2. Finding all points of continuity in the function (if any), and checking
if the function is continuous at a given point or a given interval.
I think something you could use to do this is denoms:
denoms(eq, symbols=None)
Return (recursively) set of all denominators that appear in eq
that contain any symbol in iterable ``symbols``; if ``symbols`` is
None (default) then all denominators with symbols will be returned.
Examples
========
>>> from sympy.solvers.solvers import denoms
>>> from sympy.abc import x, y, z
>>> denoms(x/y)
set([y])
>>> denoms(x/(y*z))
set([y, z])
>>> denoms(3/x + y/z)
set([x, z])
So the singularities are located where the denominators are zero -- so the
union of all solutions to the denominators being zero should be that set of
points.
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