The realization space is
  [1   0   1                 x1   1   0              2*x1 - 1   1         1        0                 x1]
  [0   1   1   -x1^2 + 3*x1 - 1   0   0                     0   1   -x1 + 1   x1 - 1   -x1^2 + 3*x1 - 1]
  [0   0   0                  0   1   1   -x1^3 + 3*x1^2 - x1   1        x1      -x1               x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^7 - 6*x1^6 + 15*x1^5 - 18*x1^4 + 10*x1^3 - 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1^4 - 4*x1^3 + 8*x1^2 - 5*x1 + 1, x1 - 1, x1^2 - 3*x1 + 1, x1^4 - 5*x1^3 + 10*x1^2 - 6*x1 + 1, x1^3 - 4*x1^2 + 6*x1 - 2, x1 - 2, x1^3 - 2*x1^2 + 3*x1 - 1]