We can already solve that one using LambertW (but we need to implement
all the branches,
https://code.google.com/p/sympy/issues/detail?id=4006).

Can these work with trig functions (via equivalence from complex
exponentials)? A more classic example of a root that can't be
expressed in closed-form is cos(x) = x.

Aaron Meurer

On Sun, Feb 2, 2014 at 5:46 AM, someone <[email protected]> wrote:
> Hi,
>
>> Great. Those should be useful for getting solve to return *all*
>> solutions in those cases, even if just in a symbolic form.
>
> Right. I Imagine something like:
>
> TransRootOf(exp(x)-x**2, x, 0)
> TransRootOf(exp(x)-x**2, x, 1)
> TransRootOf(exp(x)-x**2, x, 2)
>
> for the three roots of this equation.
>
>> Do the algorithms work at all if there are symbolic coefficients?
>
> No, not as far as I know. This is difficult if possible
> at all. There are some results for parametric polynomials.
>
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