Comment #10 on issue 3235 by vbraun.n...@gmail.com: Sage error in master
http://code.google.com/p/sympy/issues/detail?id=3235

mpmath internally has different backends to do the computation. It uses mpir/mpfr if possible (i.e. if used from within Sage) and falls back to some python code otherwise (slow).

By the way mpfr.h has a #define MPFR_PREC_MIN that you would ideally use, though of course that isn't that easy to access from pure Python. From within Sage you can get it via

sage: from sage.rings.real_mpfr import mpfr_prec_min
sage: mpfr_prec_min()
2


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