The realization space is
  [1   0   1                 1   1   0         1   1         1                 0                 1]
  [0   1   1   x1^2 + 2*x1 - 1   0   0         0   1   -x1 + 1                 1   x1^2 + 2*x1 - 1]
  [0   0   0                 0   1   1   -x1 + 1   1        x1   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 + 2*x1^2 - 3*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1^4 + 5*x1^3 + 4*x1^2 - 6*x1 + 1, x1^2 + 3*x1 - 1, x1^4 + 5*x1^3 + 3*x1^2 - 9*x1 + 2, x1, x1^4 + 5*x1^3 + 4*x1^2 - 6*x1 + 2, x1^4 + 5*x1^3 + 4*x1^2 - 7*x1 + 2, x1^4 + 5*x1^3 + 3*x1^2 - 9*x1 + 3, x1^2 + 3*x1 - 2, x1 - 1, 2*x1 - 1, x1^2 + x1 - 1, x1^2 + 2*x1 - 2, x1^2 + 2*x1 - 1, x1^3 + x1^2 - 5*x1 + 2, x1 + 3, x1^4 + 6*x1^3 + 6*x1^2 - 8*x1 + 2, x1^3 + 3*x1^2 - 1, x1 + 2, x1^4 + 5*x1^3 + 4*x1^2 - 5*x1 + 2, x1^3 + 2*x1^2 - 2*x1 + 1]