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