The realization space is
  [1   0   1   0   1    0                  1        1                  1                 1]
  [0   1   1   0   0    1                  1   x1 - 2    x1^2 - 3*x1 + 1   x1^2 - 3*x1 + 1]
  [0   0   0   1   1   -1   -x1^2 + 3*x1 - 1        1   -x1^2 + 3*x1 - 1                x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 - 5*x1^2 + 7*x1 - 1, -x1^6 + 10*x1^5 - 39*x1^4 + 74*x1^3 - 68*x1^2 + 24*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1^2 - 3*x1 + 1, x1 - 3, x1, x1 - 2, x1^4 - 6*x1^3 + 11*x1^2 - 5*x1 + 1, 2*x1^2 - 5*x1 + 1, x1^2 - 2*x1 - 1]