Mathematics - 2014-09-23 (page 2 of 3)

Balarka Sen

15:00

@MatsGranvik Note that $$x^5 + x = \frac{x}{1/(1+x^4)} = \frac{x}{ 1 - x^4 + x^8 - x^{12} + x^{16} - x^{20} + x^{24} - x^{28} + \cdots}$$

Mats Granvik

I will do a numerical check.

Balarka Sen

Try inverting that.

@MatsGranvik No, no, use that^ as an input

It's of the form x/(1 + blah*x + blah*x^2 + ...) like you wanted

Mats Granvik

ok

{1, 0, 0, 0, -1, 0, 0, 0, 5, 0, 0, 0, -35, 0, 0, 0, 285}

Balarka Sen

Yes, that works.

Congratulations.

Mats Granvik

Thanks.

Balarka Sen

15:05

Funny though. I am interested in seeing your technique.

Mats Granvik

It is not entirely new.

Balarka Sen

Oh?

Mats Granvik

There is something called the INVERT transform, written with large letters in the OEIS. This algorithm is a generalization of the invert transform, applied infinitely many times.

Balarka Sen

Link?

Mats Granvik

oeis.org/transforms.html

Balarka Sen

15:08

Heya @anon

anon

hi

Balarka Sen

nvm about my previous question, it was silly.

i was confused by the notations

interesting @Mats. I am going to implement that in my machine, I think.

Studentmath

@Balarka!

Balarka Sen

@Studentmath!

Nick

@BalarkaSen!

@Studentmath!

Balarka Sen

15:16

@Nick!

Studentmath

@Nick!

Nick

@anon!

anon

ho hum.

Nick

@BalarkaSen: I have finally digested what you said to me about integration constants. Thank you for that. I realized stuff after about 93 problems.

Huy

For a relative max/min at $x_0$ of a function $f: \mathbb{D} \to \mathbb{R}$, $f'(x_0)$ AND a change of sign of $f'(x)$ at $x_0$ is necessary and sufficient, right?

Nick

15:17

@Huy: Yes

Studentmath

It seems like I won't be able to advance my analysis in my uni-studies before graduating anymore. It's stuck on calculus+multi.var calculus, without real epsilon-delta proofs (and soon set-point topology but that doesn't count in). Any suggested books one can read to advance up?

Hopefully not too boring, yet rigirious and stuff.

Huy

@Nick: do you by any change remember if there is another sufficient and necessary condition? I remember the second derivative being strictly positive/negative being sufficient, but not necessary.

Nick

@Huy: sorry, I only know enough monotonicity to graph basic functions. I don't know any textbook points.

Balarka Sen

horrible internet connection

Nick

@BalarkaSen: get Idea, Sirji

Balarka Sen

15:21

haha

Nick

Ermagard Ermagard Ermagrad, i forgot. I have a huge boolean algebra test tommorow and I don't know potatoes about K-Maps!

What do I do. What do I do?

Studentmath

Solve questions with solutions about K-Maps

Balarka Sen

@Huy $f$ must be differentiable at $x_0$ for one.

Huy

@BalarkaSen: Thank you very much for your information.

The Game

@Chris'ssis Cleo is TF ??

Balarka Sen

15:24

@Huy =P

glad to be of no help

Chris's sis

@TheGame I was inclined to believe so.

Nick

@Studentmath: I accidently burnt my textbook. Any good links!

The Game

@Chris'ssis Why ?

Studentmath

@Nick you accidently burnt your textbook?

Balarka Sen

Ah, @TheGame

The Game

15:26

5 hours ago, by Chris's sis

@robjohn I have an indirect proof that Cleo is Tunk-Fey ..

Balarka Sen

What book, @Studentmath?

Nick

@Studentmath: In a huge dramatic gas cylinder explosion.. which is irrelevant, right now. Because I need to know how to use K-Maps in half an hour and all that google is giving me is gibberish.

Studentmath

@Balarka suggest me books!

Will Hunting

@Studentmath That is my job, lol.

Chris's sis

@TheGame I think that one was a proof done in a hurry. However, I think Cleo might be Tunk-Fey, or at least someone close to him, her.

Studentmath

15:27

@Nick a huge dramatic cylinder explosion is never irrelevant. But don't you have some course-website with tests? I will give it a google-search try.

@Willhunting @Balarka I need to advance up my analysis. I had calculus and multi.var calculus, not epsilon-delta proofs. I skimmed through Rudin's honour's calculus too. Anyhow, rather something not too boring as I will have to force myself to find time to read and practice it, also something rigirious =.

The Game

@Chris'ssis But, why do you think so ?

Chris's sis

@TheGame by the way, did you see this answer? I got the real generating function of $$\sum_{n=1}^\infty \frac{H_nx^n}{n^3}$$ The one in the proof is wrong. math.stackexchange.com/questions/909228/…

Will Hunting

@Studentmath Then just read the whole of Rudin thoroughly.

The Game

@Chris'ssis no. I didn't

Studentmath

Which one of Rudin?

Nick

15:29

@Studentmath: It was a year ago, burnt down a relative's house. Charred up a lot of my novels and textbooks. No one got hurt. Except my relative who lost a large chunk of his house and property.

Studentmath

@Nick hrmpf kvvayusenanagar.edu.in/userfiles/file/BOOLEAN.pdf got 5 questions on k-maps. Not sure if they are relelvant level-wise.

The Game

@Chris'ssis Hence your suspicion ?

Studentmath

@Nick eecg.utoronto.ca/~jayar/ece241_06F/solved4.pdf This looks much better

Balarka Sen

@Student Rudin.

Principles of mathematical analysis

Studentmath

Thanks @Will @Balarka

Will Hunting

15:32

@Studentmath Anytime you need a book recomm, just ask me!

Nick

@Studentmath: Holy crap. You're batman! Thank you very very very much!

Balarka Sen

@Studentmath jasper will only give you hipster books.

Studentmath

@Nick glad to be of help :P

Will Hunting

Don't forget to thank me when you win the Fields medal, lol.

Studentmath

@Will @Balarka Rudin's hipster?

Will Hunting

15:34

@Studentmath I don't know what he means by hipster, so no comments.

Balarka Sen

oh by the way @Studentmath @Nick.

dis

Nick

@Studentmath: He'll also give you nice educational books. Actually, he won't give it to you. You have to sneak into house, take it and leave an IOU and hope he won't notice until you finish reading it.

Studentmath

@Balarka I wonder if searching Grrrh will have similliar result

Chris's sis

@TheGame You should note that Tunk-Fey is a specialist in handling the polylogarithm. On the other hand, I noted that Cleo answered a lot of questions where handling the polylogarithm, generalized harmonic numbers wisely you get great results.

The Game

@Chris'ssis They made the same mistake, right ?

@Chris'ssis Why don't you post the correct answer ?

Nick

15:36

@BalarkaSen: I bet you can't find the last time I said misbehaving in this room

The Game

@Nick You just did

Balarka Sen

you already said it, @Nick

Nick

The n-1 th time, genius.

Chris's sis

@TheGame Not really. I wrongly noted something. Only Tunk-Fey made a mistake.

The Game

@Nick The n-1th time what ?

Balarka Sen

15:38

OK, I need to leave now. my internet connection is too disturbing.

Nick

@TheGame: I liked Hippa better

Studentmath

brb

The Game

@Nick But now you're gonna lose every day :)

@Chris'ssis Doesn't he say that his answer matches Cleo's ?

Nick

@TheGame: The n-1 th time I said the m word, if you have just witnessed the nth iteration.

The Game

@Nick Aww you didn't fall for it :P

Nick

15:40

@TheGame: I paused and I thought.

Chris's sis

@TheGame Initially he wrote $$\color{purple}{\frac{7\pi^4}{720}+\frac{\ln^42}{24}-\frac{\ln2} 8 \zeta(3) + \operatorname{Li}_4\left(\frac12\right)}$$ (if I'm not wrong)

Nick

Now, let me go screw with Karnaugh.

The Game

@Chris'ssis Indeed

Chris's sis

@TheGame I think he had a great luck to answer that question ...

The Game

Hehe

Chris's sis

15:42

@TheGame Do you know why? Look at that relation in $(2)$. The value that remains out due to a wrong application of the variable change is then recovered by I don't know what means.

The Game

Nope. I'm not good enough :)

Let's compare with the old one

Chris's sis

@TheGame the generating function there is wrong, that's clear.

The Game

@Chris'ssis $(3)$ is the same

Chris's sis

@TheGame Yeap, it's wrong.

The Game

Wait

Let me find where the difference comes

What I'm saying is that up to (3), the proof is the same for different results

Chris's sis

15:48

@TheGame Hold on a second to explain you something ...

The Game

@Chris'ssis The only difference I see is the computation for $x=1/2$

Chris's sis

That nice difference, that is $\pi^4/120$, you only get for $x=1/2$ since there an interesting thing that happens and one can make use of that invoked reflection formula.

@TheGame The problem appear from $(2)$. The rest of the work is not safe.

@TheGame For instance, if you check $(3)$ for $x=1/3$, you get different numerical results.

The Game

@Chris'ssis Where exactly is the problem ?

What line in (2)

Chris's sis

(I mean the right side is different from the left side)

The Game

What line is the first wrong one ?

Chris's sis

15:53

$$\begin{align}
\color{green}{\int\frac{\operatorname{Li}_3(1-x)}x\ dx}&=\operatorname{Li}_3(1-x)\ln x+\int\frac{\ln x\operatorname{Li}_2(1-x)}{1-x}\ dx\qquad x\mapsto1-x\\
&=\operatorname{Li}_3(1-x)\ln x-\color{blue}{\int\frac{\ln (1-x)\operatorname{Li}_2(x)}{x}\ dx}.\tag2
\end{align}$$

@TheGame I refer at that variable change.

The Game

What are the rules for variable changes on indefinite integrals ?

If there were bounds, they would change too

Chris's sis

@TheGame If you like this way, then you can use it too in your problems. :-)

The Game

Uh ? What do you mean ?

Chris's sis

@TheGame Did you read the comments below (referring to that answer)? Just take a look there.

The Game

@Chris'ssis Ok. In the meantime, can you answer my question about the var change ?

'@ SuperAbound I don't have a rigorous explanation but I think the constant of integration will adjust the final result.'

WAAAT ???

That's not maths -__- that's cooking

Chris's sis

15:58

@TheGame that was my point ...

The Game

Even I, who do not know much about this stuff, saw that -__-

@Chris'ssis I believe you have found a good way to get the solution ?

Chris's sis

@TheGame Sure, I have the correct generating function.

The Game

@Chris'ssis How do you do it ? (or, is it secret ?)

Chris's sis

@TheGame kind of ...

The Game

Ah :/

For the book ?

Chris's sis

16:01

:D

@TheGame You know what? I'm sure many here would say I just lie.

The Game

@Chris'ssis Btw that might be a weird question, but do you have any idea on the book's price ? For instance, @Ted 's book are really expensive because of the publishers

@Chris'ssis Nono you've already solved way harder stuff

That is beautiful

Chris's sis

@TheGame I need to use one more formula to make it more beautiful.

(working on it)

The Game

@Alizter Hullo !

You just lost

robjohn

@Chris'ssis where does Tunk-Fey's computation go wrong?

The Game

14 mins ago, by Chris's sis

$$\begin{align}
\color{green}{\int\frac{\operatorname{Li}_3(1-x)}x\ dx}&=\operatorname{Li}_3(1-x)\ln x+\int\frac{\ln x\operatorname{Li}_2(1-x)}{1-x}\ dx\qquad x\mapsto1-x\\
&=\operatorname{Li}_3(1-x)\ln x-\color{blue}{\int\frac{\ln (1-x)\operatorname{Li}_2(x)}{x}\ dx}.\tag2
\end{align}$$

Alizter

16:07

hi @hippa

Chris's sis

@robjohn As I said above, from $(2)$ on.

@TheGame maybe my math is criticized sometimes, but with my math I get great results. And soon I get this one

The Game

@Chris'ssis By who ?

Chris's sis

$$\sum_{n=1}^\infty \frac{H_nx^n}{n^4}$$

@TheGame There are always some. :-)

@TheGame Oooooo, I should ask a question on main.

The Game

What one ?

~~maybe I can answer it!~~ uh no

Chris's sis

@TheGame $$\sum_{n=1}^\infty \frac{H_n}{2^n n^4}$$

The Game

16:18

Haha

They'll just think it's a ripoff of the previous

Chris's sis

They'll make use of the already known generating function (divide by $x$ and integrate again):-))))))))))

The Game

Hehe

Then ask $\displaystyle\sum_{n=1}^\infty \frac{H_n}{3^n n^4}$ and by using $x=1/3$ they'll be wrong :D

Will Hunting

My life is complete. I have gotten the 16 books that I need to study. 12 math, 1 LaTeX, 1 English, 1 French, 1 German.

The Game

@WillHunting Then it's not complete, you still have to study them

@WillHunting Burn the German one

Will Hunting

Since I only mentioned my 12 holy books, let me now mention all of my 16 holy books...

The Game

16:23

$12=16$. Q.E.D.

Balarka Sen

Spare us!

"Since I only mentioned" only?

Best. Comment. Ever.

Will Hunting

Marsden and Weinstein: Calculus I, Calculus II, Calculus III
Cohn: Classic Algebra, Basic Algebra, Further Algebra
Rudin: Mathematical Analysis, Real and Complex Analysis, Functional Analysis
Lee: Topological Manifolds, Smooth Manifolds, Riemannian Manifolds
Kopka and Daly: Guide to LaTeX
Living Language English Complete Edition
Living Language French Complete Edition
Living Language German Complete Edition

Someone now please star my 16 holy books. They will prepare me for the GRE general paper, the GRE math paper, the PhD qualifying exams, and the foreign language exams.

The Game

Why would one star them ?

I don't have any of those exams in my country

Will Hunting

@TheGame Because it would be a good set to use for anyone intending to do a math PhD in the US or Canada?

Balarka Sen

I won't star anymore.

The Game

16:27

@WillHunting We don't need to star them

The chat log will be there if we need them

Will Hunting

@TheGame OK. =(

The Game

And, who buys a book on LaTeX -__-

Will Hunting

I have taken a few years to come up with this list, lol.

Now anyone who reads the transcript only has to follow it, lol.

Hey @ParthKohli

Mats Granvik

@BalarkaSen
http://math.stackexchange.com/questions/584866/algorithm-for-reversion-of-power-series

I put the reversion algorithm there.

Parth Kohli

@WillHunting Good evening.

Will Hunting

16:36

@ParthKohli Please admire my list of 16 holy books above, lol.

Chris's sis

@TheGame I don't refer to myself now, but I only wanna say one needs to be highly skillful to deal with those sums, otherwise you have no chance.

I work for some hours on it.

The Game

@Chris'ssis I know :)

The Game

16:53

afk

Chris's sis

Go jogging, I need to free my mind from all thoughts. :-)

bbl

The Game

17:11

back

user60887

Does anyone know what I can look into for possible research topics that ties together probability and some aspect of gambling like poker?

Will Hunting

Hey @nablablah

The Game

@user60887 blackjack theory

The Game

17:36

@nablablah gyazo.com/0ff2ac07a6dec209123a59b12421226b :C

Chris's sis

18:10

@TheGame there is something to fix in my generating function formula. Not a big problem.

Done

The Game

@Chris'ssis Show me :D

Chris's sis

@TheGame Let's choose $x=1/3$, or do you want another value?

The Game

For any $x$ :D

The general one

Chris's sis

(1/72)*(4*Pi^4 - 12*I*Pi*Log[3]^3 + 3*Pi^2*(Log[2]^2 + 10*Log[3]^2) +
3*(5*Log[2]^4 - 5*Log[3]^4 +
6*Log[2]^2*(PolyLog[2, 1/4] - 2*PolyLog[2, 2/3]) +
24*Log[3]*PolyLog[3, 1/3] +
6*Log[2]*(PolyLog[3, 1/4] + 4*PolyLog[3, 2/3]) +
24*(PolyLog[4, -(1/2)] - PolyLog[4, 2/3] - 2*PolyLog[4, 3]) -
3*Log[839808]*Zeta[3]))

Will Hunting

OMG

The Game

18:20

@Chris'ssis Uh ugly in mathematica :)

Chris's sis

For $x=1/4$?

(7*Pi^4)/360 + (1/8)*Log[4/3]^4 - Log[4/3]^3*Log[2] -
Log[4]^4/24 + (1/2)*Log[3]^2*PolyLog[2, -(1/3)] + (1/2)*Log[4]^2*
PolyLog[2, 1/4] +
(1/2)*PolyLog[2, 1/4]^2 + (1/4)*
Log[4/3]^2*(Log[4]^2 - 2*PolyLog[2, 3/4]) - (1/2)*
PolyLog[2, 3/4]^2 +
(1/6)*Pi^2*(Log[4/3]*Log[4] + Log[4]^2 + PolyLog[2, 3/4]) +
Log[3]*PolyLog[3, -(1/3)] + Log[4/3]*PolyLog[3, 1/4] +
Log[3]*PolyLog[3, 1/4] +
Log[3]*PolyLog[3, 3/4] + PolyLog[4, -(1/3)] + PolyLog[4, 1/4] -
PolyLog[4, 3/4] - PolyLog[4, 4] - Log[4]*Zeta[3]

Oh, let me try another one ...

The Game

I mean, it looks so much better in LaTeX :D

Will Hunting

It looks cool in mathematica.

marcelolpjunior

Hi

I will do a search on my university course in mathematics, there are 110 students in the course, and how do I scale my sample?

The research seeks to explain the socioeconomic reality of college

nullgeppetto

Hi all! A quick stat question: If $\mathbf{e}\sim N(0,\sigma I_n)$ what is the expected value of the product $(\mathbf{u}\cdot\mathbf{e})(\mathbf{v}\cdot\mathbf{e})$, where $\mathbf{u}$, $\mathbf{v}$ are $n$-dimensional vectors (not random). Please help! Thanks a lot!

Chris's sis

18:29

Where is @BalarkaSen to see the polylog and the polygamma at the same table?

$$\sum_{n=1}^{\infty} (-1)^n \frac{H_{2n}}{n^3}=$$

(1/960)*(-((711*Pi^4)/4) +
10*Pi^3*(128*ArcTan[2 + I] - 29*I*Log[2]) + 530*Pi^2*Log[2]^2 -
10*(6*Log[2]^4 - I*PolyGamma[3, 1/4] + I*PolyGamma[3, 3/4] -
192*(Log[4]*(PolyLog[3, 1/2 - I/2] + PolyLog[3, 1 - I]) +
4*(PolyLog[4, 1/2 - I/2] - PolyLog[4, 1 - I]))) +
120*I*Pi*(3*Log[2]^3 -
48*(PolyLog[3, 1/2 - I/2] + PolyLog[3, 1 - I]) + 35*Zeta[3]))

The Game

That is disgustingly beautiful :D

Carpediem

18:44

I have a question on topology

Chris's sis

@TheGame Some time ago you showed me this math.stackexchange.com/questions/765198/… amd told me I'm not there ...

Carpediem

Can someone help me ?

The Game

Yeah @Chris'ssis

Chris's sis

@TheGame Yeah, I'm not, and I don't wanna ever be there. ;) (this doesn't mean I cannot do nice things)

The Game

@Carpediem Ask your question first :)

@Chris'ssis Why ?

Carpediem

18:46

@TheGame Ok.. wait

I have two topologies

$\mathcal{T}_3=$ the topology having as basis all open rays $(- \infty, a)$ $\mathcal{T}_4=$ the topology having as basis all open intervals $(a,b)$ and all one-point sets $\{c\}$, such that $c \in \mathbb{Q}$

I am having trouble finding the closure of $A=(2,\sqrt{7})$ in each of these topologies

I think in $\mathcal{T}_4, \bar{A}=(2,\sqrt{7}]$

The Game

Ah not my field sorry. Maybe someone else in the chat knows.

MLM

How do you approach and understand this type of question?

I do not get how you can get the gradient (delta f) from multiplying 19 (max) by the unit vector of the first. What makes the max special?

Daniel Fischer

@Carpediem You're right for $\mathcal{T}_4$. You should be able to say why you're right, though. For $\mathcal{T}_3$, consider $x < 2$ and $x > \sqrt{7}$. Which has neighbourhoods not intersecting the interval?

@MLM The gradient always points in the direction of steepest growth. So if the directional derivative is largest in direction $v$, then the gradient is a multiple of $v$.

MLM

19:01

@DanielFischer ahh this "gradient always points in the direction of steepest growth" really cleared it up

Thank you

The Game

@Chris'ssis So ?

Chris's sis

@TheGame I only do math for fun, not for being told I'm a guru or something like that. ;)

The Game

@Chris'ssis That doesnt mean you have to refuse being considered good :)

worshsip the guru @Chris'ssis

3

Chris's sis

@TheGame lolll :D

The Game

@DanielFischer Do you remember how one shows that any positive polynomial in $\mathbb{R}[X]$ is the sum of two polynomials squared of $\mathbb{R}[X]$ ?

If it's positive then it can be expressd $P=a\displaystyle\prod_{k=0}^p(x^2-2\Re(b)+|b|^2)$

I think there's some Laplace Identity to convert $A^2+B^2$ into something useful, but I can't remember for sure

@Chris'ssis , do you know ?

Huy

19:17

@TheGame: I recall using $(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$ for that proof.

Chris's sis

@Huy Exactly. I was trying to remember it. :-)

Huy

Didn't know it had a name though. :)

Chris's sis

@TheGame see @Huy's answer

@Huy There was a nice question given on some local contest here that used the identity above.

Huy

@Chris'ssis: I don't really like the typical kinds of contests, but what question was it?

Chris's sis

@Huy I have it here on some paper. Let me find it.

The Game

19:21

But here I don't have anything in the form $(a^2-b^2)(c^2+d^2)$ do I ?

Huy

@TheGame: I think we expressed the polynomial in a different way.

The Game

@Huy I have $P=a\displaystyle\prod_{k=0}^{2p}(x-b_k)$, where all the roots $b_k$ have a conjugate root

Huy

@TheGame: That's not the factorisation into irreducibles yet, right?

The Game

Hence my expression above (it was supposed to be $b_k$ not $b$)

It's just the expression using roots

Huy

I think you can express it with irreducibles and then you can apply the identity.

ccorn

19:24

This question seems interesting to me. I can come up with ${}_2F_1$-based expressions for $E_2$ that contain three ${}_2F_1$s, but there might be something simpler.

Huy

PS: Apparently it's Fibonacci's identity. en.wikipedia.org/wiki/Brahmagupta%E2%80%93Fibonacci_identity

The Game

@Huy The above form is already with irreductible polynomials

They all have degree $1$

Chris's sis

@Huy

Prove that for any $m,n\in \mathbb{N}$, we have $x, y \in \mathbb{N}$ such that

$$(m^4-m^2+1)(n^4-n^2+1)(m^4+3m^2+1)(n^4+3n^2+1)=x^2+y^2$$

ccorn

@Chris'ssis Each factor can be written as a sum of two squares. Euler takes over.

The Game

Euler wins

Chris's sis

19:32

@ccorn Or we can use Lagrange's identity ...

The Game

Ye even easier

Lagrange 2 - 1 Euler

It doesn't help with my problem though :)

Alizter

Tunk-Fey = Cleo. That explains a lot.

Carpediem

@DanielFischer

The Game

Oh Balarka sen-pai is there

Balarka Sen

@Chris'ssis Beh easy.

Carpediem

19:36

Still not sure how to find in $\mathcal{t}_4$

Chris's sis

@BalarkaSen It was given on some math contest, and some kids were really in trouble with it.

Balarka Sen

Haha, that's because they never Eulered.

The Game

@BalarkaSen Help me on my problem ? I' just missing one step

Balarka Sen

what problem?

The Game

24 mins ago, by The Game

@DanielFischer Do you remember how one shows that any positive polynomial in $\mathbb{R}[X]$ is the sum of two polynomials squared of $\mathbb{R}[X]$ ?

21 mins ago, by Huy

@TheGame: I recall using $(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$ for that proof.

18 mins ago, by The Game

But here I don't have anything in the form $(a^2-b^2)(c^2+d^2)$ do I ?

There

Balarka Sen

19:40

Yes, that's a famous problem, IIRC.

The Game

I know

But i can't find that last step

Balarka Sen

I don't think only that identity is involved in the proof.

Let me recall it.

The Game

27 mins ago, by The Game

If it's positive then it can be expressd $P=a\displaystyle\prod_{k=0}^p(x^2-2\Re(b)+|b|^2)$

Balarka Sen

Wait a sec, it's false as you have stated it @Hippa

The Game

Supposed to be $b_k$

Balarka Sen

19:43

$-1 \in \Bbb R[x]$ cannot be written as sum of squares, for example.

The Game

And ?

I didn't say that only positives one could

I just wanna show that all positives ones do

Positive

By that I mean $P(X)\geq0,\forall X$

Balarka Sen

Ah you mentioned positive polynomials.

The Game

Oh wait

I just realized It can have real roots too

Balarka Sen

I have no idea what you are talking about (O_o)/

The Game

So $P=a\displaystyle\prod_{k=0}^q(x-a_k)\prod_{k=0}^p(x^2-2\Re(b_k)+|b_k|^2)$

Balarka Sen

19:45

Unfortunately I have to go. Can't think about that yet.

The Game

$a_k$ are the real roots

$b_k$ the complex roots, conjugated

Balarka Sen

Search for Hilberts 17th problem in one variable, maybe?

The Game

@BalarkaSen Mh ok

Balarka Sen

Anyways, got to go

The Game

I'll ask on main

Alizter

19:46

I managed to get 12/19 in a test I fell asleep in in maths

still highest in the class

Balarka Sen

cool

i got 3 less than the highest this time.

bleh

rehband

Good evening!

Alizter

@BalarkaSen tests never mean anything

no mathematician solved an important problem under pressure

Balarka Sen

i know

Alizter

$\pm$ a few pressures

Balarka Sen

19:48

i was actually not under pressure though LOL

i had a fever and were on the teachers room in a comfortable and nice and peaceful atmosphere

Alizter

@BalarkaSen Would you like a hard elementary algebra problem?

Balarka Sen

i won't like anything now since i got to go.

byes.

Alizter

4

see if anyone can solve this

Ice Boy

@Alizter by elementary algebra do you mean the algebra taught in elementary school?

Alizter

@IceBoy pre uni

Ice Boy

19:56

icic

Balarka Sen

@Alizter That's just from MHB

Alizter

@BalarkaSen I got it from somewhere else

these problems usually circulate

Balarka Sen

Aha. Give me the link.

It'd be helpful for the internet spy thingy I am doing right now.

Huy

@Alizter: "no mathematician solved an important problem under pressure" What about Dantzig?

Alizter

20 mins ago, by Alizter

$\pm$ a few pressures

Huy

20:09

I see. So you withdraw your previous statement.

cxseven

that's just some modus ponens and modus tollens reasoning infants are born with

Chris's sis

@TheGame

The Game

Wow

Chris's sis

@TheGame If you kill the imaginary part, you get nicer forms.

cxseven

@Alizter there seem to be either no solutions or infinite. is the smallest wanted or something?

Alizter

20:41

@cxseven There definitely is a solution

cxseven

@Alizter if a,b,c,d,e,f solves the equation then ak,bk^2,ck^4,dk,ek^2,fk^4 also does

Alizter

@cxseven The answer is 64 if you must know

and also they are all equal

Khallil

Can't you just hammer the algebra out, @Alizter?

cxseven

@Alizter 64*k^14 is another solution for abcdef

Alizter

@Khallil yes. That was the answer

Khallil

20:46

Square, group the appropriate terms, square, rinse and repeat.

cxseven

a von Neumann answer

Khallil

I'll save it to my desktop and try it when I get some time. Thanks for the problem, @Alizter. ^_^

cxseven

i think my statement is verifiable without even doing any of that

Alizter

@cxseven not my problem. Literally I did not create it.

cxseven

then whoever did has a problem

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$Mathematics$ Mathematics