Hi all,

Consider the following sequence of constructions:

sage: R = PolynomialRing(ZZ, ['x1', 'x2', 'x3'])
sage: S = PolynomialRing(R, ['x4'])
sage: T = S.extend_variables(['x5', 'x6'])
sage: type(R)
<type 
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular'>
sage: type(S)
<class 
'sage.rings.polynomial.polynomial_ring.PolynomialRing_integral_domain_with_category'>
sage: type(T)
 <class 
'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_with_category'>

What I'd like: extend R with a few extra variables. I also have a matrix 
over R that I'd like to interpret as a matrix over 
R-with-a-few-extra-variables.
What I get: only the ring S has the method extend_variables. Neither R nor 
T have it. Why is that? What's the proper way to extend R?

Cheers,

Stefan.

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