Comment #9 on issue 3560 by [email protected]: solve() is a giant mess
http://code.google.com/p/sympy/issues/detail?id=3560
@asmeurer: With a multivariate system of equations, there's no such thing
as "the solution for a specific variable". Also, in general, there is no
way to iterate over the solution set (since it can be infinite and even
uncountable). So I don't understand what you're suggesting.
Anyway, my idea here is actually to quit trying to improve solve() and to
create a robust and reliable way of finding the set of values satisfying a
boolean expression (I'll call it newsolve()), that can be used in library
code without complicated pre- and post-checks. Compatibility with solve()
and use in interactive sessions should explicitly not be a concern at first.
I think that what we need most is a way to represent symbolic solution
sets. newsolve(f(x), x) should return something like FilteredSet(Reals,
Lambda([x], Eq(f(x), 0)), and newsolve(x**2 + y**2 < 1, [x, y]) something
like
FilteredSet(CartesianPower(Reals, 2), Lambda([x, y], x**2 + y**2 < 1)).
So we need more expressivity in building symbolic sets and also boolean
Lambdas.
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