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    @egreg If you do it after unicode-math you would get \mathinner {\unicodecdots } instead of \mathinner {\cdotp \cdotp \cdotp} for \cdots and this is not what you want. For \vdots and \ddots there is not difference, whether you do it before or after loading unicode-math. Commented 17 hours ago
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    @dedded If you load amsmath explicitly, you should do it indeed after storing \cdots into \latexcdots (this is the reason, why I've named the commands \latex… and not \ams… ;-)). Commented 17 hours ago
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    @egreg I don't store and restore \dots. So with my code \dots uses the amsmath definition \ifmmode \@xp \mdots@ \else \@xp \textellipsis \fi and therefore IMHO should behave like explained in amsmath. Commented 16 hours ago
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    @dedded With unicode-math \vdots is just the character . Similar for \vdots. Just add, e.g., \\ShowCommand\ddots \ShowCommand\latexddots at the beginning of \AtBeginDocument so see the difference of the definition in the log file and on the terminal. Commented 16 hours ago
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    @dedded I've added the useful \ShowCommand commands to my example, but commented them. You can activate them to see the difference of the definitions. Commented 16 hours ago