Express domain membership

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assume() is a wrapper for the function with the same name in Maxima. You can find out about the syntax with the usual method of adding a ? after the function name:

sage: assume?

In this case, to indicate that the variable x is in ZZ, you need to type:

sage: assume(x, 'integer')

Unfortunately, Sage relies on two different backends for symbolic computations, Maxima and Pynac. Each of these uses a different method to indicate domains. We haven't reconciled these through the same interface yet. In order to indicate that a variable is real to Pynac, you can do:

sage: var('x', domain=RR)

At this moment, Pynac does not have different domains for ZZ or QQ. It only knows about RR, CC and NN.

I don't know if you actually need symbolic expressions, otherwise tests are very straightforward:

sage: x=12
sage: x in ZZ, x in QQ, x in RR
(True, True, True)

Note that tests using pure Python isinstance give different output, no surprise:

sage: isinstance(x, Integer), isinstance(x, ZZ)
(True, False)