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You can then create the quotient of P by I as follows:

sage: Q = P.quotient(I)
sage: Q
Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field of size 2 by the ideal (x^5 + 1, y^5 + 1, z^64 + 1)

You can then work in the quotient as follows:

sage: A = Q(x^4+x*y^2)
sage: A
xbar^4 + xbar*ybar^2
sage: B = Q(x^2)
sage: B
xbar^2
sage: A * B
xbar^3*ybar^2 + xbar

As you can see, xbar^6 was replaced by xbar.