The realization space is
  [1   1   0     2*x1   x1^2 + 2*x1 + 1   x1^2 + 2*x1 + 1   1   0   x1 + 1   x1 + 1    0]
  [0   1   1   x1 + 1            x1 + 1     x1^2 + x1 + 2   0   0        1   x1 + 1    1]
  [0   0   0     2*x1              2*x1              2*x1   1   1       x1       x1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^9 + 4*x1^8 + 9*x1^7 + 14*x1^6 + 15*x1^5 + 12*x1^4 + 7*x1^3 + 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 + 1, x1^2 + x1 + 1, x1 + 1, x1 - 1, 2*x1^2 + x1 + 1, x1^2 + x1 + 2, 2]