Comment #4 on issue 2343 by [email protected]: as_poly returns None
http://code.google.com/p/sympy/issues/detail?id=2343

The geometry module is the environment of interest. Let's say the user
want to find the intersection of an ellipse and a parabola. The
equation of the ellipse can be constructed from the  Ellipse object
(as I did in the pasted example). It has default 'x' and 'y'
variables. Then the user might define their parabola and then send
these two equations to solve...which will fail because the ellipse's
variables are not the same (hash) as the local ones they are using. So
I think the user should either send their own variables (e.equation(x,
y)). If they don't then the perhaps dummies should be used so visually
it alerts the user to the fact that these are not (fully) accessible
to them....but the results are not that visually pleasing....but
that's better than thinking you can't do anything with them.

An alternative to the solving problem is to internally match variables
by name, replacing the variables in the equation with those given by
the user. Also, for the equation set that I showed, *not* providing
variables would have worked so long as there were only two variables
to be solved for.

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