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I want to compute all degree <=d polynomials from GF(2)[x1, x2] and then evaluate them at a certain polynomial input

eg degree d <= 1 and evaluation at (p^2, p^3 +1)

0 -> 0

1 -> 1

x1 -> p^2

x1 + 1 -> p^2 + 1

x2 -> p^3 + 1

x2 + 1 -> p^3

x1 + x2 -> p^2 + p^3 + 1

x1 + x2 + 1 -> p^2 + p^3

I want to compute all degree <=d polynomials polynomials, of form f1(x1)g1(x2)+f2(x1)g2(x2), from GF(2)[x1, x2] and then evaluate them at a certain polynomial input

eg degree d <= 1 and evaluation at (p^2, p^3 +1)

0 -> 0

1 -> 1

x1 -> p^2

x1 + 1 -> p^2 + 1

x2 -> p^3 + 1

x2 + 1 -> p^3

x1 + x2 -> p^2 + p^3 + 1

x1 + x2 + 1 -> p^2 + p^3