The realization space is
  [1   0   1   0   1    0            x1 - 1         x1^2 - 2*x1     x1^6 - 5*x1^5 + 8*x1^4 - 3*x1^3 - 3*x1^2 + 2*x1        x1 - 2                 x1^4 - 4*x1^3 + 4*x1^2]
  [0   1   1   0   0    1            x1 - 1       x1^2 - x1 - 1        x1^6 - 4*x1^5 + 4*x1^4 + 2*x1^3 - 4*x1^2 + 1        x1 - 1        x1^4 - 3*x1^3 + 2*x1^2 + x1 - 1]
  [0   0   0   1   1   -1   x1^2 - 2*x1 + 1   x1^3 - 2*x1^2 + 1   x1^7 - 6*x1^6 + 13*x1^5 - 11*x1^4 + 5*x1^2 - 2*x1   x1^2 - 2*x1   x1^5 - 4*x1^4 + 4*x1^3 + x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 1 generator
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 - x1 - 1, x1 - 2, x1^2 - 3*x1 + 3, x1^4 - 4*x1^3 + 6*x1^2 - 3*x1 - 1, x1^3 - 3*x1^2 + 2*x1 + 1, x1^3 - 2*x1^2 + x1 - 1, x1^4 - 3*x1^3 + 3*x1^2 - x1 - 1, x1^5 - 4*x1^4 + 5*x1^3 - x1^2 - x1 - 1, x1]