This makes the definitions much easier to read, by removing the need to
use Group() and Suppress(): previously, these would be used to nest the
parsed tokens and remove the unnecessary ones (e.g, braces), but such
tokens can also easily be ignored by giving names to the tokens we use
(instead of accessing them by position). (See e.g. the implementation
of subsuper, which is also somewhat simplified.)

Also remove a few other pyparsing combinators that are not
needed: Combine (just concatenate the strings ourselves), FollowedBy
(use lookahead regexes), Literal (use plain strings, in particular
braces which are very common).

Also remove right_delim_safe, as self._right_delim already includes the
backslash-escaped closing brace rather than the unescaped one
(right_delim_safe dates back to when it didn't).

The error message for a^2_2^2 now changed to "double superscript" as
we now simply check for subscripts and superscripts one at a time, and
fail when we see either two subscript or two superscripts, emitting the
corresponding error.

(I played a bit with the parser to try and see what's wrong with pyparsing 3
and got there; unfortunately this patch doesn't fix the incompatibility :-()
Edit: This seems to fix support with pyparsing 3. It's not totally clear why, though...
A much more minimal fix would be

diff --git i/lib/matplotlib/_mathtext.py w/lib/matplotlib/_mathtext.py
index 73e6163944..fbf58b5df1 100644
--- i/lib/matplotlib/_mathtext.py
+++ w/lib/matplotlib/_mathtext.py
@@ -2046,7 +2046,7 @@ class Parser:
         p.accentprefixed <<= Suppress(p.bslash) + oneOf(self._accentprefixed)
         p.symbol_name   <<= (
             Combine(p.bslash + oneOf(list(tex2uni)))
-            + FollowedBy(Regex("[^A-Za-z]").leaveWhitespace() | StringEnd())
+            + Suppress(Regex("(?=[^A-Za-z]|$)").leaveWhitespace())
         )
         p.symbol        <<= (p.single_symbol | p.symbol_name).leaveWhitespace()

I still don't know whether that's a bug or an intended API change on pyparsing's side.

PR Summary

PR Checklist

• Has pytest style unit tests (and pytest passes).
• Is Flake 8 compliant (run flake8 on changed files to check).
• New features are documented, with examples if plot related.
• Documentation is sphinx and numpydoc compliant (the docs should build without error).
• Conforms to Matplotlib style conventions (install flake8-docstrings and run flake8 --docstring-convention=all).
• New features have an entry in doc/users/next_whats_new/ (follow instructions in README.rst there).
• API changes documented in doc/api/next_api_changes/ (follow instructions in README.rst there).