@Jonas: may I ask you to give the last vote here?

@tb Done!

Wonderful, thanks!

Speaking of voting, anyone around who hasn't voted here (and is able to)?

@HenningMakholm Where should I vote?

On the up-arrow for "etymology", if you have one.

Oh, right I see. I don't have the required scored on that tag.

Oh well.

Anyone want to give me a one-line (estimated) clarification of something in Dummit's book about the CRT for Ideals?

I could make it a full-fledged question if need be.

I can grasp that last statement intuitively, with regular ideals of Z, but can't seem to formally justify it. Like I said, I'll copy this over to main if that's better.

What is the question?

that the kernel is what is claimed?

Related: math.stackexchange.com/q/51620/7850

My question is how to prove that the kernel is the intersection of A and B

Set inclusion in both directions?

if x \in A \cap B, then is it clear that x is in the kernel?

yes, since phi(x) = (x mod A, x mod B) = (0, 0) = 0

Then maybe x∉A^B => x ∉ kernel(phi)?

I might be moving into the light... stop the presses.

The least you can say is that Gerry's treatment with a sledgehammer is effective :)

Yes.

Wow.

That's an ideal question.

so quiet...

alo alo

echo echo

I wonder how one text-pantomines a cricket's chirp

Dunno: Oh, boy! might be a bit too cryptic, but that's the best that came to mind.

oh - nice pull

So, how's life at Brown?

(If you don't mind my asking a personal question)

Is anyone else facing hiccups at the main site? I am. I am not sure if my internet connectivity is to blame.

Brown is treating me very nicely

Hi everyone

@Srivatsan: No, not at all, but there were others complaining earlier today (or was that your?)

and no - no hiccups for me

No, I wasn't complaining earlier. I just went home (=coffee shop :)) from school. So my internet connectivity just got much worse.

Hi @J.M. Your gravatar looked like a silver ring. =)

Somewhat, yes. :)

What is it?

He's slowly converging to Gortaur's eye...

Something I got from heavily tweaking parametric equations of the torus... :)

@JM By the way, when I looked on your profile, there's a somewhat ugly greyish line at the right border of your picture.

Huh, I must've slipped on cropping. I should fix that later...

Mathjax looks a little funny(=dark) too...

That was a quick disappearance...

@JM Do you know how they do that?

Oh, sure. Unregistered users have an option to nuke their accounts...

Ah.

If you don't mind me asking, @mixedmath, what areas are your interests in?

@Srivatsan: Did you try emptying the cache and restarting your browser?

Yes, "Shift-Refresh" and all that...

@tb What would that help?

Well, there's the possibility something gummed up JS, which affects MathJax...

Shift-Refresh forces your browser to pull from the site instead of from the cache, clearing the cache ensures a clean slate...

In other words: the magic trick that works since windows were introduced in OSes

@tb =) Magic trick worked.

But, seriously? =)

Is J.M.'s explanation not good enough?

@tb No no, I meant it rhetotically.

Never mind.

t.b.'s right, 'cept I'd put it a bit later: when Mosaic first showed up. :)

:) for this specific issue, right

@srivatsan: I like number theory, and I'm currently leaning towards analytic number theory

though I have yet to actually declare whether I will do analytic or algebraic (but I say I'll do one or the other all the time)

What does "declare" mean? Do you have to wear badges at your department?

Well, what happens is that when I become more certain, I have to give a detailed presentation

a sort of 'topics exam'

in the area of my choice before I get my thesis advisor

so I use 'declare,' but what I really mean is that I'm having trouble choosing an advisor

I really like both Dr. Hoffstein and Dr. Silverman, but one is very analytic and one is very algebraic

Thanks for the explanations!

;p

@mixedmath Oh, you must go to Brown. Do you know my friend Wade? He's a second year there.

If you like both (people and subjects) so much, maybe you can just flip a coin... :)

Yeah - he's preparing for his Topics now

He leaves a very good impression for Silverman's students

JM - maybe - I have a bit more time left

Sorry if I'm dense: Roughly: you apply for grad school, get a temporary admission, and you have some sort of test-year and those Topics before you're definitely admitted and the actual fun starts?

I didn't know that he had decided already. Wade is very strong, yes.

Say hi for me if you get the chance. We went to Michigan together.

Hoffstein advised Brubaker, didn't he? Brubaker has done ridiculously well.

Yes, I think he did

And many of Hoffstein's students are still in contact - it's a good community

@tb - yes, more or less. At Brown, we have to acquire a certain amount of 'qualification credits' - sort of like qualifying exams, except that there are classes attached to them

then you give a Topics exam (which is really a presentation - but they get to ask you questions throughout and afterwards, so I suppose it's sort of an oral exam)

That's nice.

@mixedmath so, "show us the stuff you're made of, and only then will we let you play"...

I think it's good for rooting out people who don't like to work. For everyone else it's kind of a waste.

Off to work for me. Later, y'all.

Later, J. M.

See you, @J.M.

Later

Okay, I get it then. They introduced a similar procedure two or three years after I started with my thesis. For me, there only was a huge administrative overhead to overcome, but nothing in terms of exams. Things have changed since then but I think students who come directly from the ETH mills can still bypass that system.

Interesting. I suppose I never really thought of the system changing.

Well, there was the Bologna process with the goal of synchronizing university schedules all over Europe following more-or-less the American model during the first decade of this century. At the same time they started reforming the graduate schools as well (actually, introducing would be a more appropriate term). Anyway, it will take some time until everything works smoothly, in the meantime we trust on social Darwinism.

@anon =)

(the smiley hides a link)

@Srivatsan This is nuts.

Interesting. I come back from work and the latest chat message is for me. @Srivatsan: Cool... But to be frank, I'm not sure if I follow the coloration that well. It seems you skipped writing some of the steps (specifically in the very first line). :( Also, how you knew to decompose x/(1-x/2) as you did is something the colors don't reveal (afaik) and seems too "clever" for me to see naturally...

Damn I've just noticed that I need to graduate next week. I'm not yet finished...

Weren't you warned a few days ago that you eventually get busier as the date goes near? :)

Yes, I was.

You really can't delegate at least some of the things you need to deal with?

Not really, no.

What're the odds that you make it, then?

If I work very hard, don't get ill and so on I'm pretty sure I will make it.

commutator magic puzzle rules 8)

now that i solved it, i remember seeing a variation of it in elementary school

some kids were memorizing its solution for N = 5 and used their fingers as nails

i remember trying to repeat that trick but failing. turns out i didn't know enough homotopy theory at the time :D

Fingers as nails?

the puzzle: find a way to hang a picture by a string using N nails in such a way that if you remove any one nail it falls

the solution is very beautiful imo

especially since i found it without any hints (except the title of the puzzle)

which is in itself a dead giveaway really

@JM Oy. Again with the avatars. You should be arrested.

what is your new avatar?

it looks cool, but i have no idea what it illustrates :)

@AsafKaragila For what? :P

@JM For changing avatars more often than once in a lifetime!

@AlexeiAverchenko Something I got after heavily modifying the parametric equations of the torus.

is this... thing still homeomorphic to a torus?

@AsafKaragila Under what court of law, König? Yours?

I wrote my answer about the ordinals whilst sitting in a algebraic topology class.

@AlexeiAverchenko I think not... I changed quite a lot of things...

@JM For example. However my laws are lazy and nihilistic.

@AsafKaragila you should be executed for that

(Besides, I like opening my artwork to critique... :) )

@AlexeiAverchenko Shut up.

@AsafKaragila wow, that's harsh :)

Help, help, Alexei is being oppressed!!

Well, he did vote for me. I think.

solving commutator magic by myself made my self-esteem immune to lowering for the next couple of days :P

Alexei, do you play chess by any chance?

maybe you can solve it too, asaf... oh, i forgot you don't pay attention in AT classes :P

Well, he just defined the fundamental group. I know that already.

@JM indeed i do, i got 1400-1500 on chess cube

Also, I do pay attention. I can divide my attention when I'm not interested.

@AsafKaragila prove it, solve the puzzle! :P

I am not interested.

@Alexei: put it this way, the König is like the king in chess. He's king, but he can't move much... ;)

Meanwhile, I must prepare sauce for my fusilli. Later.

And there is almost always regicide.

hello everybody

@JonasTeuwen If only things were that easy, eh?

there is definitely benefit from chat of MSE: I had a question which I couldn't solve for some time, and just reading your last 10 comments I resolved it

Was your question "How to kill a king"?

you cannot kill a king, you can only checkmate him

I do not mate with any king. I would mate with a queen if I was single, and the queen was hot.

@Gortaur go on :)

@Asaf exactly, queen was hot. only the princess can be hot in a present time

in chess, queen is a real killer if you ask me

@AlexeiAverchenko KMS

@Gortaur Queen? I do not like them. Freddy Mercury is not my kind of vocals, or sexual preference.

@AsafKaragila your two last posts concern mating with males. everything ok, Asaf? ;)

@AsafKaragila two blaspemies in half an hour - amazing!

@Gortaur Well, it was you who suggested mating with kings and with Queen.

@AsafKaragila if checkmates reminds you mating, and queen reminds you Mercury (whom you don't love) then definitely maybe )

Riiiiiiiight.

@Asaf Anyway, it just increases my doubts that you're ok. Again were giving a class? Or the proof does not go well

@Gortaur Nah. I had to sit through algebraic topology... :-)

@AsafKaragila and you're neither into geometry nor in algebra ) I remember )

And I have to sit through another algebra class. The horror... the horror.

@Asaf: be brave. I'm going to see my SV so see you later

Your SV?

the SuperVisor

Ah.

@Asaf, are you bad enough Konig to save the President?

@Gortaur Checkmate is some kind of killing no?

@AlexeiAverchenko if you want to save, press ctrl+s or F5

@JonasTeuwen rather way of scaring kings

@anon Updated my answer with some more details. Thanks for your comments/critique. =)

@Srivatsan good morning, East Coast )

Morning, @Gortaur

how're you doing, the weather is cold already?

Not cold enough for me =)

I like the cold here

This week has been a little warm. Next week will be colder, I'm told (touch wood =))

@Srivatsan it's about +12C here in Delft. Though in Volgograd it's already -12C. Quite shocking, it is 800 km to the South from Delft

@Gortaur Oh, you guys speak Celcius or Fahrenheit? =) +12C is very warm, no?

+12C is about 54-55F

usual Fall temperature I would say

I am comfortable with both scales.

quite warm for November

Yes, that's what I meant.

Right, I try to arrange a room to give my MSc thesis defense in and there are none available in this building 8-).

@JonasTeuwen At first glance, I thought Building 8 is the name of some building.

Hi @Jonas

Hah. Hi!

there is certainly a building 8

though I don't know where is it in our campus

@JonasTeuwen you have to give it only at EWI building?

at 3mE there are usually some of empty rooms to give MSc presentation

No it can be somewhere else as well, but they have to go back to their office afterwards to decide about the grade, and then that will take longer etc. Plus there is a big parking behind EWI.

@Gortaur To clarify, I too don't like cold beyond a point. -12C is almost as cold as it gets here. The minimum is like -15 to -20, and it stays that low for a few days. That's not that bad, I'd say.

@Srivatsan I agree if there is snow. February in Volgograd is quite depressive because there is no snow, all dirty, naked trees and -20

@Gortaur Does sound depressing. =)

one should take a deep breath and wait for the May when there is no snow, all blooming, naked beautiful girls and +30 )

Naked girls? Where?

@JonasTeuwen not here. I remember the beginning of really warm spring days at my university. you can just stay at the entrance of it and see the beauty coming inside

They go naked to the university? Cool.

there they do know how to dress

after living in Sweden and here for 2 years, I would call girls in cute mini-dresses naked

@JonasTeuwen anyway, so what about a room?

Oh, right.

I need to find one. Maybe I'll check across the street tomorrow.

Afternoon all.

Afternoon Henning

@HenningMakholm afternoon

though fishing in Sweden was much more cool than in Russia

either girls or the fish. strange choice

@Henning: are you to fishing?

How about going fishing with the girls?

@JonasTeuwen What are you proposing: fly them to Sweden? =)

@Srivatsan or to fly the fish into Russian lake )

though when you're go fishing with girls it does not matter much if there is fish

No, I don't fish.

Wait, who's fishing for girls?

@JM have you ever numerically integrated in MATLAB?

single or multiple? Then again, are you talking about DEs or actual integrals?

ok. I'm talking about Int[f[x,y,z],{z=0..1}]

wait, wait... you have a multiparameter function, but you only want to integrate with respect to one of those parameters?

yes

Doesn't sound very numerical to me, unless you fix the other parameters.

ok, the problem is the following. There is a toolbox that calls @F[x,y]. I mean in this toolbox there is a routine like R(a,b,@F) where F is a function

F[x,y] = Int[f(x,y,z),{z=0..1}]

I just need to define it somehow

Oh, so you make an m-file for F...

@JM yes

previously I've defined F[x] = Int[f[t],{t=0..x}] through m-file using quad routine

Have you seen this?

but now I need to define F as an integral with parametrs

@JM no ) Contains the function called by the function function as a nested function

The examples in that link involve fzero(), but it should still apply to quad(), quadgk(), or whatever your choice is...

in fact I used such definitions of functions already, let me think a bit please...

It's certainly up to you, but if the calling sequence for the integrand is simple enough, you might get away with the anonymous approach.

@JM let me try it, thanks

@JM: how do you think, for nested functions can nested function be defined inside a loop?

Not sure, I haven't tried myself.

(I don't have MATLAB on my current computer, sorry.)

nevermind

oh no, I forgot to put a semicolon ((

poor command window

@Gortaur Don't worry. The command window doesn't have any feelings.

@JonasTeuwen I cannot even make it active to press ctrl+c )

I had to kill the process

rm -rf is better if we're talking about matlab.

@JonasTeuwen how should it be used in Windows?

1 step: install Linux? )

Yes. First format c:.

Then install Linux, then install matlab, then give matlab the rm -rf.

old story

Then it must be quite good if it is repeated...

I have never done anything better to my computer than removing windows.

I need to go home, throw out the paper left from furniture

Good luck.

it's odd that I can do it only at 18-00 Tuesday

like everybody here have to finish their work before 6pm and live in 15 minutes to his/her job

Cygwin can give you an rm -rf in Windows.

@JonasTeuwen tank you. you too

@HenningMakholm Wonder why someone starred that comment =)

Maybe because it is excellent advice.

True, it is.

What do you use instead of matlab?

I try to avoid such situations. Otherwise numpy, scipy or maybe octave.

there is also R

I wonder why the universities teach with things like matlab instead of free software

Right, but that is for statistics. There is many more. Maxima, Sage, Axiom, GAP, etc.

Probably because it is way easier to learn to use.

@QED MATLAB's pretty established. You do know that Moler's a leading (numerical) linear algebra expert, no?

no I didn't know that

It was intended from the beginning to be a front end for things like LINPACK and EISPACK and all those other fancy FORTRAN libraries.

'course, times have changed, and we now have more choices. Inertia's a problem, though.

@JM, hope I was not preempting you here?

if someone doesn't use the world "algorithm" they probably don't mean algorithm

I imagine he just wants some advice on solving things like this, not a decision procedure

Still a good answer though

I instinctively take "method" to mean "algorithm". Perhaps an occupational disease?

yes

Oh, well... I was working on a problem on and off during the morning. Since Swapan's answer wasn't complete, and since no one else answered there was no banner. I finished my answer, only to see that Swapan edited his answer and it was accepted.

C'est la vie.

@robjohn good morning. La vie is indeed like this )

@Gortaur Good morning. I didn't mean to enter griping and not say hello.

Hello all!

Ooh, a new feature @All :-D

@All cheap ugg boots buy em here

@QED kill uggs with fire!

X)

because of that and related stuff girls here do not know how to dress

@QED: are you down under?

I am up above

Okay, I wondered because of the UGG reference.

typical sort of thing spammers sell

@robjohn excuse me, but this question does mean smth? really?

anyone here can tell me why is this true, please?

3^-1 = x (mod 11)

Hello, BTW.

that doesn't make any sense Gigili

Hell0

x=4

3^-1 = 1/3 = 1/3 (mod 11) x)

ugh

because 3x4=12=1 mod 11

what does that "mod" do?

x=y mod 11 iff 11 | x-y

"3^-1 = x (mod 11)" is not true or false

that is x and y differ by a multiple of 11

@robjohn Great, thank you.

@QED no, it seems to be a problem whose answer is x=4 mod 11

@Gigili See Modular Arithmetic

@QED You're right, I should have asked "how to solve it" ..

To find modular inverses use the euclidean algorithm

@robjohn Oh, that mustn't be "=" .. right?

I combined several algorithms into this one

should be triple instead of double

treat it as a 3 place relation: _ = _ (mod _)

@Gigili If you specify "mod" = is okay, but \equiv is better. What QED said

Got it, thank you @robjohn and @QED

x\equiv y\pmod{m}

congrats, @rob ) finally

how did you do that?

wow, it's much simpler on the paper

oh it's just an image

@Gortaur took a while :-0

math on the web is just abysmal

@robjohn could you please remind me how to do it? I've forgotten the address

Also the 'm' should be on top of \equiv

http://latex.codecogs.com/gif.latex?x\equiv%20y\pmod{m}

@robjohn tanks

@Gigili the standard way in most pubs is the way I wrote it, though I have seen it the way you mention.

@AsafKaragila: whenever you be here, could you please pin this message which contains the address to use LaTeX in this chat?

@Gortaur I put it in my profile until Asaf adds it here.

@robjohn nice idea, Mean Square

why do you love this sum so much?

haha

I just put it there since it was in the only question on my profile.

I have shortened to \LaTeX so that things don't scroll.

@QED what you laughin' at? :-)

"mean square"

@QED that how @rob calls himself in the profile, nothing more )

I am a crotchety old man who abides by the social norms, whether those norms obey the triangle inequality or not.

my lower bound for your age is 50. is it right?

@Gortaur that is a lower bound.

ok. it was based on the car incident in 70s

Ah, I also mentioned that I started grad school at Princeton in 1981.

@robjohn sorry, grad school is BSc?

what do people do at grad school?

Grad(e) undergraduate homework, mostly.

lol

No, MSc and PhD at Princeton.

@robjohn hm... before thinking about your age I was assuming you're about 42

@Gortaur That's nice :-)

I believe that BSc is undergraduate at most US institutions.

oh yeah, you're right

Does anyone like puzzles?

@QED we hang out on MSE...

Isn't it fun that I can pin stuff from the outside? I wasn't even in the room.

You have three natural numbers "buckets of pebbles" and the rules are you can take two of the buckets A and B and move the pebbles around to get 2A and B-A (when A <= B).

@AsafKaragila You have tools that don't require your presence.

Can you empty one bucket?

I can do anything I want to. I am invincible.

so for example if we started with (3,5,7) you could take 3 from the 5 bucket to get (6,2,7) then take 2 from the 7 bucket to get (6,2,5) then... (4,4,5) then (0,8,5) done

Hm, each such operation has determinant 3 when viewed as a linear transformation.

On the other hand it preserves the 1-norm.

So you can make 2^k A and B-2^k A, as long as 2^{k-1}A\le B

Huzzah. I have a concrete topic for my thesis. Now I just have to start doing actual research.

Since I don't have a clue how to solve it I made the computer draw some graphs, but they didn't help either. I also found examples where the simple reduction strategies like "always reduce the top two" or "always reduce the bottom two" loop.

so it's hard enough that you might find it interesting

@Asaf, what is the topic?

Why not ask it on the main site?

Vector spaces without the axiom of choice.

I don't want solutions

well, I do, but I want to come up with it myself

Solutions such as Saline?

@HenningMakholm det is 2 I think...

@AsafKaragila what are the fields? btw, thanks for pinning

You could always resolve not to look at answers until you have a solution.

It is concrete, but not that concrete.

I have various of consistency results that I want to extend, prove or otherwise.

@robjohn I get something like \pmatrix{ 2 & 0 \\ -1 & 1}.

@HenningMakholm and the det of that is 2

Gah! I cannot do determinants anymore.

Anyway, my idea was to try to derive a limit for the number of operations you can do because you bump into negative space, but that's shot down by QED's finding of loops anyway.

Why would you want to compute things?!??!?!

@AsafKaragila which things?

Determinants.

usually we do computations for people like us to have an opportunity to chat in the chat

or to drive cars

or whatever