# Roots in a solution

When I solve the equations I obtained from the code in this question, I get a number of solutions. Most of them complex numbers, whereas the single real solution simply prints as r1 when first executing the code, as r2 next, and so on. So I gather that this is some root which Maxima or whoever is doing the solving cannot reduce to radicals.

So far, so good, but I'd still like to be able to get an idea of what that thing represents. Saving my solutions to a list of dictionaries, I've been able to isolate that value, but I can't seem to find any reasonable methods to obtain further details. In particular, r.n() tells me that it

TypeError: cannot evaluate symbolic expression numerically


So what can I do? how can I figure out what this thing actually represents? I believe that it might be some root of a polynomial which still contains one variable from my equation. But how can I obtain that polynomial?

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If you check out the documentation for solve, you'll see that

In some cases there may be infinitely many solutions indexed by a dummy variable. If it begins with z, it is implicitly assumed to be an integer, a real if with r, and so on:

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