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Pynac/ginac tracks latex_name, so its a bit tricky to get at it.

The assumptions (like domain="real") are tracked in Sage:

sage: var('xt1', domain='real') 
xt1
sage: assumptions(xt1) 
[xt1 is real]
sage: forget(xt1, 'real') 
sage: assumptions(xt1) 
[] 
sage: assume(xt1 > 0)

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