Reusing variable names is generally a recipe for confusion:

R.<x1,x2>=PowerSeriesRing(SR)
P.<x1,x2>=PolynomialRing(QQ)

Now R and P have variables that print as "x1" and "x2", but of course they 
are still different variables. Now compare

sage: f   
x1*x2 + O(x1, x2)^3
sage: f[2]    # the degree-2 part in the power series variables
x1*x2

sage: f2
x1*x2 + O(x1, x2)^3
sage: f2[0]    # the degree-0 part in the power series variables
x1*x2


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