Hi Buck, I asked Mike Rubinstein, who has implemented the incomplete Gamma function in various situations (e.g., I think he did the first ever open source implementation that was general enough for me to use for my research), written papers mentioning issues, etc., what he thinks, and here's his response: "Sounds like he wants to implement the incomplete gamma function. He doesn't provide any detail about implementation, just the naming conventions. The different ways of normalizing, or whether one is looking at gamma(a,x) or what he calls lower_gamma(a,x) makes little difference for the end result... one can get one from the other.
Depending on the relative size of the parameters, it makes more sense to compute gamma(a,x) or lower_gamma(a,x). The fact that he is using the letter x suggests he is thinking of implementing it for real values of x. Might be worthwhile to allow both parameters to be complex. Certainly that would be better from the point of view of anyone who uses functions of a complex variable. The incomplete gamma function changes its behaviour when a is close to x. That's where things get a bit tricky (for truncation bounds), especially in the complex plane. Section 3.4.2 of my paper: http://arxiv.org/pdf/math/0412181v1.pdf (published in Recent Perspectives in Random Matrix Theory and Number Theory, F. Mezzadri and N.C. Snaith editors, 407-483, 200) has a discussion about how I've computed the incomplete gamma function. Some of my code for that is here: https://code.google.com/p/l-calc/source/browse/include/Lgamma.h https://code.google.com/p/l-calc/source/browse/src/Lgamma.cc (there's actual code in the .h file because of templates) Regarding his 'open questions', ex about notation as in `log_gamma() = gamma(log=True)', I don't have any preferences. Best, Mike" On Thu, Jan 21, 2016 at 8:48 AM, Buck Evan <workithar...@gmail.com> wrote: > > > On Thursday, January 21, 2016 at 12:18:18 AM UTC-8, Buck Evan wrote: >> >> >> >> On Wed, Jan 20, 2016, 22:11 Nils Bruin <nbr...@sfu.ca> wrote: >>> >>> On Wednesday, January 20, 2016 at 9:25:59 PM UTC-8, Buck Evan wrote: >>>> >>>> I've written up a proposal in this google document, and set it to be >>>> globally readable, commentable. >>>> >>>> >>>> https://docs.google.com/document/d/1zEzIz0TCgC1aEKCQmHQkI5EVLlRnwsvrZOnAAClUcdM/edit# >>>> >>>> >>>> I have the next couple of weeks to try to get (parts of) this >>>> implemented. >>>> Let me know which parts are most/least disagreeable, if you would. >>> >>> There is already a ticket that significantly overlaps in scope: >>> >>> http://trac.sagemath.org/ticket/16697 >>> >>> It even has comment from someone who shares your name. >> >> >> Yes, that's me. This proposal closed that ticket. > > > Typo: This proposal *closes* (would close) that ticket. > > -- > 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. -- William (http://wstein.org) -- 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.
