The realization space is
  [1   0   1            1   0   1    1    0                  1                1                1]
  [0   1   1   -x1^2 + x1   0   0    0    1                  1   -x1^2 + x1 - 1   -x1^2 + x1 - 1]
  [0   0   0            0   1   1   x1   -1   -x1^2 + 2*x1 - 2                1               x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 - 2*x1^2 + 3*x1 - 1, -x1^7 + 4*x1^6 - 10*x1^5 + 15*x1^4 - 17*x1^3 + 13*x1^2 - 8*x1 + 2)
avoiding the zero loci of the polynomials
RingElem[x1^2 - x1 + 1, x1 - 1, x1^2 - x1 + 2, x1^2 - 2*x1 + 2, x1, x1^3 - x1^2 + 1, x1^2 - 2*x1 + 3, x1^4 - 2*x1^3 + 4*x1^2 - 2*x1 + 1, x1^3 - x1^2 + 2*x1 - 1, x1^4 - 3*x1^3 + 5*x1^2 - 3*x1 + 1]