I ran into an assertion error when trying to return a sorted list whose key 
was a certain linear combination of eigenvalues of the Laplacian matrix 
over graphs on nine vertices. Digging into it a bit, the failure happened 
when comparing an algebraic real number against the same number that was 
constructed differently (starting with the graph complement). Digging 
further, the error happens when finding roots of a certain degree 56 
polynomial over AA (all the roots are real) but there is no error doing the 
same thing over QQbar.

Here is a minimal working example:

P.<z> = QQ[]
rootlist = (z^8 - 32*z^7 + 425*z^6 - 3044*z^5 + 12789*z^4 - 32090*z^3 + 
46672*z^2 - 35734*z + 10917).roots(AA)
problem = rootlist[-1][0] - rootlist[0][0] - 9

problem.minpoly().roots(AA)

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