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