> Surely the bug is related to the fact that the last call to resultant returns 256*(sqrt(7)^2-7) instead of 0.
I looked at this a bit more. The macro what-the-$ev is involved in checking for spurious roots. And it's
radcan that tries to simplify an expression to zero. But in solving these equations, radcan tries to simplify
(for example)
2*sqrt(7)+sqrt(4-sqrt(7))*(2^(1/2))^3+2
to zero, but is unable to crunch it to zero.
--Barton