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Regex Puzzle: Match a pattern only if it is between two $$ without indefinite look behind

I am writing a snippet for the Vim plugin UltiSnips which will trigger on a regex pattern (as supported by Python 3). To avoid conflicts I want to make sure that my snippet only triggers when contained somewhere inside of $$___$$. Note that the trigger pattern might contain an indefinite string in front or behind it. So as an example I might want to match all "a" in "$$ccbbabbcc$$" but not "ccbbabbcc". Obviously this would be trivial if I could simply use indefinite look behind. Alas, I may not as this isn't .NET and vanilla Python will not allow it. Is there a standard way of implementing this kind of expression? Note that I will not be able to use any python functions. The expression must be a self-contained trigger.

If what you are looking for only occurs once between the '$$', then:
\$\$.*?(a)(?=.*?\$\$)
This allows you to match all 3 a characters in the following example:
\$\$) Matches '$$'
.*? Matches 0 or more characters non-greedily
(?=.*?\$\$) String must be followed by 0 or more arbitrary characters followed by '$$'
The code:
import re
s = "$$ccbbabbcc$$xxax$$bcaxay$$"
print(re.findall(r'\$\$.*?(a)(?=.*?\$\$)', s))
Prints:
['a', 'a', 'a']

The following should work:
re.findall("\${2}.+\${2}", stuff)
Breakdown:
Looks for two '$'
"\${2}
Then looks for one or more of any character
.+
Then looks for two '$' again

I believe this regex would work to match the a within the $$:
text = '$$ccbbabbcc$$ccbbabbcc'
re.findall('\${2}.*(a).*\${2}', text)
# prints
['a']
Alternatively:
A simple approach (requiring two checks instead of one regex) would be to first find all parts enclosed in your quoting text, then check if your search string is present withing.
example
text = '$$ccbbabbcc$$ccbbabbcc'
search_string = 'a'
parts = re.findall('\${2}.+\${2}', text)
[p for p in parts if search_string in p]
# prints
['$$ccbbabbcc$$']

How to match substring or whole string

In Python regex, how would I match only the facebook.com...777 substrings given either string? I don't want the ?sfnsn=mo at the end.
I have (?<=https://m\.)([^\s]+) to match everything after the https://m.. I also have (?=\?sfnsn) to match every thing in front of ?sfnsn.
How do I combine the regex to only return the facebook.com...777 part for either string.
have: https://m.facebook.com/story.php?story_fbid=123456789&id=7777777777?sfnsn=mo
want: facebook.com/story.php?story_fbid=123456789&id=7777777777
have: https://m.facebook.com/story.php?story_fbid=123456789&id=7777777777
want: facebook.com/story.php?story_fbid=123456789&id=7777777777
Here's what I was messing around with https://regex101.com/r/WYz5dn/2
(?<=https://m\.)([^\s]+)(?=\?sfnsn)

You could use a capturing group instead of a positive lookbehind and match either ?sfnsn or the end of the string.
https://m\.(\S*?)(?:\?sfnsn|$)
Regex demo
Using the lookarounds, the pattern could be:
(?<=https://m\.)\S*?(?=\?sfnsn|$)
Regex demo

Putting a ? at the end works, since the last grouped lookahead may or may not exist, we put a question mark after it:
(?<=https://m\.)([^\s]+)(?=\?sfnsn)?

Does this regex fail, or do I need to modify the regex to support "optional followed by"?

I am trying the following regex: https://regex101.com/r/5dlRZV/1/, I am aware, that I am trying with \author and not \maketitle
In python, I try the following:
import re
text = str(r'
\author{
\small
}
\maketitle
')
regex = [re.compile(r'[\\]author*|[{]((?:[^{}]*|[{][^{}]*[}])*)[}]', re.M | re.S),
re.compile(r'[\\]maketitle*|[{]((?:[^{}]*|[{][^{}]*[}])*)[}]', re.M | re.S)]
for p in regex:
for m in p.finditer(text):
print(m.group())
Python freezes, I am suspecting that this has something to do with my pattern, and the SRE fails.
EDIT: Is there something wrong with my regex? Can it be improved to actually work? Still I get the same results on my machine.
EDIT 2: Can this be fixed somehow so the pattern supports optional followed by ?: or ?= look-heads? So that one can capture both?

After reading the heading, "Parentheses Create Numbered Capturing Groups", on this site: https://www.regular-expressions.info/brackets.html, I managed to find the answer which is:
Besides grouping part of a regular expression together, parentheses also create a
numbered capturing group. It stores the part of the string matched by the part of
the regular expression inside the parentheses.
The regex Set(Value)? matches Set or SetValue.
In the first case, the first (and only) capturing group remains empty.
In the second case, the first capturing group matches Value.

Using regex to find multiple matches on the same line

I need to build a program that can read multiple lines of code, and extract the right information from each line.
Example text:
no matches
one match <'found'>
<'one'> match <found>
<'three'><'matches'><'found'>
For this case, the program should detect <'found'>, <'one'>, <'three'>, <'matches'> and <'found'> as matches because they all have "<" and "'".
However, I cannot work out a system using regex to account for multiple matches on the same line. I was using something like:
re.search('^<.*>$')
But if there are multiple matches on one line, the extra "'<" and ">'" are taken as part of the .*, without counting them as separate matches. How do I fix this?

This works -
>>> r = re.compile(r"\<\'.*?\'\>")
>>> r.findall(s)
["<'found'>", "<'one'>", "<'three'>", "<'matches'>", "<'found'>"]

Use findall instead of search:
re.findall( r"<'.*?'>", str )

You can use re.findall and match on non > characters inside of the angle brackets:
>>> re.findall('<[^>]*>', "<'three'><'matches'><'found'>")
["<'three'>", "<'matches'>", "<'found'>"]
Non-greedy quantifier '?' as suggested by anubhava is also an option.

Match a sentence

I wish to chop some text into sentences.
I wish to match all text up until: a period followed by a space, a question mark followed by a space or an exclamation mark followed by a space, in an non greedy fashion.
Additionally, the punctuation might be found at the very end of the string or followed by a /r/n for example.
This will almost do it:
([^\.\?\!]*)
But I'm missing the space in the expression. How do I fix this?
Example:
I' a.m not. So? Sure about this! Actually. Should give:
I' a.m not
So
Sure about this
Actually

You can achieve such conditions by using positive lookahead assertions.
[^.?!]+(?=[.?!] )
See it here on Regexr.
When you look at the demo, The sentences at the end of a row with no following space are not matched. You can fix this by adding an alternation with the Anchor $ and using the modifier m (makes the $ match the end of a row):
[^.?!]+(?=[.?!](?: |$))
See it here on Regexr

Try this:
(.*?[!\.\?] )
.* gives all,
[] is any of these characters
then the () gives you a group to reference so you can get the match out.

Use a non-greedy match with s look ahead:
^.*?(?=[.!?]( |$))
Note how you don't have to escape those chars when they are in a character class [...].

This should do it:
^.*?(?=[!.?][\s])