The realization space is
  [1   1   0                      x1 - 1   0   1   1                           0                      x1 - 1         1      x1 - 1]
  [0   1   1   -x1^3 - 4*x1^2 + 4*x1 - 1   0   0   1                      x1 - 1   -x1^3 - 4*x1^2 + 4*x1 - 1   -x1 + 1       -x1^2]
  [0   0   0                           0   1   1   1   -x1^3 - 3*x1^2 + 5*x1 - 2   -x1^3 - 3*x1^2 + 5*x1 - 2        x1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^4 + 3*x1^3 - 6*x1^2 + 4*x1 - 1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, x1^3 + 3*x1^2 - 5*x1 + 2, x1^3 + 4*x1^2 - 6*x1 + 2, 2*x1^4 + 6*x1^3 - 13*x1^2 + 7*x1 - 1, x1^4 + 4*x1^3 - 3*x1^2 - 3*x1 + 2, x1^3 + 3*x1^2 - 4*x1 + 1, 2*x1^5 + 6*x1^4 - 12*x1^3 + 4*x1^2 + 2*x1 - 1, x1^5 + 6*x1^4 + x1^3 - 21*x1^2 + 19*x1 - 5, x1^5 + 4*x1^4 - 4*x1^3 - 4*x1^2 + 6*x1 - 2, x1^6 + 6*x1^5 - 23*x1^3 + 27*x1^2 - 12*x1 + 2, x1^5 + 3*x1^4 - 6*x1^3 + 5*x1^2 - 3*x1 + 1, x1^5 + 4*x1^4 - 4*x1^3 - 3*x1^2 + 4*x1 - 1, x1^2 + x1 - 1, x1^4 + 3*x1^3 - 7*x1^2 + 5*x1 - 1, x1^3 + 4*x1^2 - 4*x1 + 1, x1^2 + 4*x1 - 3, x1^2 + 4*x1 - 2, x1^2 + 3*x1 - 2, 2*x1^3 + 6*x1^2 - 11*x1 + 4, x1^6 + 6*x1^5 + 3*x1^4 - 16*x1^3 + 6*x1^2 + 4*x1 - 2, x1^3 + 3*x1^2 - 6*x1 + 3, x1^5 + 6*x1^4 + 2*x1^3 - 18*x1^2 + 14*x1 - 3, x1^3 + 4*x1^2 - 2*x1 - 1, x1^6 + 7*x1^5 + 4*x1^4 - 27*x1^3 + 24*x1^2 - 8*x1 + 1, x1^6 + 7*x1^5 + 5*x1^4 - 25*x1^3 + 16*x1^2 - x1 - 1, x1^6 + 7*x1^5 + 3*x1^4 - 29*x1^3 + 32*x1^2 - 15*x1 + 3]