I have a challenge I've been puzzling over related to convergents. You can calculate the successive convergents from a continued fraction [a0; a1, a2, ...] by calculating the product of 2 2⍴(a0 1 1 0) and 2 2⍴(a1 1 1 0) and 2 2⍴(a2 1 1 0) and so on

My question is if I had a list representing a continue fraction, could I feed them into one APL function that would calculate the convergent (matrix multiplication and all) in one go?

⎕←+∘÷\2 1 2 1 1 4 1 1 6 1 1 8

@ngn
2 3 2.666666667 2.75 2.714285714 2.71875 2.717948718 2.718309859 2.71827957 2.718283582 2.718281718 2.718281835

I'm not sure how to do it since my idea is, one dfn does 2 2⍴(an 1 1 0), that's called on each number and then the matrices are multiplied together with (+.×)/

oh

@Sherlock9 ^ something like this?

Yeah, I that would be one way. I was trying to take that particular approach to learn more about operating on lists, but that would have been my next question

Oh and I wanted to calculate the numerators and denominators, and not necessarily the decimal form

⎕←+.×\{2 2⍴⍵,1 1 0}¨2 1 2 1 1 4 1 1 6 1 1 8

@ngn
┌───┬───┬───┬────┬─────┬─────┬──────┬───────┬────────┬─────────┬─────────┬──────────┐
│2 1│3 2│8 3│11 8│19 11│87 19│106 87│193 106│1264 193│1457 1264│2721 1457│23225 2721│
│1 0│1 1│3 1│ 4 3│ 7  4│32  7│ 39 32│ 71  39│ 465  71│ 536  465│1001  536│ 8544 1001│
└───┴───┴───┴────┴─────┴─────┴──────┴───────┴────────┴─────────┴─────────┴──────────┘

@Sherlock9 ^

Ooh yes I was just getting to that but with the dfn separated out and without the ,

Thanks a bunch

⎕←(+.×){2 2⍴⍵ 1 1 0}¨1 2 2 2 2 2 2

@Sherlock9
┌───┬───┬───┬────┬─────┬─────┬──────┐
│1 1│3 1│7 3│17 7│41 17│99 41│239 99│
│1 0│2 1│5 2│12 5│29 12│70 29│169 70│
└───┴───┴───┴────┴─────┴─────┴──────┘

Convergents of the square root of 2. Excellent :D

huh... how did that even work without a backslash

@ngn There was a backslash, but it is invisible due to markdown. The bot looks at raw text before rendering.

Oh heck it's formatting

@Adám mine was visible though

@ngn You monospaced your code with four leading spaces.

⎕←+.×\{2 2⍴⍵ 1 1 0}¨1 2 2 2 2 2 2

@Sherlock9
┌───┬───┬───┬────┬─────┬─────┬──────┐
│1 1│3 1│7 3│17 7│41 17│99 41│239 99│
│1 0│2 1│5 2│12 5│29 12│70 29│169 70│
└───┴───┴───┴────┴─────┴─────┴──────┘

Huh. Very strange

@Sherlock9 What is strange?

Hehe:

⍞←2 \1

@Adám 1 1

Oh :-(

This time I monospaced it by adding four spaces at the beginning but ngn's code doesn't seem to have the same big border

⍞←(2)(1)

@Adám 1 1

@DyalogAPL !

@Sherlock9 Ah, you put the backslash inside the paren, no?

Oh

I am completely out of practice with SE's markdown

@Sherlock9 So the escape for some reason works on round parens, but not on curly braces.

@Sherlock9 It is pretty insane in chat.

Oh, is there an easy way to populate a list with copies of one number? Phi's convergents are [1; 1 1 1 1 1 1 1 1 1 1 1]

@Adám Ah there is a misunderstanding. My first attempt was not escaped, my second attempt was. I think that was the problem and not the parens

⎕←(11)1

@ngn
SYNTAX ERROR

⎕←11⍴1

@Sherlock9
1 1 1 1 1 1 1 1 1 1 1

I should have guessed

@Sherlock9 or 11\ 1. a backslash solves everything :)

oh that is weird

Not unexpected

But definitely funky

just kidding. ⍴ is the usual way to do it. backslash in this case is "expand"

Ohh. I thought it was a thing scan did

⍞←11(1)

@Adám 1 1 1 1 1 1 1 1 1 1 1

@DyalogAPL !

@ngn @Sherlock9 Another reason to use ⍴ is that it won't bite you later if you make it into a train.

or if you've got markdown in your shell for some reason :P

@Sherlock9 You're kidding, right?

@Adám I am, but also what is this Dyalog bot in this chat if not an interactive shell with markdown?

@Sherlock9 Right, but "proper" usage of the bot would be with at least four leading space (hey, even a regular APL session has six leading spaces).

I genuinely hadn't considered that (I've seen the 6 leading spaces, but not observed them)

@Sherlock9 So if you try to use _snake_case_names_ in your shell, it makes the text italic?

It could. I genuinely hadn't thought that far ahead

Although

Discord has also has the annoying tendency to turn 2*3*4 into 2 3 4

@Sherlock9 tbf, I've contemplated having code comments render as markdown.

Which wouldn't be bad with a competent IDE

But that also depends on the IDE remaining competent

⍞←*3*.2

@Adám 3.475474233

⍞← 3.2

@DyalogAPL C'mon!

⍞← 3.1

@Adám 3.052995299

@DyalogAPL Pretty close!

⍞←1 1 1*1 1 1

@Adám 2.718281828 2.718281828 2.718281828

@DyalogAPL !

⍞←~\1 1 1

@Adám 1 0 0

⍞←~(1 1 1)

@DyalogAPL Hello

⍞←~(1 1 1)

@Adám 0 0 0

@DyalogAPL OK, what about:

⍞←~(1 1 1)

@Adám 1 0 0

@DyalogAPL Inconsistently off-by-one

Hah, is the bot working in Malbolge today?

@J.Sallé No, the bot is behaving normally. But the intersection of Markdown and APL is interesting. URI's intersection with APL is also fun: Try it online!

@Adám lol that's interesting

@J.Sallé So basically, the idea is that any character which plays a role in markdown (parens are used in links) causes a preceding backslash to be invisible to humans but visible to the bot, so the challenge is to come up with a plausible APL expression where the backslash can be removed and the expression still would work (but obviously would give a different result).

I see

I'll try to come up with something interesting later if I can hahahah

sounds fun

The only real candidates are \ * ( ) [ ]

@nathanrogers Just saw this on github, might interest you: github.com/jayfoad/DyalogOpenGL

@H.PWiz Jay already sent that to me a little bit ago. Thanks for the heads up! I've been playing with it, and APL basically directly translates from C

@H.PWiz it only includes GLUT, and so doesn't use the modern Vertex Array method, and uses the old fixed function pipeline method. but it is usable for my purposes