The realization space is
  [1   0   1                                          x3   0   1    0             1                                              x3             1    1]
  [0   1   1   x1*x3 + x1 - x2^2 - x2*x3 + 2*x2 + x3 - 2   0   0    1             1       x1*x3 + x1 - x2^2 - x2*x3 + 2*x2 + x3 - 2            x1   x2]
  [0   0   0                                           0   1   1   -1   x2 + x3 - 1   -x1 + x2^2 + 2*x2*x3 - 2*x2 + x3^2 - 2*x3 + 2   x2 + x3 - 1   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal with 4 generators
avoiding the zero loci of the polynomials
RingElem[x1*x3 - x2^2 - x2*x3 + x2, x2 - 1, x1*x3 - x2^2 - x2*x3 + 2*x2 - 1, x1 - x2, x1*x3 - x1 - x2^2 - x2*x3 + 2*x2, x1 - 1, x1 - x2^2 - x2*x3 + 2*x2 + x3 - 2, x1 - x2^2 - 2*x2*x3 + 2*x2 + 2*x3 - 2, x1*x2 + x1*x3^2 + x1*x3 - x1 - x2^3 - 3*x2^2*x3 + 3*x2^2 - 2*x2*x3^2 + 6*x2*x3 - 4*x2 + x3^2 - 4*x3 + 2, x1*x3 + x1 - x2^2 - 2*x2*x3 + 2*x2 + x3 - 2, x1 - x2^2 - 2*x2*x3 + 2*x2 - x3^2 + 2*x3 - 2, x1*x2 + x1*x3^2 - x1 - x2^3 - 3*x2^2*x3 + 3*x2^2 - 2*x2*x3^2 + 6*x2*x3 - 4*x2 + x3^2 - 3*x3 + 2, x2 + x3, x2 + x3 - 1, x1*x3 + x1 - x2^2 - 2*x2*x3 + 2*x2 - x3^2 + x3 - 2, x2, x3 - 1, x1*x3^2 - x1 - x2^2*x3 + x2^2 - x2*x3^2 + 4*x2*x3 - 2*x2 + x3^2 - 3*x3 + 2, x3, x1*x3 + x1 - x2^2 - x2*x3 + 2*x2 + x3 - 2, x1*x3 + x1 - x2^2 - x2*x3 + 2*x2 - 2, x1 + x2 + x3 - 1, x1 + x2 + x3 - 2, x2 + x3 - 2, x1, x1*x2*x3 + x1*x2 + x1*x3^2 - 2*x1 - x2^3 - 2*x2^2*x3 + 4*x2^2 - x2*x3^2 + 5*x2*x3 - 6*x2 + x3^2 - 4*x3 + 4, x1*x2*x3 + x1*x2 + x1*x3^2 - x2^3 - 2*x2^2*x3 + 2*x2^2 - x2*x3^2 + 2*x2*x3 - 2*x2 - x3, x1 - x2^2 - 2*x2*x3 + 2*x2 - x3^2 + 3*x3 - 2, x1*x2*x3 + x1*x2 + x1*x3^2 - x1*x3 - 2*x1 - x2^3 - 2*x2^2*x3 + 4*x2^2 - x2*x3^2 + 5*x2*x3 - 6*x2 + x3^2 - 3*x3 + 4]