Put a [: in front of +/ On Apr 12, 2016 5:32 PM, "Skip Cave" <[email protected]> wrote:
> I thought I would polish my J skills by trying to write a function to > approximate the infinite sum > > 1 + 1%2^2 + 1%3^2 + 1%4^2 + 1%5^2 .... > > NB. First get the integers > > 1+i. 10 > > 1 2 3 4 5 6 7 8 9 10 > > > NB. Now make a verb "g" that will take a right argument of the number of > terms. > > g =. 1+i. > > g 10 > > 1 2 3 4 5 6 7 8 9 10 > > NB. It works! > > > NB. Now to test squaring the integers > > 2^~1+i. 10 > > 1 4 9 16 25 36 49 64 81 100 > > > NB. Now add that to the verb > > g =. 2^~1+i. > > g 10 > > 1 4 9 16 25 36 49 64 81 100 > > NB. That works! > > > NB. Now test calculating the inverses > > 1%2^~1+i. 10 > > 1 0.25 0.111111 0.0625 0.04 0.0277778 0.0204082 0.015625 0.0123457 0.01 > > > NB. Add that to the g verb > > g =. 1%2^~1+i. > > g 10 > > 1 0.25 0.111111 0.0625 0.04 0.0277778 0.0204082 0.015625 0.0123457 0.01 > > NB. That works! > > > NB, Now we test summing all the terms up > > +/1%2^~1+i. 10 > > 1.54977 > > NB. Yep, that's right for just 10 terms. > > > NB. Double check > > 1 + (1%2^2) + (1%3^2) + (1%4^2) + (1%5^2) + (1%6^2)+ (1%7^2)+ (1%8^2)+ > (1%9^2) + (1%10^2) > > 1.54977 > > NB. Yep, everything is OK. > > > NB. Now add the sum insert to the verb g, just like the test > > g =. +/1%2^~1+i. > > g 10 > > 11 10.25 10.1111 10.0625 10.04 10.0278 10.0204 10.0156 10.0123 10.01 > > > NB. ;-( the sum didn't work in the verb g! What happened? > > > Skip > > > Skip Cave > Cave Consulting LLC > > On Tue, Apr 12, 2016 at 11:45 AM, R.E. Boss <[email protected]> wrote: > > > > From: Chat [mailto:[email protected]] On Behalf Of Dan > > > Bron > > > Sent: dinsdag 12 april 2016 15:47 > > > > > One of the most memorable and enjoyable examples (for me, anyway) of > > > using J for this kind of work was your (REB’s) exploration of Grey > Codes > > a few > > > years back. I distinctly remember writing a Grey Code function I > thought > > > must be close to the limit in performance, because it used bitwise > > functions, > > > and was about as close as you could come to writing a C or assembler > Grey > > > Code program without actually leaving J proper. > > > > > > But then you went and beat me anyway. By a not insignificant margin. > > > > This I remember distinctly as well. :-) > > (see also http://code.jsoftware.com/wiki/Puzzles/Gray_Code from which I > > learned it was Dec 2006) > > That was because of mine (I think) superior representation of the (binary > > reflected) Gray(!) code, completely inspired by J, a notation which I'm > > still struggling to sell to the mathematical/computer-scientist world. > > I wrote about it also in > > http://journalofj.com/index.php/vol-4-no-2-december-2015 (but I never > see > > an announcement when a new number is released). > > Next time I will reveal the hyper-orthogonal Hilbert curves. > > > > > > R.E. Boss > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
