The realization space is
  [1   1   0   0        1        1   0                       1                           1                           1                     1]
  [0   1   1   1   x1 - 1       x1   0                       0                           1                      x1 - 1                    x1]
  [0   0   0   1   x1 - 1   x1 - 1   1   -x1^3 + 3*x1^2 - 2*x1   -x1^3 + 4*x1^2 - 4*x1 + 1   -x1^3 + 4*x1^2 - 4*x1 + 1   -x1^3 + 3*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^7 + 8*x1^6 - 25*x1^5 + 38*x1^4 - 27*x1^3 + 4*x1^2 + 5*x1 - 2)
avoiding the zero loci of the polynomials
RingElem[x1^2 - 3*x1 + 1, x1 - 1, x1 - 2, x1^3 - 3*x1^2 + 2*x1 - 1, x1, x1^4 - 5*x1^3 + 8*x1^2 - 4*x1 + 1, x1^2 - 2*x1 - 1, x1^3 - 4*x1^2 + 5*x1 - 3]