The realization space is
  [1   0   1     2*x1 - 1   0   1    0        x1      2*x1 - 1                2*x1^2 - x1              2*x1^2 - 3*x1 + 1]
  [0   1   1   -x1^2 + x1   0   0    1        x1    -x1^2 + x1   x1^3 + 2*x1^2 - 3*x1 + 1   -x1^4 - 2*x1^3 + 3*x1^2 - x1]
  [0   0   0            0   1   1   -1   -x1 + 1   2*x1^2 - x1         -2*x1^2 + 3*x1 - 1           2*x1^3 - 3*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[x1^2 + x1 - 1, x1, x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^3 - x1^2 + 2*x1 - 1, x1^4 + 2*x1^2 - 3*x1 + 1, 2*x1 - 1, 3*x1^3 - x1^2 - 2*x1 + 1]