I don't think there is currently any expression that causes minpoly to hang...not saying that one couldn't be constructed. It would be instructive to see if the approach that radsimp takes before getting to the minpoly fallback is successful in handling such an expression (if one can be found).

<a few minutes later>

ok, this hangs

```
>>> z
1/sqrt(sqrt(7)/7 + 2*sqrt(2) + 3*sqrt(3) + 5*sqrt(5))

but

>>> denom(radsimp(z))
296620024101625
>>> 
```