fml, wolfram usurped one of my package's function names

RIP Slice

hmm, turns out Slice has been hiding in GeneralUtilities` all along, but somehow it gets loaded now, so it turns red

ok, panic averted ^^

somehow Rasterize now adds GeneralUtilities to the $ContextPath

would that be considered a bug?

{"System", "Global"}

{"GeneralUtilities", "System", "Global`"}

Guys, this question is arguably unclear, but it's really not the duplicate of linked question: mathematica.stackexchange.com/q/216794/1871

@ChrisK I'd call this very odd as well. Let me ask one of the devs..

@andre314, not that you need to ask a question, but did not see a question on OpenCascadeLink - did I miss it?

No, you didn't miss anything. I will ask the question in a few days.

@andre314, OK, sounds good.

More info: github.com/szhorvat/IGraphM/blob/master/IGraphM/Kernel/… I would like to know if Windows/Linux are affected and if the Pause timing I used is sufficient to work around the issue on these platforms. Please ping me if you could perform the test.

To be clear, this is not a bug in my code, it's a bug in Mathematica.

@TimStone @halirutan Arund now would be a good time to update the syntax highlighting for this site. Many v12.0 symbols are no highlighted. Not sure when the last update was.

@HenrikSchumacher May I ask you a math question (related to mathematica.stackexchange.com/questions/173081/…) ?

@anderstood Yess....

I'm not sure if I should start a new chat room. I'll start here.

@HenrikSchumacher I need a few minutes to write down the question properly

Okay...

@HenrikSchumacher Mmh, that's quite rasterized :/ Let me find a solution

Ah, that's much better.

@anderstood Hm. What do you mean with "gradient of a vector field"?

In a general differential geometric context, this does not make sense.

What comes closest to that is the covariant derivative.

Often written as $\nabla V$. And pronounced "nabla of V", not "gradient of V"...

So V(phi(.)) defines an application from R^3 to R^3. I would like the gradient of this application.

Do you by any chance mean the derivative?

The derivative can be computed with the chain rule.

If W is the above-mentioned application from R^3 to R^3, I would like the "matrix" whose component (1,1) is "limit (W(x + \epsilon, y, z) - W(x,y,z)) / \epsilon", etc.

Yeah, you mean the derivative.

OK

So $DW$ that take applies to a direction and a point

So you want the (Fréchet) derivative of U = D\psi \cdot V.

Exactly. I wanted to compare the expressions obtained from U = D\psi \cdot V and U = W(\psi( - ))

And do that in Mathematica... I am confused about Grad vs D

Okay, suppose that v is a tangent vector to p in \mathcal{M}.

They by the product rule, you have That's DU(p) v = D^2\psi(p) (V(p), v) + D\psi(p) DV(p) v

Here D is the Jacobi matrix.

And D^2\psi(p) is the second derivative, an \mathbb{R}^3-valued bilinear form.

So D^2\psi(p) is basically a 3-dimensional array...

If you substitute p = \varphi(X) v = D \varphi(X) \, u (where u is a tangent vector of \mathcal{N} at X) then you obtain the expression for DW(X) \, u

So DW(X) \, u = D^2\psi(\varphi(X)) (V(\varphi(X)), D \varphi(X) \, u) + D\psi(\varphi(X)) DV(\varphi(X)) D \varphi(X) \, u

Does that answer your question?

I need some time to answer your question :D

(Probably it raises more than it answered...)

Thank you so much. I'll try to implement this to see if it matches.

@Szabolcs I managed to reproduce the issue on Windows 10 with IGraphM 0.3.114. But it seems a bit random what exactly happens: Sometimes, it doesn't hang at all. Sometimes, it hangs directly after the Needs["IGraphM`"] command is issued. And sometimes, it only hangs after the startup message of IGraphM is printed. Also, killing the kernel does indeed fix the issue.

Ah, well of course my question does not make sense if I don't show the whole bilinear product :

@anderstood =D Yepp. Seems to be correct.

Starting with D[psi[r, phi, z], {{r, phi, z}, 2}], you have to multiply V and {v1, v2, v3} into the last two slots.

You can also do it like this: (D[psi[r, phi, z], {{r, phi, z}, 2}].{v1, v2, v3}).V[r, phi, z] or this (D[psi[r, phi, z], {{r, phi, z}, 2}].V[r, phi, z]).{v1, v2, v3} because the second derivative is symmetric in the last two slots.

@HenrikSchumacher I think I finally understood my difficulty. DU(p) does not apply to cartesian coordinates: it acts on the tangent space of \mathcal{M}! So I should compare DW(X) and DU(p)D\varphi(X). Do you agree?

@anderstood Yes!

Aaaah =) I'm going to take a small walk :)

@ChrisK I'd say so.

I filed a bug report. Let me know if you have any questions.

@Searke @ChrisK Ilian also said that this is not a feature :)

Well, I may have double reported it then. that's fine. ...

@Searke I was about to open an issue, but saw your message. I only talked to Ilian.

@Searke Thanks folks! It seems pretty obscure and in the end, not too consequential (at least for me)

Hey guys. For anyone with science questions that you may have wanted to ask Stephen before, he's doing a livestream Q&A at 1:00 CST. All questions are fair game! twitch.tv/Stephen_Wolfram

@HenrikSchumacher I'm trying to expand my scheme with the different manifolds/tangent spaces ; is it correct that DU is defined from T_p \mathcal{M} to T_{W(X)}(T_X \mathcal{N}) ?

I mean DU(p) instead of DU

where X = \Psi(p)

That's where things become complicated. DU is a map from TM to TTM.

Double tangent bundles can be super confusing.

Unless M is a vector space.

Sorry, it should be TM \to TTN.

Now there are two maps from TTN: The canonical foot point map \pi_TN \colon TTN \to TN and D \pi_N, where \pi \colon TN \to N is the canonical footpoint map of the tangent bundle TN.

@anderstood If you can, stay away from this! It causes severe headache!

Geometers tend to use covariant derivatives.

For example, if V is a vector field on M, then \nabla V(p) \colon T_pM \to T_pM is linear map on that tangent space.

But one has to make a choice for defining \nabla... Typically, when M is a Riemannian manifold, one chose \nabla such that it is generated by the Riemannian metric in a certain way. Keyword: Levi-Civita connection.

This is an interesting topic on its own, but a bit to much to explain in a chat room... ^^

IIRC, the book Arthur Besse - Einstein Manifolds.

Athur Besse is btw. not a real person; like Bourbaki, it's a pseudonym of a circle of mathematicians.

I'm having a much harder time grabbing the 'tongue' to show more information about the current function in 12.1...

@HenrikSchumacher Ok. I've heard about Levi-Civita connections (as I remember, roughly, it describes variations of derivatives). I looks simple (in terms of number of pages for example) but I find differential geometry very difficult to learn on its own!

@LukasLang Thank you! Can you try one more thing? Can you try Pause[1]; Needs["IGraphM`"] instead and confirm that this eliminates the hang? Perhaps you could also try to have a rough estimate of how long the pause needs to be to avoid the hang. But don't spend too much time on it. On my machine I need 0.6 seconds to avoid the hang, thus in the workaround I used 1. I am trying to figure out if 1 s is enough for everyone.

Yes, a very ugly hack, but what can you do?

@Szabolcs On my machine, I couldn't get it to hang for pauses >= 0.1 seconds, but this is on a fairly powerful desktop, and it's not really reliable in the first place. Even without any pause, I am having a hard time to reliably hang the front-end at the moment... But from what I've seen, 1 second should definitely be enough