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