Mathematics - 2017-02-19 (page 5 of 7)

Alessandro Codenotti

13:01

Connected components in $\Bbb Q$ are the singletons

It also is a counterxample to the plausible sounding statement that connected components are clopen

(Which is true for spaces with a finite number of them)

@Balarka are you still here?

Kenshin

Hello

is anyone here good with latex?

Astyx

Maybe Balarka is actually sleeping ?! :o

Paul Plummer

13:18

Maybe... Or he could just be eating or something, I think it is about that time there

@Kenshin Generally you just ask your actual question here

Kenshin

@PaulPlummer do you know a good latex editor that can be used to create pdf's with latex?

Paul Plummer

Have you tried google, basically every editor does that

Personally I use Kile

user84215

hello

user84215

is there anybody?

user84215

is there any better place to discuss math?

user84215

13:29

where are you?

DHMO

@aminliverpool just ask; don't ask to ask

@Kenshin TeXstudio

user84215

is there any better place to discuss math ?

Mats Granvik

brilliant.org

Paul Plummer

No this is the pinnacle of places to discuss math,

DHMO

@aminliverpool depends on which type of math

Kenshin

13:33

@DHMO thanks i'll give that one a go

DHMO

@Semiclassical hi

Mats Granvik

Can you do addition, the white asked.
What is:

user84215

You cannot type mathematics well. And members are not active enough

Mats Granvik

1=?
1+1=?
1+1+1=?

DHMO

@aminliverpool learn to use latex. It's useful.

Also you haven't told me which type of math

Paul Plummer

13:37

Maybe if you actually started talking about math, someone would be interested in what you wanted to discuss....

user84215

I mean advanced math. the formulas dont appear well.

Mats Granvik

$\mu(n) = -{\sum_{d|n}}_\limits{d<n} \mu(d)$

DHMO

@aminliverpool "advanced" math is quite broad

Paul Plummer

Look at the side bar, there is a link to get latex to render here, just follow the instruction

Smit

Hey, I an back.. or i wasnt gone... What is the height of a binary tree? is it log(n+2) / log2 and take the ceiling of it?

user84215

13:39

why dont formulas appear like in main math stack exchange?

Smit

@aminliverpool because it chat! ahaha!

DHMO

@aminliverpool because you haven't installed latex in chat

read the chat description

Mats Granvik

@aminliverpool because you need to save a certain link as a bookmark, then click it every time you enter chat.

user84215

How can I install latex in chat?

DHMO

@aminliverpool Read the chat description.

Mats Granvik

13:41

@aminliverpool go to: math.ucla.edu/~robjohn/math/mathjax.html

user84215

thank you. my problem is resolved

user84215

Can I ask set theory question here? the set theory room is not active.

DHMO

@aminliverpool Yes.

I've said that 15 minutes ago

15 mins ago, by DHMO

@aminliverpool just ask; don't ask to ask

user84215

speak about examples of uncountable sets which don have any perfect subset.

DHMO

depends on the topology

Paul Plummer

13:49

take an uncountable set with the discrete topology

Semiclassical

hi chat

user84215

I mean in real numbers with ordinary topology.

Alessandro Codenotti

The more I read about it the weirder the relationship between meagre sets and nullsets becomes

DHMO

@aminliverpool subset of $\Bbb R$ under usual topology having no perfect subset?

user84215

uncountable one

s.harp

13:51

should be impossible

user84215

prove it.

s.harp

or need some negation of choice shennanigans

user84215

suppose we have CH

Paul Plummer

You don't need some negation of choice, if the continuum is not $\aleph_1$ and the reals contain a subset of cardinality $\aleph_1$ then that would be an example

Alessandro Codenotti

Can't you have perfect subsets of $\Bbb R$ of cardinality $\aleph_1$ if CH is false?

Paul Plummer

13:54

No, perfect subsets of the reals always have cardinality of continuum

user84215

suppose CH

Alessandro Codenotti

Interesting, how do you show that? I can show that they must have cardinality $>\aleph_0$

s.harp

You want them to be perfect in $\Bbb R$ and not in the subset topology of the subset you are considering?

user84215

excuse me dont suppose CH, instead assume axiom of choice

Paul Plummer

The argument is basically the same as proving the cantor set always has cardinality continuum, a diagonlization

user84215

13:56

please bring example

Paul Plummer

Examples of what? Are you trying to have a conversation or are you a vampire?

4

s.harp

Do you want them to be perfect in the topology of $\Bbb R$ or perfect in the subset topology?

Paul Plummer

I did assume choice and I didn't suppose CH @aminliverpool

user84215

in topology of R

Alessandro Codenotti

@PaulPlummer Ah, right, nowhere dense perfect subsets of $\Bbb R$ are homeomorphic to the Cantor set after all (and those not nowhere dense obviously have cardinality $\mathfrak{c}$)

s.harp

13:58

intuition says the closed subsets of $\Bbb R-\Bbb Q$ are basically discrete + discretlely spaced accumulation points

Alessandro Codenotti

I'm missing a compact probably in my previous message

Astyx

What's a perfect subset ?

Alessandro Codenotti

a closed set with no isolated points

DHMO

Perfect set

In mathematics, in the field of topology, a perfect set is a closed set with no isolated points and a perfect space is any topological space with no isolated points. In such spaces, every point can be approximated arbitrarily well by other points: given any point and any topological neighborhood of the point, there is another point within the neighborhood. The term perfect space is also used, incompatibly, to refer to other properties of a topological space, such as being a Gδ space. Context is required to determine which meaning is intended. In this article, a space which is not perfect will be...

Astyx

Thanks

Alessandro Codenotti

14:01

$[0,1]$ is the obvious example, the cantor set is the not so obvious example

@Astyx a fun question Balarka asked me a while back: are there perfect subsets of $\Bbb R$ containing no rationals?

DHMO

@AlessandroCodenotti $\Bbb R \setminus \Bbb Q$?

Smit

Repost: What is the height of a binary tree? is it log(n+2) / log2 and take the ceiling of it?

Astyx

Since my intuition says no, I'd bet on yes

Alessandro Codenotti

@DHMO not closed

Astyx

Well there is obviously the empty set ?

But I guess that's not the question

Paul Plummer

14:04

Yah @AlessandroCodenotti Although you can do a direct argument, find two closed disjoint intervals which contain things, and in those find two closed disjoint intervals

Alessandro Codenotti

@Astyx yeah, nonempty is more interesting

@PaulPlummer Right, makes sense

Astyx

@Smit Depends on your tree

DHMO

@AlessandroCodenotti that's mind-boggling... I'm still thinking

Astyx

You could remove the rationnals one by one using the théroème des fermés emboités of which I do not know the english name

Alessandro Codenotti

@Astyx I believe this is usually called Cantor's lemma

Astyx

14:11

I'm not sure ... It states that if you have a sequence of decreasing (for inclusion) closed sets, the limit is a closed set

Alessandro Codenotti

Cantor's intersection theorem apparently

Smit

@Astyx It is binary tree with 256 records at its internal nodes, what is the maximum comparisons needed in order to find a existing records in the tree?

Astyx

Oh yes you need it to be compact of course

Alessandro Codenotti

$\text{diam}(F_n)\to0$ is enough for complete metric spaces and closed $F_n$, which is the version in the French wiki (it's also in the English wiki, you need to scroll a bit)

Astyx

@Smit Is it a complete ordered tree ? If so I'd say $\log_2{256} = 8$ or maybe 9 depending on what you want exactly

@Alessandro Yep that's it, thanks :)

Smit

14:14

@Astyx they haven't mention anything.

Astyx

They have

Smit

oh yeah... misread it!

Astyx

"A binary search tree" implies alot of things

DHMO

@AlessandroCodenotti So it is a yes or no? (Just tell me this)

Smit

So is it 9 or 8?

Because we take the ceiling of the log value right? @Astyx

Alessandro Codenotti

14:15

@DHMO what exactly is a yes or no?

DHMO

@AlessandroCodenotti is there a perfect subset of R containing no rationals

Zach Hauk

good morning math.se

Alessandro Codenotti

@DHMO yes

hi @zach

Astyx

Depends what you mean by finding. If you know the element you are searching for is in the tree, then it's 8, else it's 9

Yes, here the ceiling is the same as the log itself since $256= 2^8$ @Smit

DHMO

@AlessandroCodenotti I'm still mind-boggled... and still thinking

Astyx

14:17

Hi @Zach, how are you ?

Zach Hauk

tired

how about you?

Astyx

Well go to sleep instead of procrastinating on this chat :p

I'm fine for my part

user84215

I am going to mix up. it is better to separate questions.

Zach Hauk

I just woke up

satyatech

Hi

Astyx

14:19

@Smit Try and convince yourself as to why what I said is true (if it is, I might even be mistaken :p)

Zach Hauk

i didn't have much sleep though.

user84215

Is there any place to chat privately?

Astyx

You can create chatrooms by clicking on usernames @aminliverpool

I have to go, I'll probably be back

Have a nice day everyone

Zach Hauk

alright, you too

user84215

I also want to go. Goddbye.

Sha Vuklia

14:26

Hi guys. I would like to show that for any non-negative sequence $(a_n)$ with limit $a\in\mathbb R$, it holds that $a_n^{1/k}\to a^{1/k}$, for any $k\in\mathbb N$. So I need to show that for each $\epsilon>0$, there is a $N$, such that for all n>N, it holds that $|a_n^{1/k}-a^{1/k}|<\epsilon$.

I was thinking of factoring out $(a_n^{1/k}-a^{1/k})$, just like $(a^n-b^n)$ can be factored out. Can I use something like this: $(a_n^{1/k}-a^{1/k})=(a-b)(a^{-\frac{k-1}{k}}-b^{-\frac{2k-1}{k}}-...-?)$. I'm a bit confused because of all the fractions, so I'm not sure if this could work out?

LeGrandDODOM

@ShaVuklia continuity hasn't been taught yet ?

Sha Vuklia

Uhm, yes it has been. So I can use that?

Alessandro Codenotti

Just as I was getting convinced that null sets and meager sets are quite orthogonal notions comes the Erdös-Sierpinski duality theorem to prove me wrong once again

LeGrandDODOM

@ShaVuklia lookup sequential continuity

Sha Vuklia

I know the definitions

For each sequence $(x_n)$ that goes to $x_0$, we have that $\lim f(x_n)=f(x_0)$

LeGrandDODOM

14:30

@ShaVuklia what's the relevant $f$ here ?

Sha Vuklia

$f(x)=x^{1/k}$, I think?

LeGrandDODOM

yes

Sha Vuklia

But then I have to show that $f$ is continuous

That's just rewording the problem, isn't it?

LeGrandDODOM

yes, it depends on what you already know

Paul Plummer

@AlessandroCodenotti Oh that is interesting, did not know that one.

Sha Vuklia

14:32

I know some limit theorems

maybe i'll have to refresh those

LeGrandDODOM

do you know that $\ln$ and $\exp$ are continuous ?

Sha Vuklia

I had forgotten that, but I can use it

Hermine

Hi, I have a simple question: will any 6 vectors in R^4 always span R^4?

LeGrandDODOM

it's very straighforward then

Hermine

Oh no, clearly no :|

LeGrandDODOM

14:35

@Hermine 0,0,0,0,0,0 doesn't span much

Alessandro Codenotti

@PaulPlummer I found in Oxtoby's "Measure and Category", it's a short book full of interesting stuff

Sha Vuklia

hm

Hermine

@LeGrandDODOM Yeah, thanks!^.^

Sha Vuklia

Should I use something like this $e^{\ln x^{1/k}}=x^{1/k}$ ?

it must be that

$e^{\frac{1}{k}\ln x}$

Paul Plummer

Did you figure out Balarka's problem? I think you were wanting to see if you could use Baire category to get it, did you end up getting that to work? If so I would be curious how that went @AlessandroCodenotti

Sha Vuklia

14:40

Thanks! @LeGrandDODOM

LeGrandDODOM

you're welcome

Alessandro Codenotti

@PaulPlummer which problem?

Mats Granvik

What is:
1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=?

Paul Plummer

the one about perfects without rationals, maybe I am mixing up things though @AlessandroCodenotti

Sha Vuklia

@MatsGranvik 133

Alessandro Codenotti

14:42

ah, yep, I did solve it with some help from Balarka and just a little bit of measure theory. I know how to do it with Baire category now too though

Mats Granvik

@ShaVuklia Right!

Alessandro Codenotti

The idea is to consider rational translates of the usual middle-thirds Cantor set and show that they can't cover $\Bbb R$ @PaulP

Sirmimer

How do i isolate $x_1$ in this equation: $p_1x_1+p_2(\frac{p_2x_1^{z-1}}{p_1})^{\frac1{z-1}} = m$

Paul Plummer

I am not exactly seeing where you are going although my first thought was to see how one could come up with an element that did not give any rationals, and I would guess (say looking at base three expansion) a sufficiently random number would do that. @AlessandroCodenotti

Alessandro Codenotti

if $C+r=\{c+r|c\in C\}$ where $C$ is the Cantor set then if we can find an $x_0\not\in\bigcup_{q\in\Bbb Q} (C+q)$ we have that $C+x_0$ is a perfect subset of $\Bbb R$ containing no rationals. But $C+r$ has empty interior, so $\bigcup_{q\in\Bbb Q} (C+q)$ must have empty interior too since $\Bbb R$ is a Baire space and we can find our $x_0$

Paul Plummer

14:54

Although I think just a "direct" construction would work, enumerate rationals, and at every level of your "cantor set construction" you make sure your closed sets missed whatever rational was in the list and take intersection

Alessandro Codenotti

"empty interior" should actually be "nowhere dense", but it's the same for closed subsets

@PaulPlummer nice, that should work

Paul Plummer

Wait, why would any $x_0$ make that true, why couldn't it take an irrational rational translate of a cantor number to a rational number? (I have been up all night, wasn't able to sleep maybe it is obvious, but I am not seeing it)

Alessandro Codenotti

if there were $c\in C$ such that $c+x_0=q\in\Bbb Q$ then we'd have $x_0$ in a rational translate of the Cantor set, but we chose it appositely outside all of those

Paul Plummer

Ah

Alessandro Codenotti

there might be a sign mistake now that I write it out explicitely, but it shouldn't make any difference

Topologicalife

15:03

Hi there.

Alessandro Codenotti

Hi

Topologicalife

How can I get the equation of the hyperbola that 'envelop' this wave? wolframalpha.com/input/?i=plot+4*3*cos(3x)+-+8*x*sin(3x)+from+x+%3D+-‌50+to+x+%3D+50

Mm.

I don't know how shall I paste the link.

Paul Plummer

@AlessandroCodenotti Your proof is cool, because it works for all meager sets

Alessandro Codenotti

Oh, right, I didn't even notice it! But that's true, every meager set has a translated copy not containing any rational

Topologicalife

Here is the link: pastebin.com/2bgRpaUf

Paul Plummer

15:08

Haha I thought that was basically the point of your proof since you explicitly use it (although I think you misspoke a bit you have $C$ is nowhere dense, and the translates give a meager set, since after translating you do get a dense set)

Alessandro Codenotti

oh, indeed, "empty interior" was the correct property, I don't know why I thought I needed nowhere dense instead, it's not true that the result is nowhere dense

Paul Plummer

Yah, empty interior works to

So much math, and some much of it I wan't to do. @AlessandroCodenotti I think you mentioned that you are doing this sort of thing for a project for undergrad I think... Did you choose the project or was it assigned? And I guess related, is this the sort of math you are most interested in?

Alessandro Codenotti

Every semester we have a series of 8 lectures (4 pairs) that are non mandatory and cover more advanced topics that won't be in mandatory courses, to get credits for them the students who attended have to write something about one of the 4 topics (Typesetting the lecture notes properly in LaTeX and then adding some interesting related theorem or applications is enough)

this semester we had Baire spaces, noncooperative games, congruent numbers and numerical methods for rectangular linear systems

Zach Hauk

15:27

uhh i wish i could ask @Akiva something right now

Akiva Weinberger

@ZachHauk Coincidentally enough, I turned on my phone less than a minute after you wrote that

Zach Hauk

LOL

Akiva Weinberger

which is very strange

Zach Hauk

indeed.

Akiva Weinberger

I woke up like ten minutes ago

Zach Hauk

15:30

I was wondering, does a parent have to come with me on the plane...?

Akiva Weinberger

No, you could be an "unaccompanied minor"

DHMO

@AkivaWeinberger @AlessandroCodenotti How to denote "subsets of N which are finite"?

Zach Hauk

but then, how do i get to the university?

Akiva Weinberger

They could pick you up at the airport

Alessandro Codenotti

I've seen $\mathcal{P}^\text{fin}(\Bbb N)$ before but I don't think that's standard notation

Zach Hauk

15:31

oh, sweet

i bet my parents will still say no

Akiva Weinberger

@DHMO Maybe $\mathcal {P^{<\omega}}(\Bbb N)$?

DHMO

@AkivaWeinberger nunca lo he visto

Zach Hauk

if they don't let me i'll just say "can i at least apply it's free"

Akiva Weinberger

Yo he visto $\Bbb N^{<\omega}$ para secuencias finitos

Alessandro Codenotti

Of course out of those 4 topic everyone is free to choose based on personal interest @PaulP

Akiva Weinberger

15:34

@ZachHauk …Isn't there an application fee?

Zach Hauk

uhh no

DHMO

@AkivaWeinberger por ejemplo?

Akiva Weinberger

@ZachHauk mathcamp.org/prospectiveapplicants/tuition.php

Zach Hauk

where does it say there's an application fee?

also, i'm probably going to apply for financial aid

Akiva Weinberger

@DHMO Es $\bigcup_{k=0}^\infty\Bbb N^k$

Paul Plummer

15:36

That is a neat program at your school @AlessandroCodenotti

DHMO

@AkivaWeinberger interesante

Akiva Weinberger

> @ZachHauk At the time of registration, we ask for a deposit of 25% of the expected camp fee (taking scholarships into account). The remaining 75% will be payable on the first day of camp.

Zach Hauk

that's registration

not application

> Registration for Mathcamp 2017

Your child was accepted: congratulations! The next step is to register for this summer's program. The registration deadline for most students is . (There may be some exceptions: for instance, alumni must register in April, and students admitted in May off of the waitlist will have registration deadlines in June.)

CowperKettle

Good evening. I asked a terminology question on ELL SE that someone might know the answer to here.

0

Q: How do we call these two parts of the s-curve?

I'm translating a text where a 4-parameter dose-response log curve is fitted to experimentally obtained data. The text says: The obtained dose-response curve (S-shaped) should contain points on the upper and lower plateaus and at least 4 points in the linear region and bending regions. As ...

Akiva Weinberger

@ZachHauk Oh.

Here it explicitly states "There is no application fee" mathcamp.org/prospectiveapplicants/howtoapply.php

so you're right

Alessandro Codenotti

15:40

They published the 4 topics for this semester but I forgot what they are...

Anyway I have to go now, have a nice day everyone!

Cardinal

Hi guys.

Zach Hauk

@Akiva oh boy..

> and the classic "Finite Simple Group of Order 2" by the Klein Four Group.

Cardinal

suppose we have 4 independent but not identically distributed random variables.
Now we order them in ascending order.
Now how can I find the CDF (or PDF) the kth random variable?

Is there any clear and detailed explanation on order statics and this ordering problem.

CowperKettle

cool

Cardinal

In fact I need a global function which takes into account all of the 4 random variables.

@CowperKettle Hi cop:-)

CowperKettle

15:52

@Cardinal did you try to ask this on Cross Validated?

@Cardinal Good evening, Cardinal!

Cardinal

@CowperKettle Nop, never heard that!

Akiva Weinberger

@ZachHauk That's a great song

Zach Hauk

heh

CowperKettle

@Cardinal It's here

Cardinal

@CowperKettle I see. Thanks I will go there.

CowperKettle

15:53

(0:

Cardinal

0:)

DHMO

how do you say "consider the above polynomial restricted to F_4"?

T_01

hey guys i have a question.. is there a general approach for equation systems, where i have products of different variables?..

DHMO

@T_01 no

T_01

hm

maybe im doing something wrong?
i want to test if a polynom f is reducible.
so i want to find 2 polynomials whose product is f - right so far?

DHMO

15:59

@T_01 yes

Akiva Weinberger

Maybe "the above polynomial over F_4"?

s.harp

The restriction of $p$ to $\Bbb F_4$ is prefectly fine tho

T_01

okay, lets take a polynom of deg 4, with factors $i_1, i_2, i_3, i_4$.
then i take 2 polynomials f,g:
$f = a_1x^2 + a_2x + a_3$ and g = $b_1x^2+b_2x^2+b_3$
and then i calc their product, and i want the factors of the result
to equal $i_1$ to $i_4$.
This gives me an equation system with 6 variables and 4 equations

@DHMO right?

tonytouch

Hello I have to show that cosh x =1 <-> x = 0. I know that cosh x ≥ 1.
I have tried this, but idk if its wrong:
coshx ≥ 1 ≥ x = 0, is that correct?

DHMO

@AkivaWeinberger is it valid though? Does F_4 equal (mod 4)?

How should I say (mod 4)?

T_01

16:02

no F_4 is not mod 4

mercio

o.o

Paul Plummer

They are different things

mercio

hi

T_01

as far as i know $F_4 := F_2[X]/(X^2+X+1)$

DHMO

cosh x = 1
(e^x + e^-x)/2 = 1
e^x + e^-x = 2
e^2x + 1 = 2e^x
e^2x - 2e^x + 1 = 0
(e^x - 1)^2 = 0
e^x - 1 = 0
e^x = 1
x = 2niπ

Paul Plummer

16:03

Maybe you want Z/4Z instead

DHMO

@PaulPlummer can I say "the above polynomial over Z/4Z"?

Sophie

LCM(1,2...n) on a log scale

Paul Plummer

@DHMO Why not?

tonytouch

Thank U DMHO

DHMO

@T_01 you already have their factors...

@PaulPlummer just asking you for confirmation

T_01

16:04

what do you mean ?

DHMO

@PaulPlummer Should I say 0=4 or 0$\equiv$4?

Paul Plummer

Unless you have your polynomial originally over some other ring and it doesn't really make sense to compare (I am guessing you are working with integer coefficients)

s.harp

@DHMO Do you want to restrict the domain of the polynomial to a subdomain or do you want to view the polynomial as taking values in $\Bbb Z_4$ by taking mod 4 after evaluation?

DHMO

@T_01 you can just use the factors, right

mercio

you mean log(lcm(1..,)) ona normal scale ?

DHMO

16:05

@s.harp the latter

T_01

@DHMO what do you mean by i have them? i want to actually calculate them

DHMO

@T_01 you said their factors are $i_1, i_2, i_3, i_4$

T_01

of my polynomial, i want to reduce

so i want the factors of the product of 2 general polynomials to equal this factors

s.harp

In that case (if your polynomial takes values in $\Bbb Z$) you call what you are doing "composing the polynomial with the map $\Bbb Z\to\Bbb Z_4$"

DHMO

do you have the actual values of the factors?

Akiva Weinberger

16:06

@DHMO Yeah I was wondering why you'd want F_4

Z/4Z makes more sense.

T_01

yes

i_1 to i_4 are given

DHMO

what are they?

@s.harp should I say 0=4 or 0$\equiv$4?

T_01

in my case 1, -1, 4, 5

and i am in $F_{11}$

DHMO

@T_01 your polynomial is A(x-1)(x+1)(x-4)(x-5).

T_01

so -1 is 9 of course

mercio

16:07

what's a factor

DHMO

@T_01 -1 is 10

T_01

wait

yes sorry

s.harp

@DHMO I would say $0\equiv 4$

DHMO

@s.harp thanks

s.harp

but this is not the word of god i am giving on this

T_01

16:08

@DHMO why

mercio

because i $\Bbb F_{11}$, $10+1=0$

so $10$ is $-1$

DHMO

@mercio I guess he is asking how I generated the polynomial from its factors

T_01

okay i think you just took the zero points

mercio

well i don't know what he means with "factor"

T_01

but what if i dont know them?

mercio

16:09

do you know what "factors" mean

T_01

yes? a is the factor of aX^2

mercio

and you said you knew the factors, $i_1$,...,$i_4$

DHMO

@T_01 your field is a unique factorization domain, if I am not mistaken

mercio

no, that's called a coefficient

T_01

so?

of well

@mercio you're right, sorry

DHMO

16:11

@T_01 wait, I thought your polynomial is degree 4

T_01

yes. sorry

there are 5 coefficients...

DHMO

which 5?

T_01

i have:
$f = X^4+10X^3+4X^2+5X+3$ in $F_{11}$

DHMO

@T_01 does it have any zero points?

T_01

i dont know - but if it doesnt have - then it does'nt mean it is'nt irreducible. And that is what im talking about

if it have zero points, of course it is irreducible this is kind of easy to reduce it then

but what if it does'nt have any? then i have such an equation system or not?

DHMO

16:14

I was just asking you if it has any zero points

have you checked its zero points

Check if it has any linear factors

T_01

okay i will. wait

yes, it has (x-8) as a linear factor

and (x-9)

DHMO

so you have reduced your problem to a quadratic factorization

T_01

Yes. but this is not my question

assume, it doesnt have any linear factors.

s.harp

Quick question, is anybody familiar a bit with asymptotics of bessel functions?

DHMO

@T_01 no idea

T_01

16:20

well...

i write down what i have now:

let be $f, g$ in $F_{11}$, with
$f = a_1X^2 + b_1X + c_1$ and $g = a_2X^2 + b_2X + c_2$.
The product of f and g is:
$a_1a_2X^4 + (a_1b_1+b_1a_2)X^3 + (a_1c_2 + b_1b_2 + c_1a_2)X^2 + (b_1c_2 + c_1b_2)X + c_1c_2$.
Now, if i want to equal $fg$ to another polynomial, $p$, with:
$p = v_1X^4 + v_2X^3 + v_3X^2+v_4X + v_5$, we get the following equation system:
$a_1a_2 = v_1$
$a_1b_2 + b_1a_2 = v_2$
$a_1c_2 + b_1b_2 + c_1a_2 = v_3$
$b_1c_2 + c_1b_2 = v_4$
$ c_1c_3 = v_5$

all $v_i$'s are known.

how to solve this system?...

Vrouvrou

16:36

please i have $||\alpha||^2=(\alpha, \alpha)$ where $\alpha $ is $C^1$ function , what is equal to, $\frac{d}{dt} ||\alpha(t)||$

someone help me ?

s.harp

Do you know what $\frac d{dt}(\alpha(t),\alpha(t))$ is?

Vrouvrou

scalar pruduct but it is in general i have not this definition

s.harp

?

If you know what $\frac d{dt} f(t)$ is and what $\frac d{dt}g(t)$ is, do you know how to find $\frac d{dt} f(g(t))$?

Vrouvrou

$\frac{d}{dt} (\alpha(t),\alpha(t))=(\alpha'(t),\alpha(t))+(\alpha(t),\alpha'(t))$

mercio

@T_01 there was almost exactly this question not too long ago

2

Q: How to split a quartic into two quadratics?

I have a quartic in $\Bbb Z[x]$ with very large coefficients that I know splits into two quadratics in $\Bbb Z[x]$. What is the best way to do find the quadratics?

polynomials galois-theory

Vrouvrou

16:52

@s.harp are here ?

s.harp

yes

Vrouvrou

is my equality is correct ?

s.harp

yes

Use it together with $\|\alpha(t)\|=\sqrt{\|\alpha(t)\|^2}=\sqrt{(\alpha(t),\alpha(t))}$ and the chain rule to find what the derivative of $\|\alpha(t)\|$ is at points where $\alpha(t)\neq0$.

Vrouvrou

$\frac{d}{dt} ||\alpha(t)||^2=2 ||\alpha(t)|| \frac{d}{dt}||\alpha(t)||$

s.harp

ok, you can also do that

divide by $2\|\alpha(t)\|$ to find $\frac d{dt}\|\alpha(t)\|$, provided $\|\alpha(t)\|\neq0$

Transcript for

$Mathematics$ Mathematics