The realization space is
  [1   0   1   0   1    0       x1   x1^2 + 2*x1 + 1         x1^2 + x1      x1 + 1      x1^2 + 2*x1 + 1]
  [0   1   1   0   0    1       x1              x1^2             -x1^2         -x1                -x1^3]
  [0   0   0   1   1   -1   x1 + 1         x1^2 + x1   x1^2 + 2*x1 + 1   x1^2 + x1   x1^3 + 2*x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^10 + 5*x1^9 + 4*x1^8 - 3*x1^7 - 16*x1^6 - 25*x1^5 - 19*x1^4 - 7*x1^3 - x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - x1 - 1, x1 - 1, 2*x1 + 1, x1^3 + x1^2 + 2*x1 + 1, x1 + 1, x1^3 + 2*x1^2 - x1 - 1, x1^3 - 2*x1^2 - 3*x1 - 1]