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