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2014-08-21 22:00:55 +0200 commented answer How does one add new variables to a multivariate polynomial ring?

Thank you. I think I can't upvote due to not having any reputation.

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2014-08-21 21:29:35 +0200 asked a question How does one add new variables to a multivariate polynomial ring?

If I try this, it fails:

R.<x,y> = PolynomialRing(QQ, 'x, y')
R.extend_variables('z')
AttributeError: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular' object has no attribute 'extend_variables'

(But a univariate polynomial ring PolynomialRing(QQ, 'x') has an extend_variables function.)

How do I take a polynomial ring $R$ and make a new ring $R'$ with more variables, such that $R\subset R'$?