markdown-it-texmath
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It doesn't work when '$...$' is nested inside '$$...$$'
I find this usage at KaTeX website

When I use \colorbox{aqua}{$F=ma$} or \fcolorbox{red}{aqua}{$F=ma$} , it also works in vscode, but it looks bad in browser. like this

Hmm ... $\fcolorbox{blue}{red}{F=ma}$
works for me in VSCode

and in Browser

... no nesting of $'s supported ...
Emm... I know what you mean. But it is different between $ nested and not. It is just only text if you don't use $ , and it doesn't support these symbols \sum $\sum$ , \prod $\prod$ . For example, if I want to add a colored background to this formulae

I will fail.
Hmm ... you are right. According to these and these comments inherent problems with $ environment become more clear.
I'm not sure, how to deal with that inside of markdown-it-texmath. It will take some time.
Well, that's all right.