The realization space is
  [1   0   1   0   1   0        1                x1^3 - x1^2               x1^5 - 4*x1^4 + 7*x1^3 - 7*x1^2 + 4*x1 - 1                                  x1                                    x1^2 - x1]
  [0   1   1   1   1   0       x1           x1^3 - x1^2 + x1                                 x1^3 - 2*x1^2 + 2*x1 - 1                                x1^2                                x1^2 - x1 + 1]
  [0   0   0   1   1   1   x1 - 1   x1^3 - 2*x1^2 + 2*x1 - 1   x1^6 - 5*x1^5 + 11*x1^4 - 14*x1^3 + 11*x1^2 - 5*x1 + 1   x1^4 - 3*x1^3 + 4*x1^2 - 3*x1 + 1   x1^5 - 4*x1^4 + 7*x1^3 - 7*x1^2 + 4*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[x1^3 - 2*x1^2 + x1 - 1, x1 - 1, x1^2 - x1 + 1, x1^4 - 3*x1^3 + 4*x1^2 - 4*x1 + 1, x1 - 2, x1^2 - 2*x1 + 2, x1^3 - 3*x1^2 + 4*x1 - 3, x1, x1^3 - 3*x1^2 + 2*x1 - 1, x1^4 - 3*x1^3 + 3*x1^2 - 3*x1 + 1]