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 $R\subset R'$?