On Tuesday, December 20, 2016 at 3:36:19 AM UTC+1, saad khalid wrote: > > 1. It appears we don't have a native q-gamma or q-digamma function. We do > have access to q-gamma from mpmath. However, a wrapper function in Sage > hasn't been added yet: > https://trac.sagemath.org/ticket/19032 > Would adding this be a simple as importing qgamma from mpmath? >
No. Take any special function in the functions folder that derives from BuiltinFunction as example. > My worry in implementing it that way is about efficiency. If a user uses > calls qgamma many times, then it would be doing "from mpmath import qgamma" > many times, which seems pretty inefficient. Is there a more efficient way > of doing this? > The way Sage handles repeated calls of symbolic numerics is through fast_callable see src/sage/ext/fast_callable.pyx > for the gamma function in sage (I believe it uses GiNaC?), I don't see it > say "import gamma" anywhere. Does it not have to do that because GiNaC > isn't in python? Also, is there a reason we don't use mpmath for the gamma > function? > GiNaC/Pynac calls py_tgamma in libs/pynac.pyx for numerics if the argument has no gamma member (which it has if it's from RR or CC, so see these rings for which library is used). > 2. Going off of what I was talking about in question 1, how can I see the > implementation of the gamma function? I'm looking at the source in > sage/functions/other.py: > https://github.com/sagemath/sage/blob/master/src/sage/functions/other.py > As I said it depends on the type of the argument. > but I can't see the code for the actual function. I just see that it calls > something called gamma1, apparently. What is gamma1 here > gamma1 is an alias for Function_gamma() which is the one argument version. > and where can I see the code for the actual function? > For numerics see the gamma method of the resp. function argument. > It mentions that Gamma uses various libraries in sage, but it looks like > it just uses gamma1(from ginac?) and gamma_inc. Is this correct? > No. Integer arguments use libgmp, floats probably mpmath, balls use arb etc. > 3. The formula for q-digamma is for q = 1. Since we don't have an > implementation of q-digamma as far as i can tell, I was thinking I would > try to find a library with an implementation of it, import that, and then > add the q = 1 case implementation as an if statement? > Yes that is an idea. > And if I can't find a library with it, would it work okay to simply write > the formula for it directly there? Or would that be slow because it's in > python? I was thinking that since the code gets cythonized, the fact that > I'd be writing it in python wouldn't be cause it to be slow. > New numeric algorithms are best implemented in one of the numerics libraries used by Sage. I would implement it exclusively in arb (for inexact argument). -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
