Jose, If you look up the derivation of the fibonnaci series was developed you will find 1 1 2 3 5 . . .
I think it should be left out of an example of the Y form. Or, maybe it can be modified to come out correctly. I do have a way to generate the correcg formula and feel mathematicians will be more comfortable with that. Linda -----Original Message----- From: Programming <[email protected]> On Behalf Of Jose Mario Quintana Sent: Monday, December 3, 2018 6:18 PM To: [email protected] Subject: Re: [Jprogramming] Revisisting the Y combinator Linda, The choice to start the Fibonacci sequence at 0 is to conform with some of the other answers at the Rosetta Code page, Y combinator https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Frosettacode.org%2Fwiki%2FY_combinator&data=02%7C01%7C%7Cd5f47a327c0443363f9908d65975a77c%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636794759195093996&sdata=%2Fe4zXDMvVTrntKNbwZGp8rgnvkS2CZF%2FbTEq5tauOwc%3D&reserved=0 Most people start numbering items at 1 and when producing a function (Fib) for the Fibonacci sequence the correspondence is, 1 2 3 4 5 6 7 8 9 10 ... 1 1 2 3 5 8 13 21 34 55 ... Some of us, and J, start numbering items at 0. So we can use the correspondence, 0 1 2 3 4 5 6 7 8 9 10 ... 0 1 1 2 3 5 8 13 21 34 55 ... So, either way, Fib(10) is 55 and we all agree even if we disagree. (Apparently, the Fibonacci function can be extended to the complex plane and beyond using, the so-called, Binet's formula.) I hope it helps On Thu, Nov 29, 2018 at 10:40 PM Linda Alvord <[email protected]> wrote: > Jose, Somehow this surprised me. > > Y=: ($:`)(`:6) > N=: 1 :'(u@:<:@:<: + u@:<:)^:(1 < ])' > P=: (5!:1)<'N' > P Y("0) i.11 > 0 1 1 2 3 5 8 13 21 34 55 > > Y > ($:`)(`:6) > N > 1 : '(u@:<:@:<: + u@:<:)^:(1 < ])' > P > ┌────────────────────────────────────────────┐ > │┌─┬────────────────────────────────────────┐│ > ││:│┌─────┬────────────────────────────────┐││ > ││ ││┌─┬─┐│┌─┬────────────────────────────┐│││ > ││ │││0│1│││0│(u@:<:@:<: + u@:<:)^:(1 < ])││││ ││ > ││└─┴─┘│└─┴────────────────────────────┘│││ > ││ │└─────┴────────────────────────────────┘││ > │└─┴────────────────────────────────────────┘│ > └────────────────────────────────────────────┘ > > > Linda > > > ---------------------------------------------------------------------- For information about J forums see https://nam02.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7Cd5f47a327c0443363f9908d65975a77c%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636794759195093996&sdata=lCxvmrsNHIVIwirWR2FFzynosiAI4mdoYkANIdHSg0Q%3D&reserved=0 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
