Hi Hongyi,

>>>>> Hongyi Zhao <[email protected]> writes:
> According to my understanding, the `TeX-auto-global' variable setting
> is intending to set the file's store location of the comprehensive
> macro and variable hint lisp files, and the command
> `TeX-auto-generate-global' is for generating the comprehensive macro
> and variable hint lisp files.

Right. See https://www.gnu.org/software/auctex/manual/auctex/Customizing.html
.

> But based on my later tries, it seems that there is no need to run the
> above command at all, and auctex already can give wonderful and rather
> extensive completion results with its initial configuration.

As described in the above documentation, AUCTeX has built-in support for
many major packages. But it doesn't offer support for *ALL* LaTeX
packages.
Running `TeX-auto-generate-global' analyses all packages installed on
your TEXMFSYS tree at that time and generates support files which give
completions etc. So you can obtain completions for packages which
AUCTeX doesn't support by default.

But beware that `TeX-auto-generate-global' is not so smart so that it
sometimes introduces unexpected side effects.[1]

Regards,
Ikumi Keita

[1] https://lists.gnu.org/r/auctex/2021-01/msg00037.html

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