The realization space is
  [1   1   0   1   0   0        1                         x1^3 - 2*x1^2           x1           x1             x1^2]
  [1   0   1   0   1   0   x1 - 1        x1^2*x2^2 - 3*x1*x2^2 + 2*x2^2   x1*x2 - x2   x1*x2 - x2   x1*x2^2 - x2^2]
  [1   0   1   1   0   1       x1   x1^2*x2^2 - x1^2 - 2*x1*x2^2 + x2^2        x1*x2         x1^2          x1^2*x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x1^2 - x1*x2 + x2, x2, x1 - 1, x1^2*x2 - 2*x1*x2 + x1 + x2, x2 - 1, x1^2 - x1*x2^2 + x2^2, x1 + x2, x1*x2 - x1 - x2, x1, x1^2 - x1 + x2, x1*x2 + x1 - x2, x1 - 2]