yes

i dont see it being useful , since a variable will directly execute the block

if you want to store a block which executes something twice, you could shorten {{...}2*} to {...}_+

or if you have a two-part function, and sometimes only want to run half of it, you could do {...}:F{...}+:G

it's actually an open ticket for CJam btw

oh, u opened ?

no, Dennis did

I didn't know about this feature in GS until I found that ticket

I really hate this FGINTW effect

which question?

all of them ?

oh right, I thought you were talking about something specific

hi again

@Sp3000 arxiv.org/pdf/1307.8432v2.pdf in case it's relevant

Took a quick look and wasn't sure

The "can't intersect at any time" restriction's quite painful :P

@MartinBüttner Nothing interesting yet. (@Sp3000)

meh

@Doorknob Thanks

@Sp3000 you mentioned the coding problem was 10 notches harder

is this because you have to worry about collisions while doing a rotation?

Yes :/

@Sp3000 ok so this is even worse than not intersecting after every rotation

@Sp3000 I am pleased it is hard :) I hate to ask easy questions

@Sp3000 do you have any advice for how I should define rotations? I mean my intention is that you can rotate either 90 degree clockwise or anti-clockwise but you can't ever rotate a square more than 90 degrees clockwise or anti-clockwise

from it's starting orientation

but also we have to worry about what happens to the square during the rotation

does it stick out and then slide back into position?

@Sp3000 too many questions? :)

@Lembik and then you'll complain for a week that you get too few answers ;)

@MartinBüttner true!! :)

@MartinBüttner you know me too well :)

To be honest, there's still a few things which are undefined

Say you have a snake like this:

<<\
v ^
\>/

@MartinBüttner actually I was hoping some variant which could make a fortnightly challenge

(i.e. the shape is a 3x3 square with a hole in the middle)

@Sp3000 ok

Can the last one bend to become this

 /\
vv^
\>/

@Sp3000 could you try drawing to flockdraw.com/f72808 ? I can't quite visualize this

Done!

@Sp3000 I can't see how that could work.. which square has been rotated?

@So

Well here's the thing - what counts as overlapping here?

@Sp3000 I don't think that is physucally possible

@Sp3000 you are not allowed to overlap at any stage

I think the end solution is valid but achieved with a different rotation order

including during a rotation

@DominikMüller well then that's ok :)

but you can't overlap during a rotation

It's not in real life because when rotating it collides with the middle left piece

@Sp3000 right.. so it's not allowed

But that brings irrationals into play

But if you think of rotating as instananeous rotation 90 degrees

@Sp3000 well yes :) but also no... I mean all the squares are centred at integers

@Sp3000 you're just using that as a toy example, right? that form is definitely achievable with a different snake form.

@Sp3000 ah no.. I was not thinking of it as instantaneous rotation

@MartinBüttner Yeah toy example

k

@Sp3000 and do the irrationals actually create a problem given that the squares are all centred at integers? Can't we work out precisely mathematically if they would collide?

Lemme extend the pic a bit more

I wonder though if there's any shape that requires an impossible rotation somewhere along the way

@MartinBüttner I suspect yes

@Lembik I'm looking forward to an example ;)

@MartinBüttner me too :)

but there is still something I haven't specified

"the snake is green"

consider just two squares and I rotate the second one. Does it rotate in place (which would mean it would overlap the first one for some time)?

what is a sensible answer do people think?

Say I want to rotate the segment under the bar and fold it downwards to where the line is

a sensible answer is not to consider the process of rotation but to just skip ahead by 90 degrees

How do I work out if it'll hit the green square?

@Sp3000 are you referring to some picture we don't have?

@MartinBüttner back in the link

It's the bottom left pic on the flockdraw

Just drew it :)

oh, didn't see that up there

@Sp3000 ok.. so we need to intersect a square with an arc

@Sp3000 which I think is doable

@Sp3000 naively we need to do that for every square

but there is probably a smarter way

you know you can edit your message? :P

@MartinBüttner good point!

@Sp3000 did you draw the bottom right thing?

that can be done by folding the bottom left corner last

Nope

@MartinBüttner I did

oh okay

we had this one tricky example earlier where you've got two interlocking spirals

Oh right, you can fold any part of it

Is that possible without intersecting? Or ist it the same snake as the one i will draw now?

@Dominik oh good point

@Sp3000 do you see my point? I don't think arc/square intersection is a problem

Well it has the same problem as what you mentioned up there

Namely, which part of the squares count for intersections

Because if the whole square counts then we have the problem like you said about rotating a single square on the spot and intersecting its neighbour

@Sp3000 ok but if we count all overlaps it's still ok isn't it?

@Sp3000 just more fiddly

Are you sure you're not secretly planning to write a research paper on this? :P

I feel like this is heading into insane mode

@Sp3000 I am tempted to say that the first square that is rotated (the anchor square?) rotates instantly and magically but all the other overlaps count

okay, here is one example that really can't be done, because there's no other way to lay out the snake through the squares:

############# ###
#           # # #
# ######### # # #
# #       # # # #
# # ##### # # # #
# # #   # # # # #
# # # # # # # # #
# # # #   # # # #
# # # ##### # # #
# # #       # # #
# # ######### # #
# #           # #
# ############# #
#               #
#################

@Sp3000 no :)

@Sp3000 but you could if you liked :) I can't write a research paper on something I haven't solved :)

@DominikMüller for the purposes of counting, those are to be considered the same, yes

but there might be other shapes where the issue of the upper snake cannot be resolved by using a different snake path

(like the ASCII example above)

Hmm it's a little different from circle-arc I think, since it sweeps a whole quadrant

The square that intersects isn't necessarily the one furthest away

(or is it?)

@MartinBüttner then I think you snake is also possible, if the head/tail are somewhere outside the spiral, but if you remove the the 2 # inside the spiral we have our usecase I think

@DominikMüller I actually meant the spaces in that ASCII art to be significant

so there is only a single possible path because each solid square has only two solid neighbours

sorry, should have clarified

I should have looked more carefully. I just didn't notice the horizontal spaces. Anyway, that would represent a shade that is not possible without intersection while to rotating.

@Sp3000 you have a number of arcs and a number of squares. Naively you could check every pair

Why isn't 1 an answer for this in various languages?

or some other single digit number

@PeterTaylor nice collection of graph problems that have already been done!

@feersum because the source code has to be repeated cyclically if the input is greater than the length.

oh, I was reading it as Nth character

I have been wondering though if there is a language where I can print a single character n times with only using a single character repeatedly for the code (except unary, because that would be way too long)

If you make Big Band auto print the stack at the end... ;D

*stacks

That could be an interesting question - which order do you print the stacks? (Top to bottom?)

top to bottom

I think everything should happen top to bottom

well, it might be bottom to top as well, but the order has to be defined

Mathematica keeps baffling me by how cumbersome string-handling is

why on earth do I have to do StringJoin[Table["string", {n}]] to repeat a string n times... o.O

I wonder if it would be useful in a golfing language to be able to switch between modes (like math mode, string handling mode, array manipulation mode) with a single character, which will change the meaning of most or all commands permanently

At that point, it'd probably be easier to just make three languages and save a byte on each :P

like, in maths mode [1 2 3]4* would give you [4 8 12] but in array mode it would give you [1 2 3 1 2 3 1 2 3 1 2 3]

lol

Unless you need to switch back

yeah it would probably only be interesting for longer programs where you need to do a fair share in at least two of the modes

I think what CJam does is okay, lumping all the less useful things under e

I don't think there's any harm in introducing 2 char instructions

yeah

I think I'll do something similar for Big Band

although, since you only have 1 char instructions, I guess e or m would sort of toggle the mode of the voice for the next instruction

:D

@Sp3000 I just edited the sandbox about a thousand times.. I hope it is converging

@Sp3000 but please tell me if I am making it worse :)

As a general challenge, it's very interesting. But for a PPCG question... I get the feeling that the difficulty bar is a tad too high....

@Sp3000 oh!

@Sp3000 but you are the cleverest people on the internet :)

@Sp3000 is there one bit that is too hard that I can give a solution for? Is it the arc/square intersection math?

@Sp3000 for the data structures one?

Now that you mention it, snakes is a bit like lego...

But no I mean Lembik's sandbox post

@Sp3000 that was that idea :) (re: lego)

@TAbraham meta.codegolf.stackexchange.com/a/4704/9206

@Sp3000 I like codegolf.stackexchange.com/a/44928/9206

but they should have asked 3*3 :)

much more difficult

maybe next time :P

:)

I wanted to make sure there are closed form solutions to the characteristic equation

@MartinBüttner I quite like the idea of two or three challenges on the same topic of increasing difficulty.. but I know I am eccentric :)

you mean like the "Tension on a Graph" challenges? :P

@MartinBüttner I wonder if your eigen value question suffer the same challenges as mine Matrix inverse meta post ..

@Optimizer no

y not ?

matrix inversion isn't possible for some matrices. finding the eigenvalues and eigenvectors always is.

@MartinBüttner what about the precision issues pointed by Peter and xnor ?

I'm not an expert in matrix inversion, but afaik the problem arises due to matrices which are close to being singular, so that the components get blown up immensely.

matrix inversion is in general a really hard problem.

solving a 2x2 eigensystem isn't. there's a closed-form solution for arbitrary 2x2 matrices which makes it very obvious that there are no singular cases.

you can give well-conditioned conditions for matrices, like ratio of smallest to largest eigenvalues, etc.

and you can make an ill-conditioned 2x2 matrix, but it's simple enough that it's not that big of a deal

are you talking about inversion now?

the last statement was about eigenvalue

what do you mean by ill-conditioned? degenerate eigenvalues?

it means usually having very small or large eigenvalues

a 'nearly 0' determinanet

well, you can probably get stray real or imaginary parts, but you'll still get results that are accurate to the desired precision.

how is a near 0 determinant not an issue here but a big issue in inversion ?

inversion has many steps so the errors compound

I see

because you're not dividing by it

and what feersum said

python's math library is kinda brain-damaged..will have to resort to matlab

lol

in case its of any interest

@Optimizer also, you were asking about 10x10 matrices and bigger, iirc ... for a 2x2 matrix I think an inversion challenge might be possible, because it should be possible to handle weird cases if the challenge specifies how to handle them.

that would be too similar to the system of equations challenge

then it's just a 'print arithmetic expression' challenge

@feersum as is the eigensystem challenge, essentially.

at least there are some slightly different ways to do it

I don't see that as a problem, as long as said arithmetic expression is long enough and has enough structure to make golfing it interesting.

[d -c -b a]/(ad-bc) or w/e is hardly interesting enough

yeah, good point

I didn't really think it through what the closed form looked like

@MartinBüttner the mathoverflow link was meant for you

although I see it isn't really that relevant

is the general consensus that my sandbox question is just too hard for PPCG? If so, maybe I could dumb it down?

@Lembik oh yeah I got that, but forgot to reply after reading it, sorry :D ... thanks!

@MartinBüttner no problem :)

Noam D. Elkies is a grade A genius, in case you didn't know

(the person who gave the accepted answer)

@MartinBüttner is there anything in your eigenquestion that requires that two eigenvectors output for a degenerate eigenplane be linearly independent?

@feersum no (because that's not generally possible)

of course it's possible

not for all degenerate eigenvalues

in the cases that it is possible

say an identity matrix

could I have both vectors be [1 0] ?

I know. and no you don't have to output different ones.

yes

lol ok

meh, I've got two interesting nonlinear systems, which I could solve for another Mathematica snippet. for one of them, I can easily fit the solver into 100 characters, but the plotting requires about 150. for the other (the arguably more interesting one), I can plot it with 115 characters, but the solver needs 150 :|

gah, most frustrating golfing ever... there's so much duplication in these equations, and I just can't make use of it.

@MartinBüttner It may be incomplete, because I only looked through the graphs tag.

it's a really good start ;)

@MartinBüttner Not with the kind of constraints I recall from Optimizer's question. See codegolf.stackexchange.com/a/11820/194

oh, nice answer

BTW it might be possible to find a matrix such that the eigenvector calculation involves a similarly nasty matrix, but I'm too tired now to think about it.