Can someone do a simple test with IGraph/M and M12.1 on either Windows or Linux please? WARNING: This is to check a bug that hangs the FE. Save all your work first.
Instructions:
- Install IGraph/M https://github.com/szhorvat/IGraphM/#installation - Start M12.1 and Quit the kernel (important to Quit even if you just started the system) - Needs["IGraphM`"]
On macOS the FE will hang now. To recover it, just kill the kernel.
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.
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.
@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.
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?
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}) ?
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.
@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.
@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
