The realization space is
  [1   0   1   x1 - 1   0   1    0     2*x1^2 - x1      x1 - 1      x1 - 1         x1 - 1]
  [0   1   1    -x1^2   0   0    1     2*x1^2 - x1       -x1^2   -2*x1 + 1   -2*x1^2 + x1]
  [0   0   0        0   1   1   -1   x1^2 + x1 - 1   x1^2 - x1      x1 - 1      x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^10 - 20*x1^9 + 45*x1^8 - 68*x1^7 + 87*x1^6 - 93*x1^5 + 71*x1^4 - 34*x1^3 + 9*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, 2*x1 - 1, 2*x1^2 - 1, x1^2 + x1 - 1, 5*x1^3 - 4*x1^2 - x1 + 1, 3*x1 - 2, 3*x1^2 - 1]