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