Ah, Batman is epic.

The Batman curve exploded right away. It had like 20k views in two days.

ShreevatsaR still gets reputation for that answer.

Well, it was a nice answer, I think.

He deserves it. After all, "...he sure brought a large luggage when intelligence showered the Earth." =)

True.

I wonder if that is a usual way to praise someone. It sounds very peculiar to me.

@tb: Did you finish reading?

@Asaf: no, I'm still stuck at claim 1.

:P

Well, since T is a linear automorphism, if it fixes E pointwise, it fixes span(E) pointwise.

And that's really all there's to it.

So far I got.

In fact the cardinality requirement is moot.

Hm. and in the proof of claim 2 you're lacking some dollars, I think.

Fixed.

Writing such long answers is really a pain in the ass when MathJax later takes away your $\{$ and $<$

try \lbrace for the former and \lt for the latter

I know.

I forgot the \lt

well, the \lbrace wouldn't have produced that effect.

Already got used to \lbrace and all.

My problem is that now when I write TeX I always use \lt which is not standard LaTeX...

And as an analyst...

:P

@Asaf: Okay, done. I gave you +1, but I need some digesting.

Thanks :-)

I am going to have to change a bit the answer on MSE as well.

That's for some other time, though.

Well, and I didn't thank you for the exaggerated thank yous! Much appreciated, though :)

Hehe :-)

Mmm, a new version for texlive.

yet again, the question with no answers...

And finally... flash plugin native for 64bit linux. WITH nVidia vdpau support! Neat!

I wish flash would very soon be flushed down where it belongs...

Hehe, I mostly agree. I do like that I have flashblock which stops it from loading automatically.

But wait, when I toyed around with ubuntu about a year ago, they told me that 64bit support for flash was impending. What took them so long?

Yeah, I don't know.

They released a version, withdrew it, then they took a few months to release a beta version of the plugin which stayed beta for like a year.

I vaguely remember something like that.

@AsafKaragila Sure, there are a few more of these plugins and the internet becomes a much calmer place... Problem is that I'm no longer used to all these bells and whistles they add to the sites nowadays, so whenever I use another computer I risk an epileptic shock...

Haha! Yes, I completely understand that.

Not sure what this means: math.stackexchange.com/questions/76706/… :) EDIT: I meant the answer.

Oh well. I wrote an answer to get it over with.

Strange, I got a vote which was then taken away from me. I guess someone regretted :-)

Either way, it's getting late.

I should get my beauty sleep, or something like that.

They giveth and they taketh away.

Goodnight tb, Srivatsan.

Goodnight Asaf.

@Asaf: good night!

Hello

I see Jack Schmidt is not in the forum at the moment, I was discussing something with him a few nights ago

@tb Can you help me with something, if I have the polynomial in two variables like xy + x^2 - 1

and view it just as a polynomial in the variable x

when I try to factorise it into say pq, where p and q are some polynomials in the variables x and y but viewed as a polynomial in just x

can I say that the degree of p has to be 1 and the deg of q has to be 1 as well?

I am not sure if the formula deg(pq) = deg p + deg q for one variables polynomials can be adapted here.....

Why not? Isn't deg_x (pq) = deq_x(p) + deg_x(q)?

Let's say p = x^a A1(y) + B1(x,y) and q=x^b A2(y) + B2(x,y) where the deg_x B1 < a and deg_x B2 < b. Then pq = x^{a+b} (A1 A2)(y) + B(x,y) where deg B < a+b.

Now it remains to check if A1(y) A2(y) can be zero when both A1(y) and A2(y) are nonzero. That seems impossible, doesn't it?

yeah

So if I use this fact, the only way to factor xy - x^2 - 1 into polynomials with integer coefficients is (ax + by + c)(dx + ey + f)

If this is the only possibility I have eliminated it

Thanks by the way

You're welcome. Now I have to run to grab some dinner! :=)

Bye, @tb, Benjamin.

Evening, Rob. It looks pretty quiet here tonight.

I guess it is a Friday.

Hello @robjohn. Hi @Mike.

Hey, Srivatsan.

hello

Hi Benjamin.

My apologies for saying "Hi" and then "Bye," but I've got to go.

:=) No problem, Mike. Have a great weekend.

Hello Srivatsan

Hey Benjamin.

I have been thinking about your question. I am not really sure how you concluded that the factorization must look like (ax+by+c)(dx+ey+f).

yeah

I have been trying to figure that out

Well we know it has to be factored into ax +b, where a,b are functions of y

Yep. That's true.

I guess you just say that the b term has to be linear in y because there is no y^2 term in xy + x^2 -1

(Alternately, looking at y, we can factor it as c * (dy+e), where c, d, e are all functions of x.)

Actually, let's say that the factorization is (ax+b)(cx+d) where a,b,c,d are all functions of y.

Then, since the y-deg is atmost 1, a,b,c,d are all linear at most.

ok so a,b,c,d are all linear polynomials in y at most. Which means our factorisation should be:

((ay + b)x + cy + d)((ey + f)x + gy + h), a,b,c,d,e,f,g,h all integers

Complex numbers, i would say. But that's ok.

Ok sorry I did not tell you the whole question

But I would like to factor this over Z

I would like to show this is not possible

Ah, peace.

yeah

Next step would be to look at the y-deg, I guess. Since the original polynomial is linear in y, one of the two factors is linear in y and the other is constant in y.

Let's say e=0=g, so that the second factor becomes a constant in y. Then we have ((ay+b)x + cy+d)(ex+f), where a,b,c,d,e,f are all integers. (I am mixing up e,f,g,h etc., hopefully it's ok.)

I was hoping to just expand everything, bash the algebra and compare coefficients

We can still do that ;)

ok

So, effectively, we have the factorization xy-x^2-1 = (Axy+Bx+Cy+D) * (Ex+F). (some minor tweak to the first term)

ok

AE=0 (coeff. of x^2 y), AF+CE=1 (coeff. xy), BF+DE=0 (coeff. x), CF=0 (coeff. y), DF=-1 (const term), BE=-1 (coeff. x^2)

Sorry if that isn't too clear.

E is not zero (else the factorization would become trivial). So A = 0.

Wait, I think if you go back to the original form without any simplifications it is easier.

you will get ae = 0, af = 0 ag = 0, ah = 1 for ah is the coefficient of xy

then this means a= 1 and h = 1 or a = -1, h= -1 for we are working in the integers

then

this means e = f = g = 0

Um, can you state exactly which form you're using? We revised the form multiple times inline.

((ay + b)x + cy + d)((ey + f)x + gy + h)

wolframalpha.com/input/?i=Expand%5B%28%28a*y+%2B+b%29x+%2B+c*y+%2B+d%‌​29*%28%28e*y+%2B+f%29x+%2B+g*y+%2B+h%29%5D

But then you get a contradiction because the coefficient of x^2 is bf

and f = 0 so there will be no x^2 term in the expansion

I see. I guess that works.

Which of the two in the photo is you, Benjamin?

I am not the white guy

Sorry, cannot make out much about the colour. :) Left or right?

In that case I am the taller of the two on the right.

Cool.

Where are you from Srivatsan? I am from Australia.

I am *from* India. I am studying in Pittsburgh, US.

I suppose you are a first-year undergrad. I am doing my Ph.D. in CS.

Yeah, that's right.

What's the from?

I suppose when you said peace you could have said ohm shanti?? I remember at the Brahma Kumaris I stayed in Dehli their slogan was ohm shanti ohm.

As in, I grew up in India for ~21 years. I came abroad for studies.

ahhh ok. I've been to Dehli and Kathmandu, Nepal in south asia. Where are you from in India?

Er, peace was mostly a lingo that has stuck from my undergrad days. (I don't use them often, but from time to time, unintentionally). It doesn't really connotate "om shanti". ;)

sorry, maybe i'm mixing it up with a bollywood film....

What is Brahma Kumaris? Is it some place?

Oh it's some religious organisation....I went to one of its ashram's in india

I am from here: Chennai/Madras, which is in the southern part of the peninsula.

I suppose you speak tamil?

Yes. E.g., see my profile message.

ok

That's just some random nonsense. I didn't know what to say about myself ;)

You grew up in Australia?

No not really

I grew up in Malaysia

Oh, nice. Been traveling a lot, it seems...

yeah

hello

Hi Rajesh

hi

what is our thesis problem ?

sorry your

Nothing specific. :)

i mean which field it is related to

Theoretical CS.

i wonder which branch of mathematics is involved more in TCS

Well, mostly combinatorics, discrete mathematics, graph theory

Depending on the subfields, algebra will be useful. For e.g., for coding theory, you need some algebra.

these things do not serve me as a primary motivation....although problems involving them need ingenuity and are interesting

I don't follow you; can you elaborate?

i personally am not motivated towards combinatorics discrete math and the likes....i am just saying

Ok. You like apples, I like bananas. :)

if you call analysis and the likes as apples

Oh of course, lots of linear algebra and probability are useful for CS.

have you come across machine learning

Yes, my friend works in ML.

i am actually doing my phd in speech signal processing

Oh cool. Are you more applied or more theoretical?

you mean signal processing or is it in general

Your interests in particular.

theoretical......but one needs to do lot of things....

@Srivatsan : Is p != np problem......a well defined problem ?

mathematically speaking

It is, although it is unclear whether anyone understands it.

It is a well-defined problem.

hm

What makes you think otherwise? (Although that is a good thought, I should say)

i do not know much aboutit but....i was surprised to read the use of concepts from statistical mechanics in the recent attempt by Vinay (not sure of the name)......so does it involve any probability in it ?

At the first glance, no.

ok

its a purely deterministic problem then......i am a bit relieved now

But these things connect to too many other fields; so one can never say "no" for sure.

Actually, the question is about "non-determinism" which is even more puzzling than probability.

do you mean en.wikipedia.org/wiki/Nondeterministic_algorithm ?

Exactly.

Hi @yayu

Clouds are not our friend. :-(

Agreed. The weather forecast predicts showers for tomorrow. Ruins my day... =)

What did the clouds do to you, @robjohn?

They kept us from seeing all the stars we were supposed to see.

I thought you were speaking of clouds in the sense of computing.

Tough luck.

Did you kids like the trip, or were they disappointed too much?

Hi anon

Another duplicate of the question with no answer: math.stackexchange.com/questions/76881/….

hi sri, rob

Hi yayu

@SrivatsanNarayanan It is a disappointment tonight, but last night was good and tomorrow is predicted to be good.

@Asaf: Multiplication goes faster to zero than addition.?

That ClearDarkSky site is both cutely named and useful...

I'll make a tiny observation based on that "unanswerable question" from Reddit and the nutjob "arithmetic precedence" question from way before (and apparently also from Reddit): apparently it is sometimes easier to ask a question and wait for it to be closed as a duplicate, than to go through the trouble of searching if the question's been asked before...

But much less friendly. Letting others do your research for you.

good <...>, guys

Loving the placeholder... :D

second it @JM. :-)

@JM how is your plagiarizing client? )

hi all

Dunno. It's not like I'll take the trouble to stalk him. On the other hand, if he pulls that stunt of copying from MathWorld all over again, I'm blowin' the whistle on him...

and blow away his house like in 3 porks?

hi @JM

@RajeshD: hi. they do not say hello today (

Hello Raj

hi

howz the day goin

@Gortaur: Tiny English tip: it's "Three Pigs". "Three Porks" somehow implies that the wolf won and managed to cook them... ;)

@Gortaur : i didn't get you

Hello Gortaur! :-p

@JM whatever ) I was always wishing that the wolf wins

@RajeshD nevermind, I've already dropped some tears due to this reason (

ok

@robjohn Hello, Rob! :-)

today my advisor deemed me to be unfit to do any research work any where and unfit to teach at anywhere

...because?

@Gortaur What's all this noise? Its early here :-)

i do not know....he has been saying this for the past 1.5 years

Rob. are you kidding?

he said he can't recommend me anywhere either

@Gortaur I'm a-kiddin'

i am not able to understand why he says these things.....he says that my standards are dar below compared to other students....and wont be able to reach it even after 6 years

wth

are you a PhD or MSc student?

PhD

We can't really help you there, unless you find out what prompted your adviser to tell you this.

So ask your advisor first why he thinks that of you. He owes you that.

@RajeshD My usual way to treat such situations is to start with hypothesis that he is half-right and half-wrong

then you may try to iterate and realize what have been done by you and by him during your work

for the first one year whatever i did he deemed it as useless....and later for next i.5 years i ve been doin exactly what he says without asking why....i even submitted 2 conf papers....in which the entire material was written by him...i just typed...and did coding and experiments...

and you may see that percentage right/wrong will change

anyway, almost always there is a part of your fault

what is i.5 ?

"the entire material was written by him...i just typed...and did coding and experiments..." - the way you put it... exactly what ideas did you put on the table? Or all you did was grunt work?

i agree.....there could be wrong with me....but he gives very destructive critisicm and always dismissive.......he says that i cannot get any original ideas of my own and i am not able to write research level papers

sorry 1.5

yes all i did was grunt work....

"he gives very destructive critisicm and always dismissive" - then why stay under him? Clearly he is of no use to your improvement...

after i realized that he doesn't care about others ideas i have stopped putting any new ideas of mine on his table due to the fear of developing a bad rapport

@RajeshD: where are you studying?

which country I mean

India

but i have no choice......he also constantly been saying that he would cancel all the funding

Meanwhile, I'm off to the restaurant. Later.

anyway....i do not intend to bother you all with this..

ok...

@JM Enjoy. 3 porks?

@RajeshD I don't have any impression/experience related to the culture of India, and clearly we cannot tell you here what to do. I am sorry about it, but honestly speaking there are two ways: stay within his group or escape it.

The hardest task is to decide which way to take - but you should know that sometimes (as for me, it is a kind of credo) the lack of decision is worthier then making each of them

@Gortaur you know, like in the three porks? :-)

yes Gortaur......i understand there may not be precise advice......its just that i was not feeling well about it that i have typed it

I don't tell about taking hurried decisions - but you will certainly feel when the time to make it comes.

@robjohn didn't get you

I was referring to that post of mine

yes.....i'll take sometime out and relax.....thanks for the advice and concern

@RajeshD you're welcome. Good luck

@Gortaur Perhaps I was misreading your "3 porks?" to JM.

@robjohn: how were you misreading it?

also to mention please do not judge anything about my advisor...i still have a lot of respect for him....i do not complain he is bad...just that i do not understand things that are wrong with me

@RajeshD: you don't have to offer excuses

@RajeshD he may be a good mathematician, but from his comments, he doesn't sound very good to have as an advisor.

@Gortaur it sounded as if you were uncertain why he was talking about 3 porks.

@robjohn hm. more likely that @JM will take a doughnut

@Gortaur Ah, you see, I did misread your comment. I didn't see that you were referring to his imminent consumption of comestibles.

Sorry to be annoying, but does anyone here play minecraft and is free at 7 UTC today?

)))))

@Gortaur @robjohn Hi

@RamanaVenkata: hi

Good morning @Ramana :-)

@robjohn Actually its evening here I should say Good morning to you

@RonanForman I play only WOT

@RamanaVenkata it's 5 am on his clock

@RamanaVenkata Ah, I see the clock I have for your time zone is white (day) but it is almost 18:00, so it is late afternoon. Is my clock off?

@RamanaVenkata It is 5:28 here.

@RonanForman though some groups may be free at 7 UTC today

hm, I has 1350 total bounty offered

@Gortaur on 15 separate questions.

That seems to include the ones that have already been awarded.

@robjohn 1/(2n) is a lot slower in its approach to 0 than 1(n^2).

Okay, but how does that bear on the problem?

Grizzly bear?

That would be a problem indeed.

How about panda bears?

What the...

Someone upvoted the "hurry guys!" question.

Go figure...

Hurry guys?

This horrid thing

Ick!

There is a pancake breakfast here in about 20 minutes.

Yum yum yum

My wife is bringing our dog down for the rest of the weekend.

Down from where? Did you hang him on a tree?

Down to Borrego Springs for Nightfall.

Oh.

Down from Los Angeles. Lilly travels well. My wife said that she was very happy to get in the car with her.

Dogs + cars = happy.

Not all dogs travel well. We have some friends whose dog really does not like to get into the car.

I see.

much less a long car trip.

I finally broke 8K (by 5). Today will be a slow day for me since I will be AFK most of the day. Yesterday was slow, too.

Congrats. I finally finished that proof I was working on for that MO question.

Which MO q?

This one

Looks electric and dangerous.

I am off to consume pancakes. Later.

Ciao.

Hi Asaf

hi @Asaf

anyone there

hi @Doug

Like I said in a comment under Mike's answer in the Riemann sum limit question, I liked the estimate he gets. Any chance my answer can be souped up to get the same thing?

Wish Mike or J.M. was here in the chatroom. :=)

@Sri : i remember doin these types in +2 math

but they would always be given under the section integral as a limit of summation....so it used to easy since we know that this is the approach we should follow

Yes, I know what you are talking about. It's more a question of spotting the pattern than actual ingenuity; for the case of my answer, that is.

cool.....it kinda rekindle my memory of those good old days

and also memories of my teachers

we used to pounce on these type of problems desperately trying to get it into the form of function of (i/n).....especially due to the highly time limited competitive exams

I have upvoted it

Thank you, Rajesh

Bah, I have been making a number of slip-ups in commenting lately. Yesterday I posted a comment requesting the OP to accept an answer when she had clearly stated in the question that she didn't understand how to accept. Today, I posted a comment asking to add the [homework] tag when the tag was already present. Anyone been through this? ;)

So Rajesh, where do you study? City and college...