The realization space is
  [1   1   0   0   1   1               0               1                           1                       x1^2 - x1 + 1                     x1^2 - 2*x1 + 1]
  [1   0   1   0   1   0          x1 - 1              x1            -x1^2 + 2*x1 - 1                  x1^3 - 2*x1^2 + x1                  x1^3 - 2*x1^2 + x1]
  [0   0   0   1   1   1   x1^2 - x1 + 1   x1^2 - x1 + 1   -x1^3 + 2*x1^2 - 2*x1 + 1   x1^4 - 2*x1^3 + 3*x1^2 - 2*x1 + 1   x1^4 - 2*x1^3 + 3*x1^2 - 2*x1 + 1]
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, x1^2 - x1 + 1, x1^4 - 3*x1^3 + 5*x1^2 - 3*x1 + 1, x1^3 - x1^2 + 1, x1 - 1, x1^2 - 2*x1 + 2, x1^3 - 2*x1^2 + 3*x1 - 1, x1^3 - x1 + 1, x1^2 + 1, x1^3 - 3*x1^2 + 2*x1 - 1]