Comment #7 on issue 3516 by [email protected]: gcd for Rationals is much slower than it should be
http://code.google.com/p/sympy/issues/detail?id=3516
If I'm not mistaken, _rgcd works in pure Python ints rather than SymPy Integers. This makes a big difference. Look at the times in the OP. We're talking about a factor of 10X here. Maybe the polys algorithm does too, but that's something to watch for.
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