The realization space is
  [1   1   x1^2 - 2*x1 + 1   0   0   1    1   x1^2 - 2*x1 + 1                0   x1^2 - 2*x1 + 1      x1^2 - x1 + 1]
  [0   1           -x1 + 1   1   0   0    1           -x1 + 1               x1               -x1         -x1^2 + x1]
  [0   0                 0   0   1   1   x1     x1^2 - x1 + 1   -x1^2 + x1 - 1     x1^2 - x1 + 1   x1^3 - x1^2 + 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, x1 - 1, x1^3 - 4*x1^2 + 3*x1 - 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^3 - 4*x1^2 + 4*x1 - 2, 2*x1^2 - 2*x1 + 1, x1^2 - x1 + 1, 2*x1^2 - x1 + 1, x1 - 2, 2*x1^3 - 5*x1^2 + 4*x1 - 2]