The realization space is
  [1   1   0   0   1   1                               0                               x1 + x2 - 3                    x1 + x2 - 3                    x1 + x2 - 3    1]
  [1   0   1   0   1   0                          x2 - 1              x1^2 + x1*x2 - 3*x1 - x2 + 1   x1^2 + x1*x2 - 3*x1 - x2 + 1            x1^2 + x1*x2 - 3*x1   x1]
  [0   0   0   1   1   1   -x1^2 - x1*x2 + 3*x1 + x2 - 1   x1^2 + 2*x1*x2 - 5*x1 + x2^2 - 5*x2 + 6   x1*x2 - x1 + x2^2 - 3*x2 + 2   x1*x2 - x1 + x2^2 - 3*x2 + 2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 3 generators
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1 - 2, x1, x1^2*x2 + x1*x2^2 - 2*x1*x2 - x1 - x2 + 1, x1*x2 + x2^2 - 2*x2 - 1, x1^2 + x1*x2 - 2*x1 - 1, x1 + x2 - 2, x1^4 + 2*x1^3*x2 - 6*x1^3 + x1^2*x2^2 - 7*x1^2*x2 + 10*x1^2 - x1*x2^2 + 4*x1*x2 - 3*x1 - x2^2 + 2*x2 - 1, x1^2 + x1*x2 - 3*x1 - x2 + 1, x1^4 + x1^3*x2 - 7*x1^3 - 5*x1^2*x2 + 17*x1^2 + 8*x1*x2 - 16*x1 + x2^2 - 6*x2 + 5, x1^3 + x1^2*x2 - 6*x1^2 - 3*x1*x2 + 11*x1 + x2^2 - 5, x1^3 + 2*x1^2*x2 - 6*x1^2 + x1*x2^2 - 8*x1*x2 + 11*x1 - x2^2 + 6*x2 - 5, x1^4 + x1^3*x2 - 6*x1^3 - 4*x1^2*x2 + 12*x1^2 + 6*x1*x2 - 10*x1 + x2^2 - 6*x2 + 5, x1^5 + 2*x1^4*x2 - 8*x1^4 + x1^3*x2^2 - 10*x1^3*x2 + 21*x1^3 - x1^2*x2^2 + 10*x1^2*x2 - 17*x1^2 + x1*x2^3 - 7*x1*x2^2 + 11*x1*x2 - 5*x1 - x2^3 + 7*x2^2 - 11*x2 + 5, x1^2 - 3*x1 + x2 + 1, x1 + x2 - 1, x1^3 + x1^2*x2 - 3*x1^2 - x1*x2 + x1 + x2^2 - x2, x1^3 + x1^2*x2 - 4*x1^2 - 2*x1*x2 + 4*x1 + x2^2 - x2, x1^2 - 2*x1 + x2 - 1, x2 - 1, x1 - x2, x2, x1*x2 - 2*x1 + x2^2 - 4*x2 + 5, x1^4 + x1^3*x2 - 6*x1^3 - 4*x1^2*x2 + 12*x1^2 + 5*x1*x2 - 9*x1 + x2^2 - 4*x2 + 3, x1^4 + x1^3*x2 - 5*x1^3 - 3*x1^2*x2 + 7*x1^2 + 3*x1*x2 - 3*x1 + x2^2 - 4*x2 + 3, x1^3 + x1^2*x2 - 4*x1^2 - x1*x2 + x1 + x2^2 - 4*x2 + 7, x1^4 + 2*x1^3*x2 - 7*x1^3 + x1^2*x2^2 - 9*x1^2*x2 + 16*x1^2 - x1*x2^2 + 9*x1*x2 - 12*x1 + x2^3 - 3*x2^2 + x2 + 1, x1^4 + 2*x1^3*x2 - 6*x1^3 + x1^2*x2^2 - 7*x1^2*x2 + 10*x1^2 + 2*x1*x2 - 2*x1 + x2^3 - 4*x2^2 + 5*x2 - 2, x1^4 + 2*x1^3*x2 - 6*x1^3 + x1^2*x2^2 - 7*x1^2*x2 + 10*x1^2 + x1*x2 - x1 + x2^3 - 5*x2^2 + 9*x2 - 5, x1^2 + 2*x1*x2 - 5*x1 + x2^2 - 4*x2 + 5, x1^2 - 2*x1 - x2^2 + 3*x2 - 2, x1 + x2 - 3, x1^5 + 3*x1^4*x2 - 9*x1^4 + 3*x1^3*x2^2 - 20*x1^3*x2 + 29*x1^3 + x1^2*x2^3 - 13*x1^2*x2^2 + 43*x1^2*x2 - 39*x1^2 - x1*x2^3 + 12*x1*x2^2 - 29*x1*x2 + 18*x1 + x2^4 - 4*x2^3 + 4*x2^2 - 1, x1^5 + 3*x1^4*x2 - 9*x1^4 + 3*x1^3*x2^2 - 20*x1^3*x2 + 29*x1^3 + x1^2*x2^3 - 13*x1^2*x2^2 + 43*x1^2*x2 - 39*x1^2 - x1*x2^3 + 11*x1*x2^2 - 27*x1*x2 + 17*x1 + x2^4 - 5*x2^3 + 9*x2^2 - 7*x2 + 2, x1^5 + 3*x1^4*x2 - 9*x1^4 + 3*x1^3*x2^2 - 19*x1^3*x2 + 28*x1^3 + x1^2*x2^3 - 11*x1^2*x2^2 + 35*x1^2*x2 - 33*x1^2 + 3*x1*x2^2 - 10*x1*x2 + 7*x1 + x2^4 - 6*x2^3 + 14*x2^2 - 14*x2 + 5, x1^3 + 2*x1^2*x2 - 6*x1^2 + 2*x1*x2^2 - 9*x1*x2 + 11*x1 + x2^3 - 5*x2^2 + 9*x2 - 5, x1^3 + 2*x1^2*x2 - 6*x1^2 - 4*x1*x2 + 8*x1 - x2^3 + 4*x2^2 - 5*x2 + 2, x1^5 + 3*x1^4*x2 - 9*x1^4 + 3*x1^3*x2^2 - 18*x1^3*x2 + 27*x1^3 + x1^2*x2^3 - 9*x1^2*x2^2 + 27*x1^2*x2 - 27*x1^2 + x1*x2^3 - 4*x1*x2^2 + 5*x1*x2 - 2*x1 + x2^4 - 6*x2^3 + 14*x2^2 - 14*x2 + 5, x1^5 + 3*x1^4*x2 - 9*x1^4 + 3*x1^3*x2^2 - 18*x1^3*x2 + 27*x1^3 + x1^2*x2^3 - 9*x1^2*x2^2 + 27*x1^2*x2 - 27*x1^2 + x1*x2^3 - 5*x1*x2^2 + 7*x1*x2 - 3*x1 + x2^4 - 7*x2^3 + 19*x2^2 - 21*x2 + 8, 2*x1^3 + 4*x1^2*x2 - 12*x1^2 + 3*x1*x2^2 - 16*x1*x2 + 21*x1 + x2^3 - 6*x2^2 + 13*x2 - 8, x1^3 + 2*x1^2*x2 - 6*x1^2 + 2*x1*x2^2 - 10*x1*x2 + 12*x1 + x2^3 - 6*x2^2 + 13*x2 - 8]