The realization space is
  [1   1   0                       -x1*x2 + x2^2   0   1   1    0                       -x1*x2 + x2^2                               -x1 + x2    1]
  [0   1   1   -x1^2 + x1 - 2*x2^3 + 3*x2^2 - x2   0   0   1   x1   -x1^2 + x1 - 2*x2^3 + 3*x2^2 - x2            -x1^2 + x1*x2 - x2^3 + x2^2   x1]
  [0   0   0                                   0   1   1   1   x2                     -x1*x2^2 + x2^3   x1^2 - x1*x2 - x1 + x2^3 - x2^2 + x2   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[x1^3 - x1^2 + x1*x2^3 - 2*x1*x2^2 + x1*x2 + x2^4 - x2^3, x1 + x2 - 1, x1^2 - x1*x2 - x1 + x2^3 - x2^2 + x2, x1^2 - x1 + x2^3 - 2*x2^2 + x2, x1^4 - x1^3*x2 - 2*x1^3 + x1^2*x2^3 - 4*x1^2*x2^2 + 3*x1^2*x2 + x1^2 + x1*x2^3 + 3*x1*x2^2 - 2*x1*x2 - 3*x2^5 + 5*x2^4 - 4*x2^3 + x2^2, x2 - 1, x2, x1^2 - x1*x2 + x2^3 - x2^2, x1^2 - x1*x2 - x1 - 2*x2^2 + x2, x1^2 - x1 + 2*x2^3 - 3*x2^2 + x2, x1 - x2, x1 - 1, 2*x1^2*x2 - x1^2 - 2*x1*x2^2 - x1*x2 + x1 + 2*x2^4 - 4*x2^3 + 4*x2^2 - x2, x1, 2*x1^2*x2 - x1^2 - x1*x2^2 - x1*x2 + x1 + 2*x2^4 - 5*x2^3 + 4*x2^2 - x2, x1^2 - x1*x2 - x1 + 2*x2^3 - 2*x2^2 + x2, x1^2 + x1*x2^2 - x1*x2 - x1 + x2^3 - 2*x2^2 + x2, x1^2 - x1*x2 - x1 + x2^3 - 2*x2^2 + x2, x1^4 + x1^3*x2^2 - 3*x1^3*x2 - x1^3 + x1^2*x2^3 - x1^2*x2^2 + 3*x1^2*x2 + x1*x2^5 - 4*x1*x2^4 + 4*x1*x2^3 - 2*x1*x2^2 + x2^6 - 2*x2^5 + x2^4, x1^3 + x1^2*x2 - 2*x1^2 + x1*x2^3 - 3*x1*x2^2 + x1*x2 + x1 + x2^4 - 3*x2^3 + 3*x2^2 - x2, x1 + x2, x1^3 + x1*x2^3 - 2*x1*x2^2 - x1*x2 + x2^4 - x2^3 + x2^2, 2*x1^2 - 2*x1*x2 - x1 + 2*x2^3 - 2*x2^2 + x2, x1^4 - 3*x1^3*x2 - x1^3 + 3*x1^2*x2^3 + 3*x1^2*x2 - 4*x1*x2^4 + 2*x1*x2^3 - 2*x1*x2^2 + 2*x2^6 - 3*x2^5 + 2*x2^4, x1^2*x2 - x1^2 - x1*x2^2 + x1*x2 + x1 - 2*x2^3 + 2*x2^2 - x2, x1^2*x2 - 2*x1^2 - x1*x2^2 + x1*x2 + x1 - 2*x2^3 + 3*x2^2 - x2, x1^2*x2 - 2*x1^2 - x1*x2^2 + 2*x1*x2 + x1 - 2*x2^3 + 2*x2^2 - x2, x1^2 - x1*x2^2 - x1 + 3*x2^3 - 3*x2^2 + x2, 2*x1^2 - x1*x2 - x1 + 2*x2^3 - 3*x2^2 + x2]