The realization space is
  [1   1   0   -x1^2 + 3*x1 - 1   0   1   1         0           -x1^2 + 3*x1 - 1         1                 x1]
  [0   1   1       -x1^3 + x1^2   0   0   1        x1               -x1^3 + x1^2        x1               x1^2]
  [0   0   0                  0   1   1   1   -x1 + 1   x1^3 - 4*x1^2 + 4*x1 - 1   -x1 + 1   -x1^2 + 3*x1 - 1]
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[2*x1 - 1, x1, x1 - 1, x1^4 - 4*x1^3 + 8*x1^2 - 5*x1 + 1, x1^3 - 4*x1^2 + 6*x1 - 2, x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^4 - 3*x1^3 + 7*x1^2 - 5*x1 + 1, x1^2 + 2*x1 - 1, x1^3 - 3*x1^2 + 4*x1 - 1]