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MSE offers a huge variety of possibilities when it comes to writing an answer/question which might not be found elsewhere (at least all together).

I've recently read on this post, that answers can be exported to pdf with StackEdit - which is a great opportunity.

However, when I copy&paste an answer I want to download, StackEdit doesn't recognize \begin{align*} and claims

KaTeX parse error: No such environment: align* at position [...]

What can I do? Are there any alternatives for StackEdit or for begin{align*}?

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Some time back StackEdit veered away from MathJax support for $\LaTeX$ and instead took up the KaTeX package. Presently they support fewer "environments" than are provided here under MathJax.

A workaround for the particular deficiency you found is to use \begin{aligned} and \end{aligned} rather than the (unsupported by StackEdit) align* environment.

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