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A basis of the quotient ring $K[x_1,\ldots,x_n]/I$ as a $K$-vector space is also called a normal basis of the ideal $I$.
sage: R.<x,y> = PolynomialRing(QQ, order='lex')
sage: I = R.ideal(x^2+y^2-1, 16*x^2*y^2-1)
sage: I.normal_basis()
[x*y^3, y^3, x*y^2, y^2, x*y, y, x, 1]
See the documentation of normal_basis for more options (e.g., when $I$ is not $0$-dimensional).
