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