quotient ring in Sage

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If under Z2 you understand $\mathbb Z/2\mathbb Z$ (or $\mathrm{GF}(2)$), then the even coefficients in the ideal generators look strange. Anyway, here is what you want:

K.<x,y,z> = PolynomialRing(GF(2))   # ring Z2[x,y,z]
J = ideal(2*x,y^3,x*y,x^2-4*z)      # ideal generated by 2*x,y^3,x*y,x^2-4*z
R = K.quotient_ring(J)              # quotient ring Z2[x,y,z] / <2x,y^3,xy,x^2-4z>