The realization space is
  [1   1   0   x1^2 - 3*x1 + 1   0   1   1                   0    2*x1^3 - 7*x1^2 + 5*x1 - 1    1      2*x1 - 1]
  [1   0   1      -2*x1^2 + x1   0   1   0   2*x1^2 - 3*x1 + 1         -4*x1^3 + 4*x1^2 - x1   x1   2*x1^2 - x1]
  [0   0   0                 0   1   1   1     x1^2 - 3*x1 + 1   x1^4 - 4*x1^3 + 4*x1^2 - x1   x1     x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 1 generator
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 - 3*x1 + 1, 3*x1 - 1, x1^2 + 2*x1 - 1, x1^3 - 2*x1^2 + 3*x1 - 1, 2*x1 - 1, x1^3 - 9*x1^2 + 6*x1 - 1, 3*x1^2 - 6*x1 + 2]