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How can one get the current error mode. e.g., is batchmode, scrollmode, etc set? I would like to save and restore these modes in lua or be able to have a macro save the current state that can be called later to restore it.

e.g., \savemode and \restoremode

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added \interactionmode.

When used as number, \interactionmode returns one of the values 0 (batchmode), 1 (nonstopmode), 2 (scrollmode), or 3 (errorstopmode). Assigning one of these values to \interactionmode changes the current interaction mode accordingly; such assignments are always global.

Node that last part: "such assignments are always global".