# Help with matrices over multivariable polynomial ring

I want to work with matrices over a multivariable polynomial ring. I want the matrix

[x0^2,x1^2,x2^2]

[x0^4,x1^4,x2^4]

[x0^8,x1^8,x2^8]

so I can take the determinate of it. I have

R = PolynomialRing(GF(2), 3, 'x')

which is a "Multivariate Polynomial Ring in x0, x1, x2 over Finite Field of size 2". I try

M = MatrixSpace(R,3,3,sparse=True)

which is the "Full MatrixSpace of 3 by 3 sparse matrices over Multivariate Polynomial Ring in x0, x1, x2 over Finite Field of size 2". I am not even sure what "sparse" is.

Then I try

A = M([x0^2,x1^2,x2^2, x0^4,x1^4,x2^4, x0^8,x1^8,x2^8])

or

A = M([[x0^2,x1^2,x2^2], [x0^4,x1^4,x2^4], [x0^8,x1^8,x2^8]])

And it says "name 'x0' is not defined"

I have looked for examples in the Sage documentation, but I just can get Sage to make the matrix above.

Eventually, I want to do arbitrate number of variables and arbitrary n-by-n matrices.

Thank you for your help.