The realization space is
  [1   0   1    2*x1 - 1   0   1    0        x1^2             2*x1 - 1   2*x1 - 1      2*x1 - 1]
  [0   1   1   x1^2 - x1   0   0    1        x1^2            x1^2 - x1      -x1^2         -x1^2]
  [0   0   0           0   1   1   -1   -2*x1 + 1   -2*x1^2 + 3*x1 - 1   2*x1 - 1   2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (8*x1^7 - 28*x1^6 + 54*x1^5 - 57*x1^4 + 32*x1^3 - 9*x1^2 + x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 + 2*x1 - 1, 2*x1 - 1, x1^3 + 2*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, x1^2 - 5*x1 + 2, x1^2 - 3*x1 + 1, x1^3 - x1^2 - 2*x1 + 1]