for non-real values
The Mathematica docs
(http://reference.wolfram.com/mathematica/ref/HeavisideTheta.html) say:
HeavisideTheta cannot be uniquely defined with complex arguments (no Sato
hyperfunction interpretation):
In[1]:= HeavisideTheta[1+2I]
Out[1]= HeavisideTheta[1+2I]
So it seems it leaves it unevaluated. I don't know what would happen if
you tried to numerically evaluate that.
I think we should do what Maple does.
At any rate, evalf() should recursively evaluate the argument:
In [15]: Heaviside(pi*I).n()
Out[15]: Heaviside(ⅈ⋅π)
By the way, the Mathematica docs also have an interesting note:
PiecewiseExpand does not operate on HeavisideTheta because it is a
distribution and not a piecewise-defined function:
This is an interesting approach, which is to model distributions and
piecewise functions separately.
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