Let $A=k[x_1,x_2]/(x_2^2-x_1^3+x_1)$. As an example of Noether normalization, determine elements $y_1,\ldots,y_m\in A$, algebraically independent over $k$, such that $A$ is a finite $k[y_1,\ldots,y_m]$-algebra.
This is a problem in the Klaus Hulek's Elementary Algebraic Geometry. I think the book's proof of Noether normalization is not actually constructive...
Could anyone show me how to determine the $y_1,\ldots,y_m$ ?
The Krull dimension of $A$ is $1$, so almost every choice of $y\in A-k$ is good.