I saw this behavior
sage: R1.<x,y,z> = QQ[]
sage: R2.<z,x,y> = QQ[] # Rearrange variables of R1
sage: R1
Multivariate Polynomial Ring in x, y, z over Rational Field
sage: R2
Multivariate Polynomial Ring in z, x, y over Rational Field
sage: R1 is R2
False
sage: print(R1.gens(), R1.variable_names())
(x, y, z) ('x', 'y', 'z')
sage: print(R2.gens(), R2.variable_names())
(z, x, y) ('z', 'x', 'y')
sage:
It looks like the order in which we initiate the polynomials leads to
different polynomial spaces. I thought this should not be the case.
I got confused. Is it right or bug or intentional?
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