The realization space is
  [1    1   1   1   0   x1 - 1   0    1         x1^2 - 2*x1 + 1          x1^2*x2 - 2*x1*x2 + x2         x1^2*x2 - 2*x1*x2 + x2]
  [1   x1   0   0   1      -x1   0    1              -x1^2 + x1           x1^2*x2 - 2*x1^2 + x1          x1^2*x2 - 2*x1^2 + x1]
  [1   x1   0   1   0        0   1   x2   x1^2*x2 - 2*x1^2 + x1   x1^2*x2^2 - 2*x1^2*x2 + x1*x2   x1^2*x2^2 - 2*x1*x2^2 + x2^2]
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, 2*x1 - 1, x2, x1, x1^2*x2 - 3*x1*x2 + 2*x1 + x2 - 1, x1*x2 - 2*x1 + 1, x2 - 1, x1^3*x2^2 - 2*x1^3*x2 + 3*x1^3 - 2*x1^2*x2^2 - 3*x1^2 + 3*x1*x2^2 + x1 - x2^2, x1^2*x2^2 - 2*x1^2*x2 + 2*x1^2 - x1*x2^2 - x1 + x2^2, x1^2*x2^2 - 3*x1^2*x2 + 3*x1^2 - x1*x2^2 + 2*x1*x2 - 3*x1 + x2^2 - x2 + 1, x1*x2^2 - x1*x2 + x1 - x2^2, x1*x2^2 - 2*x1*x2 + 2*x1 - x2^2 + x2 - 1, x1^2*x2^2 - x1^2*x2 + 2*x1^2 - 2*x1*x2^2 - x1 + x2^2, x1 - 1, x1^2*x2 - 3*x1^2 + 3*x1 - 1, x1*x2^2 - 3*x1*x2 + x1 + 2*x2 - 1, x1^2*x2^2 - 4*x1^2*x2 + 2*x1^2 + 4*x1*x2 - 3*x1 - x2 + 1]