2009/12/3 j. arias-de-reyna <ar...@us.es>: > Hello everybody, > > I have composed a program (in Python using the mpmath library) to > compute to > high precision zeta(s) and Z(t) (the Riemann-Siegel function) by > means of the Riemann-Siegel expansion. > > I have obtained, I think that for the first time, rigorous bounds > for the terms and rest of the Riemann-Siegel expansion even for > points off the critical line. > > The program is running well and is comparable with Mathematica, even > sometimes it runs faster. I even have found cases where Mathematica > gives wrong results and my program doesn't. > > For example: > > Z(100000*^(2**20)) with 9 decimal digits > cpu Mathematica 1.719 > cpu mpmath 11.12 > (but the value given by Mathematica is erroneous -0.00112995 > the value given by mpmath 2.6302645) > Mathematica when computing to 30 digits > 2.63026450661456012104256623412 > > ===== > > Z(100000*^(2**20)) with 180 decimal digits > cpu Mathematica 25.406 > cpu mpmath 31.15 (cpu on zetasum 28.62) > > ===== > > Z(10 000 000) with 600 decimal digits > Mathematica gives an error message and > computes 505 decimal digits in cpu time 314.891 sec. > Augmenting the internal variable $MaxExtraPrecision > Mathematica computes 600 digits in 1008.19 additional sec. > > cpu time of mpmath 837.08 (giving the 600 correct digits) > > ===== > > Z(9460455379268814.253184) with 100 decimal digits > cpu time Math 4334.89 sec > cpu time of mpmath 6259.4623333 of which 6257.3257419 > spent in the zetasum > > (this is the biggest value known of Z(t) > = 937.1985242635 6253567375 .... ) > > ==== > > When I ask for moderate precision usually we have > cpu time Math < cpu time mpmath < 2*cpu time Math > > But much of the time my program spent in computing the zetasum > that almost surely Mathematica also sums. > > ====== > > But I have some fears since I am not a programmer. I do not knew > nothing about Python even the name when I started in February of > 2009 to write the program. I knew the Sage, and my first intention > was to make it for Sage. There I read for the first time of Python. > Then I saw mpmath. That was a revelation. As I use Windows my > installation of Sage were not accessible. The programs of mpmath > were accessible for me, they were my school for Python. > > So, my fear is that my program although running, must have many > mistakes of a beginner. Also I think the program can be made faster > with some modifications, for example: using a C-implementation to > compute the zeta sum. > > Fredrik Johansson advised me to post this message on this list. > > I would like to see my program (or some adequate modification) > included in the mpmath (or sage).
mpmath is included in Sage, so if you include your program with mpmath, then it will automatically get included in Sage. -- William -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
