The realization space is
  [1   1   0   0   1   1                               0                                                  x1^2*x2^2 - x1^2*x2 + x1*x2^2 - x2^3                     x2^2                x2    1]
  [0   1   1   0   0   1   x1^2*x2 - x1^2 + x1*x2 - x2^2   x1^3*x2^2 - 2*x1^3*x2 + x1^3 + 2*x1^2*x2^2 - 2*x1^2*x2 - x1*x2^3 + 2*x1*x2^2 - x2^3   x1^2*x2 - x1^2 + x1*x2   x1*x2 - x1 + x2   x1]
  [0   0   0   1   1   1                 x1*x2^2 - x1*x2                                 x1^2*x2^3 - 2*x1^2*x2^2 + x1^2*x2 + x1*x2^3 - x1*x2^2   x1*x2^2 - x1*x2 + x2^2              x2^2   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, x2, x2 - 1, x1, x1*x2 - x1 + x2^2, x1*x2 - x1 + x2, x1^2*x2 - x1^2 + x1*x2^3 - x1*x2^2 + x1*x2 + x2^3 - x2^2, x1^2*x2 - x1^2 + x1*x2^3 - 2*x1*x2^2 + 2*x1*x2 - x2^2, 2*x1*x2 - x1 - x2^2, x1^2 - x1*x2 + x2^2, x1 - 1, x1 + x2 - 1, x1^2*x2 - x1^2 + x1*x2^2 - x2^3, x1^2*x2 - x1^2 + x1*x2 - x2^2, x1^2*x2^2 - 3*x1^2*x2 + 2*x1^2 + x1*x2^2 - 2*x1*x2 + x2^2, x1^2*x2 - x1^2 + x1*x2^2 - x2^2]