Consider

sage: x,y,z=QQ['x','y','z'].gens()
sage: u,v,w=W['u','v','w'].gens()
sage: %timeit ((x+y+z)**3)(1/y,y,y**100)
10 loops, best of 3: 752 ms per loop    <=== look here!
sage: %timeit ((u+v+w)**3)(1/v,v,v**100)
10 loops, best of 3: 48.2 ms per loop  <=== look here!
Conclusion: rational functions over the rationals are unusably slow at
this time.
I even know what the reason is. Rational functions over W do not
support reduce so it
is not called during the intermediate computations which happens to be
a blessing.

William: I know you can easily fix this yourself.  If you are too busy
would you be interested in a patch? I think this kind of janitorial
work is important to improve the predictability
of sage behaviour.

Michel


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