The realization space is
  [1   1   x1 - 1   0   0   1        x1 - 1    1        x1 - 1         1        x1 - 2]
  [0   1       -1   1   0   0             0    1            -1   -x1 + 1            -1]
  [0   0        0   0   1   1   x1^2 - 2*x1   x1   x1^2 - 2*x1        x1   x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 6*x1^7 - 10*x1^6 + 4*x1^5)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - 3*x1 + 1, x1 - 1, x1 - 2, x1 - 3, x1^3 - 4*x1^2 + 5*x1 - 1]