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