The realization space is
  [1   1   0   0        1        1   0        x1 - 1          x1 - 1               1        x1 - 1]
  [0   1   1   1   x1 - 1       x1   0             0          x1 - 1          x1 - 1     x1^2 - x1]
  [0   0   0   1   x1 - 1   x1 - 1   1   x1^2 - 2*x1   x1^2 - x1 - 1   x1^2 - x1 - 1   x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^4 - 3*x1^3 + 2*x1^2 + 1, x1^7 - 5*x1^6 + 9*x1^5 - 7*x1^4 + 3*x1^3 - 2*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^4 - 4*x1^3 + 6*x1^2 - 3*x1 - 1, x1^3 - 3*x1^2 + 2*x1 + 1, x1^2 - 3*x1 + 3, x1 - 2, x1^2 - x1 - 1, x1^3 - 2*x1^2 + x1 - 1, 2*x1^3 - 6*x1^2 + 4*x1 + 1]