Mathematics

shintuku

8:00 AM

combining numpy and sympy I guess?

Vrouvrou

8:22 AM

hello

shintuku

ay

Vrouvrou

please on finite dimensional normed vectorial space, the continuity is important to fined eigenvalues ?

Vrouvrou

8:38 AM

someone here ?

shintuku

i'm here but i have no clue sorry

Vrouvrou

do you understand French ?

shintuku

par hasard hehe

Yep

how would i find the angular rotation of the earth 60 degrees north of the equatoe

Vrouvrou

@shintuku fr.wikipedia.org/wiki/Valeur_spectrale dans cet article

Si E est de dimension finie, tous les endomorphismes de E sont continus et tout endomorphisme de E injectif est bijectif, par conséquent la notion de valeur spectrale se confond avec celle de valeur propre.

pourquoi on a besoin de la continuité

?

shintuku

8:47 AM

s'il n'est pas continu, ça implique que y'a pas de bijection, non?

Vrouvrou

ah bon ? je ne sais pas

shintuku

si t'as une transformation linéaire de A à B, et que A est continu mais pas B, alors tu peux pas avoir de bijection

parce qu'il y aura des valeurs de B qui n'auront pas de représentants dans A

définition de l'injection, qui est un des deux critères de la bijection

Vrouvrou

c'est la surjectivité non ?

shintuku

ah, ouais t'as raison

c'est la surjectivité qui manque, pas nécessairement l'injectivité

shintuku

9:36 AM

@Vrouvrou non, en fait, c'est l'injectivité qui manque: la surjectivité nécessite que chaque membre de B soit associé à un membre de A. Mais l'injectivité necessite que chaque membre de A soit lui seul associé à un membre de B. Si l'injectivité manque, ça veut dire que tu peux avoir deux membres de A pour un membre de B. Alors: s'il n'y a pas de continuité chez B mais il y en a chez A, nécessairement, t'auras plus d'un membre de A pour chaque membre de B.

Koro

10:14 AM

Je sais un peu de francais. C'est tres bien de voir des gens parler en francais ici.

:)

Vrouvrou

@shintuku mais pour calculer les valeurs propres de T o regarde si T-\lambda id_E est injectif pourquoi on a besoin de la continuité de T ?

@robjohn can you help me about eigenvalue and spectral value on finite dim space

shintuku

ça me dépasse un peu désolé, mais il semble y avoir ça:

Operator theory

In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis. If a collection of operators forms an algebra over a field, then it is an operator algebra. The description of operator algebras is part of operator theory. == Single...

section "spectrum of operators"

Vrouvrou

ok thank's

shintuku

y'a aussi l'article "Spectral theory"

qui semble en lien avec tout ça

Vrouvrou

10:36 AM

merci

PM 2Ring

11:38 AM

@JairoA.delRio Welcome to the beautiful world of Apollonian gaskets and Descartes' theorem.

I should modify the code that produced that so it outputs in SVG...

@Vrouvrou Stack Exchange policy is that for reasons of moderation, chat conversations on English language sites should be in English. (Small, well-known things like bonjour are ok). OTOH, a lot of the regulars in this room, including a room owner, can read French...

@shintuku It won't kill you to do a few by hand, unless the function's really ugly... But anyway, you can easily do Hessians in SageMath, which is a giant computer algebra system built on top of Python. You can run SageMath online, so you can use it without having to install anything. If you are already comfortable with Python, you won't have any problems picking up SageMath. You can learn the basics & be doing useful stuff in a matter of hours.

Here's a short Hessian demo I stole from the docs.

shintuku

11:57 AM

wow, what an amazing thing

thanks a lot for the reference!!

PM 2Ring

No worries. I've only been using SageMath since last September. It's so big that it would be pretty hard to become an expert. So just work through the main tutorial, and then dive into the relevant section of the docs when you need to figure out some specific thing.

You can run plain Python on the SageMathCell server, but it does have a few quirks. But I just love being able to write & run Python on my phone.

shintuku

sweet

i just wanted something a bit familiar and this looks like exactly it

PM 2Ring

12:12 PM

There's an example of doing 3D plotting with SageMath at the end of this answer, which uses ephemeris data from JPL. astronomy.stackexchange.com/a/28036/16685

shintuku

holly molly, that is one smooth applet

0 lag

PM 2Ring

@shintuku Yep. You can usually guess how to do stuff, and your guess will be correct. And of course you can learn how stuff works with the usual Python help() function. The Sage docs are pretty good, although they are a bit of a rabbit warren, and occasionally sections aren't fully up to date. But I guess it's impossible to organise that much info in a completely sane way. :)

Here's another cute 3D one:

Apr 1 at 15:31, by PM 2Ring

TIL, that you can arrange 7 cylinders (of identical radii) so that the curved surface of each cylinder touches the curved surfaces of the other 6 cylinders. https://puzzling.stackexchange.com/a/109191/36040

shintuku

wow very smooth too

i don't know, I'm used to 3D lagging on websites

PM 2Ring

The three.js system is very powerful, and Sage only exposes a tiny bit of it. I could make that cylinder thing a lot prettier, coding directly in JavaScript (which can also run in SageMathCell). But I much rather code in Python / Sage. :)

robjohn

@PM2Ring I agree that most of the content on SE is in English, but if I see something in a language I don't understand and think might be interesting/problematic, I find Google Translate useful. Is there a posted StackExchange policy about language requirements? I have seen a lot of non-conclusive discussions on meta, but nothing like a policy statement. If there is one, I would like to know.

PM 2Ring

12:24 PM

@shintuku How about 4D? mikelortega.github.io/tesseract (also done with three.js)

shintuku

woah, extremely neat!

PM 2Ring

@robjohn I'll see if I can find an official statement somewhere. I learned that rule from a couple of mods who were / are ROs in the SO Python room, eg Martijn Pieters. I know there were problems a few years ago on the SO chat network with some (Android ?) programmers persistently chatting in their local language in a particular room.

robjohn

Thanks.

PM 2Ring

How's this? There may be something more FAQ-like.

69

A: Disallow languages other than English in chat

As previously discussed, we cannot effectively moderate non-English chatrooms. If concerns are raised over the appropriateness of a room's conversation, then either the conversation or the entire room is subject to deletion. If you're seeing flags like this raised, re-flag with a mod-only flag ...

So, it's more an attitude of: a bit of non-English is ok, but if things get off the rails & lots of non-English stuff gets flagged, then watch out!

And in the interests of ethnic equality, I don't think it's fair to allow French, but to clamp down on (eg) Gujarati: meta.stackoverflow.com/q/323257/4014959 Those guys love talking in Gujarati, and can get rather passionate in their chats...

robjohn

12:50 PM

@PM2Ring that looks like a nested $(-2,3,6)$ gasket (the outer circle has bend $-2$, the largest inner circle has bend $3$ and the next largest inner circle has bend $6$). Is that correct?

PM 2Ring

1:09 PM

@robjohn Yes, it's nested. I can't remember the exact details: I created that image ~10 years ago. IIRC, I used Python to create the basic gasket(s), and did the nesting by hand (probably using GIMP).

From Meta Stack Exchange: What languages are we allowed to speak in SE chat rooms?, although that's from 2012, there may be something more recent.

robjohn

@PM2Ring I have found a few things around 2017, some around 2013-2014, but most 2012 or before. I agree with Shog9 that we need to be able to moderate the site and SE is going to be held accountable for the content, so the moderators of the room (which includes room owners) should be comfortable with the language used in the room.

However, it is the CMs who are SE employees, and they need to be comfortable with the languages used so that they can moderate things.

@PM2Ring I have a bunch of non-nested gaskets that I created around 2009. I colored by generation and labeled with their bends. Thus, they are not as pretty.

PM 2Ring

1:29 PM

@robjohn I just asked the Meta SE mods: chat.meta.stackexchange.com/rooms/89/tavern-on-the-meta

robjohn

I see

PM 2Ring

@robjohn But they are informative. :) But yeah, that colour scheme's a bit jarring. My Python program uses the now-obsolete GTK2 for the GUI, and lets you choose between various colour parameterizations (like RGB, HSV, HLS) to do the colour interpolations.

robjohn

I might change the function that actually generates the object added to the image so as to make it less informative, but easier on the eyes.

PM 2Ring

1:52 PM

Here's one with discs:

Transcript for

$Mathematics$ Mathematics