Finding newlines between $$ $$ or $ $ - regex

Question

I want to replace all "\r\n" with two backslahes+newline "\\ \r\n" except the "\r\n" inside "$$ $$" or "$ $" or "\[ \]". (This is the latex syntax)
The following text
1.$$ Test
2.
3.$$ $
4. $
5. Test $
6.
7. $
8.
9. Test
should be
1.$$ Test
2.
3.$$ $
4. $ \\
5. Test $
6.
7. $ \\
8. \\
9. Test
One of my trials:
First I have replaced new lines between $$ $$ or $ $ or \[ \] with --newline--
Then I have replaced all new lines with double new lines (in latex \ equals double new line).
Then I have replaced --newline-- with new line.
private static String replaceNewLines(String original) {
String text = original;
text = replaceBetween(text, "\\[", "\\]");
text = replaceBetween(text, "$$", "$$");
text = replaceBetween(text, "$", "$");
text = text.replace("\r\n", "\r\n\r\n").replace("--newline--", "\r\n");
return text;
}
private static String replaceBetween(String text, String start, String end) {
int i = text.indexOf(start);
while (i >= 0) {
int j = text.indexOf(end, i + 1);
String before = text.substring(0, i);
String after = text.substring(j);
text = before + text.substring(i, j).replace("\r\n", "--newline--")
+ after;
i = text.indexOf(start, j + 1);
}
return text;
}

Answer 1

I would suggest going through the file in one run with a flag marked if you are in math mode or not. Depending on flag you can replace newline or not.
In more general case when nesting is possible, I would suggest using stack implementation.
Deque<String> queue = new ArrayDeque<>(Collections.emptyList());
In this case you can go through the file in one run adding appropriate strings to the stack when entering into math mode and removing them when leaving it. Again depending on the mode (i.e. on the string which is on the top of stack) replace newline or not.
You can ask when in LaTeX could nesting appear. Look at this rough example of Dirichlet function definition:
\[
\mathbb{1}(x)
=
\begin{cases}
1&\text{when $x
$ is rational number}\\
0&\text{when $
x$ is not rational number}
\end{cases}
\]
Here $ $ is inside \[ \]

. Additionally you have to take into account \text{ and } as something what causes nesting. Things get complicated.
Finally, I think that you should also take into account the pair \( and \) which is equivalent $ $.
Apart from that in LaTeX there are also environments so if you have a real LaTeX source then you have to deal with \begin{equation} etc.
BTW \\ in LaTeX just breaks the line. Double \r\n starts a new paragraph. This is not the same.
You mentioned regex in tags. Achieving the same in regex is a longer story and it depends a bit on specific regex flavour. You can read about it on the page https://www.regular-expressions.info/balancing.html