The realization space is
  [1   1   0   0   1   1                           0                     x1 - 2                     x1 - 2                 x1 - 2                 x1 - 2]
  [1   0   1   0   1   0                      x1 - 2   2*x1^3 - 11*x1^2 + 12*x1   2*x1^3 - 11*x1^2 + 12*x1   x1^3 - 5*x1^2 + 5*x1   x1^3 - 5*x1^2 + 5*x1]
  [0   0   0   1   1   1   -x1^3 + 5*x1^2 - 4*x1 - 2   x1^3 - 5*x1^2 + 4*x1 + 1                         -1                     -1            x1^2 - 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^4 - 7*x1^3 + 14*x1^2 - 8*x1 - 1)
avoiding the zero loci of the polynomials
RingElem[x1^3 - 5*x1^2 + 4*x1 + 2, x1^2 - 5*x1 + 5, x1, x1 - 2, x1^2 - 6*x1 + 7, x1^4 - 8*x1^3 + 19*x1^2 - 11*x1 - 5, x1 - 4, x1^5 - 10*x1^4 + 36*x1^3 - 57*x1^2 + 38*x1 - 7, x1^5 - 12*x1^4 + 50*x1^3 - 86*x1^2 + 56*x1 - 6, x1^7 - 13*x1^6 + 65*x1^5 - 152*x1^4 + 151*x1^3 - 20*x1^2 - 36*x1 - 4, x1^4 - 8*x1^3 + 20*x1^2 - 14*x1 - 2, x1^7 - 13*x1^6 + 65*x1^5 - 153*x1^4 + 159*x1^3 - 39*x1^2 - 22*x1 - 4, x1^5 - 9*x1^4 + 30*x1^3 - 43*x1^2 + 23*x1 - 1, x1^6 - 12*x1^5 + 51*x1^4 - 93*x1^3 + 70*x1^2 - 12*x1 - 4, x1^6 - 10*x1^5 + 33*x1^4 - 35*x1^3 - 8*x1^2 + 20*x1 + 4, x1^5 - 10*x1^4 + 34*x1^3 - 42*x1^2 + 6*x1 + 14, x1^5 - 10*x1^4 + 33*x1^3 - 35*x1^2 - 9*x1 + 24, x1^6 - 10*x1^5 + 34*x1^4 - 42*x1^3 + 5*x1^2 + 18*x1 - 4, x1^3 - 4*x1^2 + 2*x1 + 2, x1 - 1, x1^3 - 5*x1^2 + 4*x1 + 1, x1^7 - 12*x1^6 + 53*x1^5 - 108*x1^4 + 110*x1^3 - 60*x1^2 + 16*x1 + 4, x1^6 - 12*x1^5 + 53*x1^4 - 107*x1^3 + 103*x1^2 - 46*x1 + 10, x1^7 - 12*x1^6 + 53*x1^5 - 107*x1^4 + 102*x1^3 - 41*x1^2 + 2*x1 + 4, x1^3 - 6*x1^2 + 8*x1 - 2, x1^6 - 11*x1^5 + 42*x1^4 - 64*x1^3 + 32*x1^2 + 4, x1^5 - 11*x1^4 + 43*x1^3 - 71*x1^2 + 46*x1 - 6, x1^6 - 11*x1^5 + 43*x1^4 - 71*x1^3 + 45*x1^2 - 2*x1 - 4, x1^4 - 8*x1^3 + 19*x1^2 - 12*x1 - 2, x1^3 - 6*x1^2 + 9*x1 - 3, 2*x1^3 - 11*x1^2 + 11*x1 + 2, 2*x1 - 3, 2*x1^6 - 22*x1^5 + 83*x1^4 - 121*x1^3 + 48*x1^2 + 14*x1 + 4, 2*x1^5 - 22*x1^4 + 83*x1^3 - 121*x1^2 + 47*x1 + 18, 2*x1^6 - 22*x1^5 + 84*x1^4 - 128*x1^3 + 61*x1^2 + 12*x1 - 4, x1^4 - 9*x1^3 + 25*x1^2 - 19*x1 - 2, x1^2 - x1 - 1, 2*x1^6 - 22*x1^5 + 85*x1^4 - 135*x1^3 + 76*x1^2 + 2*x1 - 4, 2*x1^5 - 14*x1^4 + 29*x1^3 - 19*x1^2 - x1 + 2, x1^3 - 6*x1^2 + 6*x1 + 1, x1^3 - 4*x1^2 + 3*x1 + 1, x1^4 - 6*x1^3 + 8*x1^2 - 2]