Comment #6 on issue 2205 by ronan.l...@gmail.com: "Undefined functions"
http://code.google.com/p/sympy/issues/detail?id=2205

Removing .signature doesn't cause any problem. While removing .undefined_Function, I noticed that Application needs to know about UndefinedFunction, a subclass of its metaclass, which is bad design and turns out to be linked with a problem in the handling of .nargs:
"""
.nargs describes how many arguments a function takes. It only makes sense for function objects, i.e. instances of Lambda and subclasses of Function, but not for instances of Function. There were a few cases where 'expr.nargs' was used, but 'len(expr.args)' was actually meant.
"""

All this is fixed in https://github.com/rlamy/sympy/commits/fclean-2 but there are test "failures" in dsolve() that seem to result from improvements in its capabilities. (I don't know why it happens)

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