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00:00 - 19:0019:00 - 00:00

:)
@EnjoysMath, now it's even more awesome!
Computers are stupid :/
They're not stupid, they're just misunderstood
:D
Then I misunderstand computers :)
They're stupid as long as they run Windows..
19:20
Lol :)

So, does anyone have any ideas about what I should do? I'm really frustrated. I guess I don't understand what they mean by "command line options" or else I'm starting GAP directly instead of in a "shell".

Maybe this isn't the place for this stuff . . .

Sorry.
"I've calculated the eigenvalues of a plain vanilla matrix"
Never installed GAP. No idea.
0
Q: Calculating algebraic and geometric multiplicities from given minomial polynomial of A

Bolz Let $V$ be a $K$-Vectorspace of Dimension $n$. Let the minomial polynomial of $A \in End(V)$ be $M_{A}(x) = x^{k}$ and $n = k $ Calculate all eigenvalues of the potencies $A^j$ as well as all algebraic and geometric multiplicities. Two problems before I've calculated the eigenvalues o...

Pair correlations of eigenvalues of custard creams is related deeply to Riemann's chocolate hypothesis.
Okay, I'm going to give it a rest for a while. Thank you for your time :)
19:26
@BalarkaSen I thought it made no sense, but the phrase "plain vanilla" actually exists :S
@G.T.R WAT
@Shaun, you're on GNU/Linux?
"having no special or extra features; ordinary or standard."
@G.T.R =D
Example: We chose it because it seemed, after all the baroque alternatives, the most generic, plain vanilla name we could think of.
19:29
@G.T.R Is this guy Mr. Angry/Hungry?
Yes he is
"0 up 3143 down"
Quick question
$$ \int_{0}^{\frac{\pi}{2}} \dfrac{1}{(1+x^2)(1+\tan x)} \text{ d}x $$
How would I go about starting this integral?
Ugly. Don't like integrals. Yuck.
-_-
Is it just because you're really bad at integration?
19:35
@Shisui Maybe.
Or maybe not.
Me too.
However, the fun's in the art of solving them!
=D
I don't fancy contest problems much.
Is what I posted a contest problem?
It was given to me by somebody I know.
@Shisui Well, I don't find a context from which it arises naturally.
Seems pretty made-up.
Well, it is equal to $\int sin(2x)arctan(x)dx$ with the same bounds. Don't know if I can compute it
19:39
I don't find much inspiration to do a certain problem without much context.
Oops, forget it
Bob
Bob
@Shisui..... could it be done by taking $z=arctanx$?
@Bob I was trying to guess something along those lines.
Bob
Bob
$\frac{dz}{1+\tan\tan{z}}$
There is no closed form known. I tried a pari code to calculate numerically got this and finally arrived at this
@Shisui @Bob @G.T.R
Sometimes cheating is better than thinking =P
19:45
hello I need solve this recursion:
LOL, thanks @BalarkaSen for saving me some time
@nullgeppetto Nah, I'm actually on the dreaded Windows Vista lol:)
No problem @G.T.R
@Bob I got that too! $$ \int_{0}^{1} \dfrac{\text{d}z}{1+\tan \tan z} $$
I knew the moment that this is a contextless problem not worthed to think about much.
19:47
@Shaun, oh God! Please escape buddy!
@Shisui So does this guy
how solve $a_1=1$, $a_{n+1}=1+1/(1+a_n)$ firts show that converge and then find the limit.
ah, that time I'm sure it is equal to $\int_0^{\pi/2} \frac{arctan(x)}{1+\sin(2x)}dx$
@nullgeppetto I haven't had any problems with it (oddly enough). Maybe this is my first one . . .
@Shaun, you know! I would say goodbye-microsoft.com !
19:50
@Shisui Ta-da!
I'm the party pooper.
Bob
Bob
@BalarkaSen...... what is this oeis site meant for ???
@BalarkaSen Oh wow, I forgot the quotient rule's square of the denominator -_-
@Bob For collecting entries on integer sequence of general interest.
It's a great stuff.
You should check it out.
@Shisui nope, I'm sure (Lucian also is)
@BalarkaSen do they usually store the decimal expansion of random constants ?
@G.T.R Of general interest.
Bob
Bob
19:52
@BalarkaSen...... i m nt getting how to use it
@nullgeppetto Yeah, maybe it is time for a replacement . . .
@Bob It depends on for what you want to use it.
In general type an arbitrary sequence and get a entry for it, for example.
@DanielFischer Can you check the number of deleted answers on this math.stackexchange.com/questions/364452/… ?
@Shisui I am sure I crushed your interest by giving these links?
=P
@BalarkaSen Completely!
I'm glad to know I wasn't being foolish by missing something obvious, however.
19:56
@Shisui Haha. I can be evil sometimes.
@G.T.R 25 answers. I guess that's the record.
@DanielFischer are there answers by high-rep users, or is it just pure gibberish ?
Bob
Bob
@BalarkaSen how did you get the link for that question ???
@Bob i ran a code at pari to get numerically approximate answer.
Some by high rep users. A couple by 10K+, several more by 1K-10K, but most by $<$ 1k, some plain trolling.
Bob
Bob
pari ??
@BalarkaSen
means ??
@BalarkaSen did you check the new IMO 2014 problems ?
Problem 1 seems fairly interesting
Salut @GTR, @Balarka, @DanielF
Good evening, @Ted.
@DanielF, I spent a good portion of today learning to count :)
20:14
$0,1,\infty$
What's so difficult about that?
LOL ... not helpful for my probability class.
Bonsoir @Ted
Ça va?
ever had a zit on your scrotum?
Non, je dois passer un oral d'allemand demain, mais je ne suis pas prêt
20:20
Quel dommage, @GTR. Peut-être que Daniel pourra t'aider ... :)
@Shaun, :)
20:44
@DanielFischer is it safe to say "Dieser Text ist ein Artikel von der Zeit veröffentlicht im July 2014"?
@G.T.R Juli, not July. And there ought to be a comma after "Artikel". But one would rarely formulate it thus. More likely one would say "Dieser Text ist ein von der Zeit im Juli 2014 veröffentlichter Artikel.", or "Dieser Text is ein Artikel, den die Zeit im Juli 2014 veröffentlicht hat." Depends on what you want to emphasise etc.
@nullgeppetto :)
Thanks, I will use the last formulation tomorrow :)
@robjohn did you manage to work on that series I showed you yesterday?
I think I know what my problem is with GAP: I don't know what they mean by "command line options". In Windows, GAP is started with a batch file, whereas otherwise, well . . .

"When you start GAP from a command line or from a script you may specify a number of options on the command-line to change the default behaviour of GAP."
GAPmanual, Section 3.1.

What I need is "gap -L file-name", I presume, since "SaveWorkspace(file-name)" returned "true".

Trying to do research with GAP is going to be a pain in the neck . . .
20:57
*hands @DanielF his deutsch-tutor badge
@Chris'ssis which series?
@TedShifrin That tag will be burninated in no time on main ;)
will be what?
:16505635$$ \sum_{n=1}^{\infty} \frac{H_n-\log(n)-\gamma}{n}$$
21:00
@TedShifrin burninated
@Chris'ssis Oh, no I haven't had a chance.
ah @DanielF, it's an Urban Dictionary word ... not, so far as I know, a true word.
This is an awesome profile "about" section: math.stackexchange.com/users/85969/hakim
anorton !!
Hi! :)
21:02
ok, I'm off to do some cooking ... see everyone later
user105491
21:36
Where's @BalarkaSen today? Hey @Ted, and bye @Ted. :-)
user105491
@anorton I agree with you on the profile thing. The LaTeX is so amazing!
I use LyX for all me LaTeX
it is nice because you can see your output as you type
and if you don't know the code for something, it has menus with icons
22:07
@robjohn OK
22:21
@Chris'ssis Heh... put a $(-1)^n$ in there and I can tell you right away. I wonder if I can use that result to get the non-alternating sum.
@robjohn Indeed. But no, you can't do that since it's of no help.
@Chris'ssis why is that?
@robjohn There is a trick to do ... I'll show you my way (just to find it since this is a real problem - many papers here).
22:36
@robjohn I think it's a really beautiful series. It was harder since I didn't give you the closed form.
@Chris'ssis I'll have to look at it later. I haven't finished looking at the series yet.
@robjohn OK
Yo @SanathDevalapurkar
@G.T.R I haven't. What's the problem?
@Chris'ssis In your method, do you compute $$\lim_{n\to\infty}\sum_{k=1}^n\frac{\log(k)}{k}-\frac12\log(n)^2$$ My answer seems to indicate it is needed.
22:52
@robjohn Yeap, it is needed. I don't see other way to do it without using this limit.
@Chris'ssis Does it have a closed form?
@SanathDevalapurkar I am reading you talks you posted in here
@robjohn mathworld.wolfram.com/StieltjesConstants.html These are those Stieltjes constants (by definition).
And I think algebraic geometry is rather algebra with a kick than geometry studied using algebraic techniques. =P
(well, both $\gamma$ and $\gamma_1$)
22:55
@Chris'ssis So that is the next term in $\zeta$ after the constant term of $\gamma$
Yeap.
@robjohn I think I saw some answers of yours using Stieltjes constant (or I'm wrong).
@Chris'ssis Then if $C$ is that constant... I get the answer $\frac{\pi^2}{12}-C-\frac{\gamma^2}{2}$
@Chris'ssis I don't think so...
I love math
It's so fun and I know it
@JasonMarsh There are two kinds of peoples in the world
@robjohn That's correct.
23:00
@Chris'ssis I can compute the partial sums of everything except the $\frac{\log(n)}{n}$ terms
I used to dominate a maths classroom in highschool and female maths teacher found it so attractive when I was solving Caculus questions.
$$\sum_{k=1}^n\frac{\gamma}{k}=\gamma H_n$$
And she gave me everything, because I am so hot when I am solving complicated mathemetics.
@robjohn Yeap
$$\sum_{k=1}^n\frac{H_k}{k}=\frac12\left(H_n^2+H_n^{(2)}\right)$$
@Chris'ssis So all I was missing was that limit.
23:05
Elementary puzzle problem : Explain the mathematical coincidence $\pi^e = e^\pi$ (i.e., show that it is not a coincidence)
Another flag, @robjohn?
@robjohn If one doesn't start on the correct track from the beginning, then one might face some difficult time with computing it.
@BalarkaSen flag?
@robjohn Oh, well. I thought... never mind.
@JasonMarsh I am not sure if I wanna know what that is.
@BalarkaSen eh? they are not equal...
@robjohn I meant $\approx$
Sorry.
23:09
because $\frac{\log(\pi)}{\pi}\approx\frac1e$?
@robjohn You can do better.
It's a puzzle, not a real problem, just as a note.
@BalarkaSen well the function $\frac{\log(x)}{x}$ reaches a maximum at $x=e$ (so it doesn't vary much near $x=e$) and $\pi$ is close to $e$
You have to find a good reason behind the phenomena, that's all.
@robjohn The function?
let him finish writing
@blue oh I didn't realize.
Apologies.
@robjohn Well, there's a much more obvious reason, I guess.
$\pi$ is not that close to $e$ =D
23:12
@BalarkaSen what reason are you thinking of? Note that $e^3\approx3^e$ even more closely
x^1/x shrinks to 1 very, very slowly
My reason : $2^4 = 4^2$
Yeah, I know it sounds lame. Well, it's a puzzle after all.
@BalarkaSen that is not a reason...
@robjohn $\pi \approx 4$ and $e \approx 2$.
there is no other $x$ so that $e^x=x^e$ other than $x=e$
@BalarkaSen why not $3^3=3^3$ and $e\approx3$ and $\pi\approx3$ is closer
23:15
@robjohn oh right.
probably that's a better reason.
@BalarkaSen I think the fact about the maximum of $\frac{\log(x)}{x}$ is better
yes. more precisely, $x^{1/x}$ has maximum at $x = e$
@BalarkaSen it's the same thing
yep.
i wonder why $\exp(\pi) \approx \pi + 20$ is called a mathematical coincidence
i guess it really shouldn't be hard to find an explanation, no?
gotta go shopping for the animals... BBL
@Chris'ssis nice problem :-)
23:19
@robjohn Yeah, I love it. :D
@blue so what did you think of my explanation?
about the galois group of $\pi$?
makes sense
@blue what's more, there is a rough way to do it : $\Bbb Z(\pi)$ is dense in $\Bbb R$ so galois group of $\Bbb Q(\pi)/\Bbb Q$ is "roughly" that of $\Bbb R/\Bbb Z$, and the deck transformation group is precisely $\pi_1(S^1) \cong \Bbb Z$. [note : this is highly non-official]
Heya @TedShifrin
hi @Balarka ... Your fever subsiding?
@TedShifrin somewhat.
i have thought of a way through that quaternion problem.
23:31
Well, when you're healthy, I want a good proof about $\mathcal Q$ :)
Oh?
no, there cannot be any quartic.
$ Q_8$ has no faithful rep to $S_n$ for $n \leq 7$
Hmmm, I wanted just a Galois theory argument, based on the fact that all the subgroups are normal.
This is a dummit-foote problem i worked out earlier.
You're the one who doesn't like groups. Don't give me representation theory.
@TedShifrin I did it using group theory =P
It's not rep theory. it's just basic group action.
23:32
Grumph.
Hehehe
they call an injective homo a faithful rep?
@blue yes.
bleh, a rep is a homo into a GL or U group
not true.
you can have a rep to a symmetric group too
23:34
yes, rep in the category of sets, instead of vector spaces
symmetric groups are much more natural than matrix groups.
@blue yes, yes.
@TedShifrin Our thinking never matches.
You've noticed this, @Balarka.
lately, yes.
When you say "blecccch" to anything geometric, it shouldn't come as a surprise.
blech, not belch, by the way.
23:36
I didn't say belch
Although it might be a good thing to do.
@Pedro: Congratulations to Argentina.
Argentina played horrible.
I don't watch.
Yeah, you're favourite is tennis.
23:37
Presumably @DanielF will be unilaterally victorious.
He doesn't watch, either.
I'm marking you down in English again, @Balarka. Go study.
well, i think there is a mathematician who played football. in the world cups too.
@TedShifrin your. typo.
LOL ... pay detention.
i am studying a lot these days.
Good.
Don't forget to have some friends, too.
@TedShifrin i have friends. but i usually do math with them in library in breaks,
23:39
Poor friends.
no, no. they are very interested.
You're infinitely more intense in math than I've ever been.
@TedShifrin What's that supposed to mean?
What I said.
bleh. i don't understand american expressions.
23:41
You know what "intense" means. It's not American.
oh, i misread.
nevermind.
@TedShifrin You've been less intense than me about math?
Redonkoulus.
Way less.
You're more intense as a 14-yr old than I was in college or grad school.
That may mean that you'll be the next superstar, or it may mean you should learn to relax and have a more well-rounded life.
@TedShifrin Well, in my defense, you can never guarantee whether i am a fluke or not.
=D
23:44
I expect we'll find out before I'm dead :D
if I can get good grades in my final year at highschool ...
well, actually i don't expect i'll sit on final year.
That might be a reasonable plan for you.
will target for some good uni after the secondary exam.
@TedShifrin Haven't seen Hippalectryon lately. What happened to him?
I haven't seen him in ages, @Balarka. I'm hoping it's just his computer that died.
@Studentmath
I worry about you and Ilan these days.
@TedShifrin Perhaps his computer died taking along him as well?
23:50
well, I think it burned his hand a few times.
seriously, he should have tried liquid hydrogen on the processor.
liquid H$_2$, huh?
yes. glad to know you recalled the notation.
I took a fair amount of chemistry in college, thank you.
oh boy.
r9m
r9m
23:53
Never seen lq. $H_2$ .. but seen liquid He ... that stuff is creepy -_-
hi @r9m
r9m
r9m
@TedShifrin hello :)
@r9m question : what's the formula of water? answer : HIJKLMNO
r9m
r9m
@BalarkaSen old -_- very old
droops ear
23:54
I haven't heard from @Ilan for quite some time, I guess he 'closes' weekend on left and right.. But I am just fine, I am rather north so I am safe(r) this round :)
Even from my distance, @Studentmath, it's very scary. I do think about you guys.
Thank you, means something to us!
Though we (and I) went thorugh Lebanon 2, that was true hell here.. and I was 12 or so, so really no need to worry about this - it's a game compared to that one
@TedShifrin The physics in our syllabus is darned hard.
physics is great when you know some math.
Just assumptions. Only assumptions. No proofs.
23:59
that's because they can't assume you know math.
See if you can find Kleppner and Kolenkow Mechanics.
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