On Mon, Mar 31, 2014 at 9:14 PM, Matthew Rocklin <mrock...@gmail.com> wrote: > http://www.evanmiller.org/mathematical-hacker.html > > I reference that blog post pretty often. I fully intend to reference it > again in my talk (if it is accepted). > > The interesting thing about the Factorial / Gamma / loggamma example is that > to find the solution you need to find someone who knows both that n! = > Gamma(n+ 1) and who knows that a loggamma routine is commonly found in lower > level languages. Those bits of information are usually held by different > experts. Ondrej said "Of course, that's obvious" when I first reposted the > article on G+.
That's funny, I forgot that I said that and just had the same reaction. However, we are still missing rational function approximation in SymPy or mpmath. That's what is used to implement things like log_gamma or erf (error function) in Fortran or C. So I have just created an issue for it: https://github.com/sympy/sympy/issues/7359 and I spent time explaining exactly how it works in it and giving examples, including for example the implementation of erf() in gfortran. Aaron, you were asking about examples of numerical cancellation. I worked out one in the issue as well. Ondrej > > You're right that this is similar to my last talk. The last one though was > mostly about an application (numerical linear algebra). I actually want to > talk a bit more about the philosophy and some of the more abstract tools > that people might actually use. Your first impression is a valuable one > though, I should go through my last talk and make sure that I'm not > repeating too much that shouldn't be repeated. > > > On Mon, Mar 31, 2014 at 6:03 PM, Aaron Meurer <asmeu...@gmail.com> wrote: >> >> That's a good point. One of the nicest things about symbolics, when you >> can get it, is that it can make things drastically more efficient by doing >> mathematical simplifications. Evaluating integrals symbolically is a nice >> example of this (especially for SymPy, which has some pretty nice algorithms >> to compute definite integrals). >> >> I'm reminded of a popular blog post (I can't find a link right now) about >> how know math is important for programmers. It has the example of how all >> these programming languages show how they they compute factorial, and how >> tail recursion can make it linear or whatever, but the actual best way to >> compute it is to use loggamma, which gives the answer in constant time. >> >> Aaron Meurer >> >> >> On Mon, Mar 31, 2014 at 7:51 PM, Tim Lahey <tim.la...@gmail.com> wrote: >>> >>> >>> >>> On 31 Mar 2014, at 20:29, Aaron Meurer wrote: >>> >>>> On Mon, Mar 31, 2014 at 11:32 AM, Matthew Rocklin >>>> <mrock...@gmail.com>wrote: >>>> >>>>> I like that you emphasized the utility for numerics, I think that this >>>>> is >>>>> likely to be a selling point for the SciPy crowd. >>>>> >>>> >>>> Yes, this was very intentional. I may need some help gathering up some >>>> nice >>>> motivating examples if this is accepted. >>> >>> >>> One motivating example for me is the integration of products of functions >>> over areas and volumes. For finite elements, you'll get products of pairs of >>> trial functions (usually polynomials). It's even more useful for products of >>> trig functions. Performing the integration of any of theses is easy enough >>> with numerical integration, but it's much more efficient to calculate the >>> integrals symbolically and then perform the evaluation for each element. >>> >>> Cheers, >>> >>> Tim. >>> >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "sympy" group. >>> To unsubscribe from this group and stop receiving emails from it, send an >>> email to sympy+unsubscr...@googlegroups.com. >>> To post to this group, send email to sympy@googlegroups.com. >>> Visit this group at http://groups.google.com/group/sympy. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sympy/AE5C61B5-8C69-49AE-BAFF-85E5AC924F8F%40gmail.com. >>> >>> For more options, visit https://groups.google.com/d/optout. >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sympy+unsubscr...@googlegroups.com. >> To post to this group, send email to sympy@googlegroups.com. >> Visit this group at http://groups.google.com/group/sympy. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/CAKgW%3D6K8F9weBP-7yjpzrN9hQ5FR54TK_QdCPqbzBdwo20zKdg%40mail.gmail.com. >> >> For more options, visit https://groups.google.com/d/optout. > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAJ8oX-HZABscP43PDuoAeWhcpBYW2w39G8qPx0%2BZCbKcYbJdJg%40mail.gmail.com. > > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sympy" group. 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