On Wed, 12 Feb 2014, William Stein wrote:
1. It is *NOT* true. Sage just directly calls the PARI C library,
which is always loaded on startup of Sage.
OK, good (or bad, which way one wants it to be...).
It's pretty likely that when the line of code in question was written
(prob in 2005 or 2006) this speed difference wasn't the case.
Maybe somebody has just tested this once for given precision? This used
about 1,5 seconds CPU time every time:
gamma(RealField(prec=10000)(3.14159))
And this one only about 0,1 seconds, except that for first time it took
10,7 seconds:
gamma(ComplexField(prec=10000)(3.14159))
And reason is of course clear, as Fredrik Johansson wrote "If you cache
Bernoulli numbers, - -".
--
Jori Mäntysalo
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