Rational simplification bug ("Quotient by a polynomial of higher degree" error message)

Just a brief note about algorithms that seem not to work (subres..)

In fact one should not choose an algorithm based on which is fastest on 
problems
that are large  (in common parlance, "astronomical"  in size.)  If these 
large problems
are infrequent, an algorithm that is very fast -- maybe even based on a 
heuristic --
for small problems can be a winner. An interesting computer algebra system,
DERIVE, was originally (maybe still) based on the assumption that large 
problems
won't occur.   In some cases the area between "too large to do with 
simplistic
methods" and "too large to do any way whatsoever" seemed to be small.
Now that memories can be gigabytes, you don't run out of memory so often,
but you lose patience.

RJF

PS.  I am sure there are smaller problems that exhibit this kind of 
behavior.  Maybe
a nice one can be constructed by taking apart your example.