One more comment on the subject. As we were trying to solve a Sturm-Lioville boundary value problem by finite difference method, we calculated eigenvalues and eigenvectors of some matrices on matlab and mathematica. In both of the programs, their 32 bit and 64 bit results were different (we tried these calculations on the same machine with different windows builds). So I want to know (in my future studies) what kind/degree/level (I have to look at my of numerical error books) I am making in my calculations. So a good multiple precision arithmetic and error estimation support on a Cas is extremely important from my point of view. If you are welcome for future development ideas on Sage, this is my personal recommendation.Thanks for all your valuable recommendations and answers. Best wishes... AAP
On Fri, Feb 6, 2009 at 3:00 AM, rjf <fate...@gmail.com> wrote: > > > > On Feb 5, 1:29 pm, William Stein <wst...@gmail.com> wrote: > > On Thu, Feb 5, 2009 at 3:08 AM, ahmet alper parker <aapar...@gmail.com> > wrote: > > > > > Dear All, > > > According to a previous conversation about Java and Python, a comment > was > > > the results of the calculations written in the same language (although > they > > > are written in a standard language) may be different from platform to > > > platform. > > Yes if you are using hardware floating-point arithmetic and the > machines are set up to allow differences in the hardware to show > through at the language level. Why would you allow such differences > to show? Typically because some hardware is both more accurate and > faster than some others. > > > I want to ask that, is it possible to calculate the error in our > > > calculations with Sage > > Unless you define what you mean by "the error", this question cannot > be answered. > You can get started on elaborating on this question by reading almost > any book on > numerical analysis. > > > >(or else like maxima, matlab etc. if you know)? Also, > > > is there big number (multiple precision arithmetic) support on Sage? > > Yes. > > > > All the answers and comments are welcome. > > > > > Sage has incredibly good support for multiprecision arithmetic. We > > have fast arbitrary precision integers, rationals, reals, intervals, > > complexes, etc., and fast linear algebra in some of these cases too. > > It is perhaps worth pointing out that support for "reals" is different > from multiprecision > support for approximate floating-point numbers. Sage does the latter. > > Why make the distinction? > Note that any polynomial of any degree in any number of variables can > be > encoded in a single real number. Let x1=e, x2=e^e, x3=e^(e^e) etc. > Now you can add, multiply etc such polynomials in the time it takes > to multiply 2 real numbers. > So computational support of real numbers is problematical. > > RJF > > > > > > > William > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
