Where is information passed on to var() stored?

edit

var('xt1',latex_name='x_{t1}')
pretty_print(xt1)
f = xt1^2 + 4
print f._latex_(); pretty_print(f)     # defining f creates a latex_name of f
var('xt1',latex_name='{xt}_1')
pretty_print(xt1)
print f._latex_(); pretty_print(f)     # redefining xt1 does not change the latex_name of f 
f = f.subs(xt1=xt1)
print f._latex_(); pretty_print(f)     # the substitution rewrites the latex_name of f

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)