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