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