Does this help?
<\i.4
+-+---+-----+-------+
|0|0 1|0 1 2|0 1 2 3|
+-+---+-----+-------+
<\.i.4
+-------+-----+---+-+
|0 1 2 3|1 2 3|2 3|3|
+-------+-----+---+-+
<\.|.i.4
+-------+-----+---+-+
|3 2 1 0|2 1 0|1 0|0|
+-------+-----+---+-+
Mike
On 04/12/2018 07:50, Linda Alvord wrote:
Here's the step that I can't understand in the Fibonacci series. How is l
different from |. ?
($|i.6)-:$|.i.6
1
(|^:(i.6)1 1)-:|.^:(i.6)1 1
1
(([:+/\|)^:(i.6)1 1)-:([:+/\|.)^:(i.6)1 1
0
(([:+/\|)^:(i.6)1 1);([:+/\|.)^:(i.6)1 1
┌───┬────┐
│1 1│1 1│
│1 2│1 2│
│1 3│2 3│
│1 4│3 5│
│1 5│5 8│
│1 6│8 13│
└───┴────┘
Linda
-----Original Message-----
From: Programming <[email protected]> On Behalf Of
lindaalvord
Sent: Monday, December 3, 2018 11:27 PM
To: [email protected]
Subject: Re: [Jprogramming] Revisisting the Y combinator
Sorry, Jose, I didn't look. 55 is the 10th term!
Linda
Sent from my Verizon, Samsung Galaxy smartphone
-------- Original message --------From: Jose Mario Quintana
<[email protected]> Date: 12/3/18 8:20 PM (GMT-05:00) To:
[email protected] Subject: Re: [Jprogramming] Revisisting the Y combinator
Linda,
Please check the Rosetta Code page, I did not produce the Fibonacci sequence, I
just showed
FIB Y 10
55
and almost everybody there agrees (and apparently so did Binet and de Moivre).
Raul showed the sequence 0 1 1 2 ... and he was not the only one.
Personally, I have no problem at all with that given the context.
I hope it helps
On Mon, Dec 3, 2018 at 7:30 PM Linda Alvord <[email protected]>
wrote:
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://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Frose
ttacode.org%2Fwiki%2FY_combinator&data=02%7C01%7C%7C4673109620904e
6c73d008d659a0b678%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636794
944120539237&sdata=VUhCaXruQBmADyjRuo3MnUsfN9Nt7wtPqv%2F6ky5r9Mw%3
D&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
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