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