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