(not sure whether this belongs to sage-support or sage-devel)

I'm preparing class for tomorrow, and ran across something I do not quite
understand:

sage: f=ZZ[x].random_element(10)
sage: g=ZZ[x].random_element(10)
sage: timeit('gcd(QQ[x](f),QQ[x](g))')
125 loops, best of 3: 2.96 ms per loop
sage: timeit('gcd(f,g)')
625 loops, best of 3: 89.2 µs per loop

I would have thought that the gcd over the rationals is no more difficult than
over the integers.  Am I mistaken?

(would be wonderful to have a quick answer, even if not 100% polished...) many
many thanks,

Martin


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