Jose, I found this from an early forum. It seems to have a "Y" approach hiding in it.
f=: 13 :',([:+/\|.)^:2^:(<`(1,1:))y' f 5 1 1 2 3 5 8 13 21 34 55 Linda -----Original Message----- From: Programming <[email protected]> On Behalf Of Skip Cave Sent: Saturday, November 3, 2018 12:25 AM To: [email protected] Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic Linda, NB. Generate the integers from 2 to 21, store them in a, and display a: ]a=.2+i.20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 NB. Take the square root of the integers in a, store them in b, and display b: ]b=.%:a 1.41421 1.73205 2 2.23607 2.44949 2.64575 2.82843 3 3.16228 3.31662 3.4641 3.60555 3.74166 3.87298 4 4.12311 4.24264 4.3589 4.47214 4.58258 NB. Find the ceiling of b (which contains all the square roots of a) >.b 2 2 2 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 NB. Mark all the places where the ceiling of b is the same as b, and display the mark vector. NB. This essentially marks every number in b that has no fractional part, i.e the numbers in b that are integers. ]m=. b = >. b 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 NB. this is the same as: (=>.) b 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 NB. Now we can use the mark vector to display only the numbers in b that are integers: m#b 2 3 4 NB: Or we can use the mark vector to select all the integers from a that have integer square roots: m#a 4 9 16 NB. Now, like most J expressions, we can do either of these things all in one line: b#~(=>.)%:a=.2+i.20 2 3 4 a#~(=>.)%:a=.2+i.20 4 9 16 Skip Skip Cave Cave Consulting LLC On Fri, Nov 2, 2018 at 9:25 PM Linda Alvord <[email protected]> wrote: > What does (=>.) do in this example? > > Linda > > > > Sent from my Verizon, Samsung Galaxy smartphone > > > -------- Original message -------- > From: Skip Cave <[email protected]> > Date: 11/2/18 12:06 PM (GMT-05:00) > To: "[email protected]" <[email protected]> > Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic > > Thanks for all the comments and help in understanding why trying to > get an extended integer result from a square root is a bad idea. > > I think the functional symmetry of square *: and square root %: led me > to subconsciously forget that the results of squared integers (all > integers) are not symmetrical with the results of the square roots of > integers (which are NOT all integers). I should remember this, since > one of my favorite J idioms is the implicit verb (=>.) for finding > integers in a list of floating point numbers: > > a=.2+i.20 > > %:a > > 1.41421 1.73205 2 2.23607 2.44949 2.64575 2.82843 3 3.16228 3.31662 > 3.4641 > 3.60555 3.74166 3.87298 4 4.12311 4.24264 4.3589 4.47214 4.58258 > > (=>.)%:a > > 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 > > a#~(=>.)%:a > > 4 9 16 > > Skip > ---------------------------------------------------------------------- > For information about J forums see > https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.j > software.com%2Fforums.htm&data=02%7C01%7C%7C4f696d5065b94098ad1c08 > d641446bd9%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63676815945102 > 0586&sdata=z54fz6QFIO4PP3iXH93jLlbZaYYL6YiSMlc6laIqwLs%3D&rese > rved=0 > ---------------------------------------------------------------------- > For information about J forums see > https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.j > software.com%2Fforums.htm&data=02%7C01%7C%7C4f696d5065b94098ad1c08 > d641446bd9%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63676815945102 > 0586&sdata=z54fz6QFIO4PP3iXH93jLlbZaYYL6YiSMlc6laIqwLs%3D&rese > rved=0 ---------------------------------------------------------------------- For information about J forums see https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C4f696d5065b94098ad1c08d641446bd9%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636768159451020586&sdata=z54fz6QFIO4PP3iXH93jLlbZaYYL6YiSMlc6laIqwLs%3D&reserved=0 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
