Hi, I’m trying to translate this Sage syntax to Python syntax (i.e. using 
sage as a Python library.) But I got stuck even on the first command.

In Sage,

>>> R.<x> = QQ[]>>> type(R)

<class 
'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category'>

Then I thought I can import it in Python like this:

import sage.rings
# OK

sage.rings.polynomial.polynomial_ring.PolynomialRing_field
# AttributeError

sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category

How would you write the same program in Python using sage as a library? And 
in general I see many unfamiliar syntax (from Python’s point of view) like 
R.<x>, QQ[], (0..20), etc. Do you think it is realistic to use sage as a 
Python library and completely not using sage (as an interpreter) itself?

c.f. Documentation on using sage as a library? 
<https://groups.google.com/d/msg/sage-support/NFtI5XqjQWg/qsW54OzeAQAJ>

Thanks.
​

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