Missatges enviats per Visvanath Ratnaweera

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But the question is "How long does it take [for the OP] to prepare [his institution to] upgrading moodle" - which needs some telepathy and other magical powers in addition to knowledge in Moodle.

May be, a good question to ask these ChatGPT and the like.
Gran somriure
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20 TB data, that is a challenge!

How do they divide between the filedir/ and the database dump?

Copying a directory of that that size will indeed take ages. You must have made it "incremental", i.e. rsync well before taking Moodle off-line and then one last time, after taking Moodle off-line?
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What Moodle knows and what Formulas question type supports is the \( \TeX \) notation. See Using TeX Notation.

That is about writing mathematical formulae. \( \LaTeX \) is a macro on \( TeX \) to produce complete documents. Moodle doesn't have that intergrated, of course you can author your documents in \( \LaTeX \) and upload them to Moodle. But this has no connection to Moodle quiz system. Same with TikZ, it is to generate SVG, I don't think there is a filter in Moodle for rendering. I may be wrong.

BTW, it is \( \TeX \) and \( \LaTeX \) or TeX and LaTeX if you can't render them. Latex is a type of a fabric.

P.S. There is a dedicated forum on this called Mathematics tools https://moodle.org/mod/forum/view.php?id=752. The experts are there. You might want to ask the moderator to move this discussion to that forum.
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You answered your own question:
> very slow after installing it on an internal network and not on the Internet

So look for the differences related to the network. Some ideas:
- the authentication server is in the Internet
- site linked to other services like repositories outside the LAN
- embedded videos on the site home
- as already pointed out by Sergio services configured to resolve the IP addresses in some DNS which is outside the LAN

The browser developer tool Network might give some hints. Otherwise the deep dive would be record the network traffic, with tcpdump and the like.