The realization space is
  [1   1               -1   0   0   1   x1^2 - x1 + 1                 -x1               0       x1      x1^2 - x1 + 1]
  [0   1   -x1^2 + x1 - 1   1   0   0   x1^2 - x1 + 1   -x1^3 + x1^2 - x1   x1^2 - x1 + 1        1   x1^3 - x1^2 + x1]
  [0   0                0   0   1   1       x1^2 - x1             -x1 + 1          x1 - 1   x1 - 1          x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^9 + 10*x1^8 - 24*x1^7 + 37*x1^6 - 40*x1^5 + 31*x1^4 - 17*x1^3 + 6*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 + 1, 2*x1^2 - x1 + 1, x1 + 1, x1^2 - x1 + 1, x1^3 - 2*x1^2 + x1 - 1]