Re: Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)

*To*: mathgroup at smc.vnet.net*Subject*: [mg88113] Re: [mg88090] Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)*From*: Syd Geraghty <sydgeraghty at mac.com>*Date*: Fri, 25 Apr 2008 05:28:10 -0400 (EDT)*References*: <200804240957.FAA28500@smc.vnet.net>

Craig, Just a (tongue in cheek) reminder that Mathematica is a wonderful all purpose environment in which to do Mathematics. 221 years ago the 10 year old Gauss would have solved the problem by coding:- n = 10000000; Timing[total = n (n + 1)/2] {0.000035, 50000005000000} Which is a whole lot faster! I realize that this is not very helpful in deciding usage of Table vs Do. But the precocious Gauss also might have tried Timing[total = Table[i (i + 1)/2, {i, 10000000}]] {20.46425400000001, {1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, <<9999974>>, 49999885000066, 49999895000055, 49999905000045, 49999915000036, 49999925000028, 49999935000021, 49999945000015, 49999955000010, 49999965000006, 49999975000003, 49999985000001, 49999995000000, 50000005000000}} or better yet Timing[Total[Table[i (i + 1)/2, {i, 10000000}]]] {31.7433, 166666716666670000000} Just to show off ... :) Cheers ... Syd PS Where would we be now if Stephen Wolfram had provided Gauss with a free Mathematica License back then? BTW What a surprising result (1666667)(1666667)(0000000) I wonder if anyone has computed this result before and explained its repetition of the first 7 digits? Syd Geraghty B.Sc, M.Sc. sydgeraghty at mac.com My System Mathematica 6.0.2.1 for Mac OS X x86 (64 - bit) (March 13, 2008) MacOS X V 10.5.2 MacBook Pro 2.33 Ghz Intel Core 2 Duo 2GB RAM On Apr 24, 2008, at 2:57 AM, W_Craig Carter wrote: > This is problem with a known simple result, but it will serve: let's > find the sum of the first 10000000 integers. > > (*let's use a do loop*) > Timing[ > icount = 0; > Do[icount = icount + i, {i, 1, 10000000, 1}]; > icount > ] > > (*this returns {10.2826, 50000005000000} on my machine.*) > (*10.28 being a measure of how long the computation took to run*) > > (*lets try a table*) > Timing[ > Total[Table[i, {i, 1, 10000000, 1}]] > ] > > (*This returns {3.25516, 50000005000000} on my machine*)

**References**:**Re: Print[Plot] vs Print[text,Plot]? (*now Do and Table*)***From:*"W_Craig Carter" <ccarter@mit.edu>