The realization space is
  [1   0   1                               x1*x2^2 - x1*x2 + x2^3 - x2^2   0   1    0             1                                      x1*x2^2 - x1*x2 + x2^3 - x2^2                                               x1*x2^2 - 2*x1*x2 + x1 + x2^3 - 2*x2^2 + x2    1]
  [0   1   1   -x1^4 - 2*x1^3*x2 + 2*x1^3 - x1^2*x2^2 + 2*x1^2*x2 - x1^2   0   0    1             1          -x1^4 - 2*x1^3*x2 + 2*x1^3 - x1^2*x2^2 + 2*x1^2*x2 - x1^2                        -x1^4 - 2*x1^3*x2 + 2*x1^3 - x1^2*x2^2 + x1^2*x2 - x1*x2^2 + x1*x2   x1]
  [0   0   0                                                           0   1   1   -1   x1 + x2 - 1   -x1^3*x2 - 2*x1^2*x2^2 + 2*x1^2*x2 - x1*x2^3 + 2*x1*x2^2 - x1*x2   -x1^3*x2 + x1^3 - 2*x1^2*x2^2 + 4*x1^2*x2 - 2*x1^2 - x1*x2^3 + 3*x1*x2^2 - 3*x1*x2 + 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[x1^3 + 2*x1^2*x2 - 2*x1^2 + 2*x1*x2^2 - 3*x1*x2 + x1 + x2^3 - x2^2, x1, x1 + x2 - 1, x1^3 + 2*x1^2*x2 - 2*x1^2 + x1*x2^2 - 3*x1*x2 + x1 - x2^2, x1 - 1, x2 - 1, x1 + x2, x1^4 + 2*x1^3*x2 - 2*x1^3 + 2*x1^2*x2^2 - 3*x1^2*x2 + x1^2 + 2*x1*x2^3 - 2*x1*x2^2 + x2^4 - x2^3, x2, x1^4 + 2*x1^3*x2 - 2*x1^3 + x1^2*x2^2 - 2*x1^2*x2 + x1^2 + x1*x2^2 - x1*x2 + x2^3 - x2^2, x1^3 + 2*x1^2*x2 - 2*x1^2 + x1*x2^2 - x1*x2 + x2^2 - x2, x1^2 + 2*x1*x2 - 2*x1 + x2^2 - x2, x1^3 + 2*x1^2*x2 - 2*x1^2 + x1*x2^2 - 2*x1*x2 + x1 + x2 - 1, x1^3 + x1^2*x2 - x1^2 + x1*x2 - x1 + x2^2 - x2, x1^3 + 3*x1^2*x2 - 3*x1^2 + 3*x1*x2^2 - 5*x1*x2 + 2*x1 + x2^3 - 2*x2^2 + 2*x2 - 1, x1^3 + x1^2*x2^2 + x1^2*x2 - 2*x1^2 + 2*x1*x2^3 - 2*x1*x2^2 - x1*x2 + x1 + x2^4 - 2*x2^3 + 2*x2^2 - x2, x1^3 + 2*x1^2*x2 - 2*x1^2 + x1*x2^2 - 2*x1*x2 + x1 + x2^2 - x2, x1 + x2 - 2, x1^5 + 3*x1^4*x2 - 4*x1^4 + 3*x1^3*x2^2 - 8*x1^3*x2 + 5*x1^3 + x1^2*x2^3 - 4*x1^2*x2^2 + 5*x1^2*x2 - 2*x1^2 - x1*x2^2 + x1*x2 - x2^3 + x2^2]