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