Comment #1 on issue 3512 by [email protected]: solve is slow for a simple set of equations.
http://code.google.com/p/sympy/issues/detail?id=3512

Try using manual=True in such cases (when you can solve faster by hand than the program can). When I do that I get a different error which I fixed in my 3512 branch (a pull request will appear in a moment). There are 5 nasty solutions, but if you make x and y real then you only get


var('x y',real=True)
(x, y)
solve([x**2 + y**2 -4, y - x**3], x,y,manual=1)
[(3**(1/6)*3**(1/3)*sqrt(-3**(1/3)*(-18 + sqrt(327))**(2/3) + 3**(2/3))/(3*(-18 + sqrt(327))**(1/6)), sqrt(3)*(-3**(1/3)*(-18 + sqrt(327))**(2/3) + 3**(2/3))**(3/2)/(9*sqrt(-18 + sqrt(327))))]


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