The realization space is
  [1   0   1     x1^2 - 3*x1 + 1   1   0          -x1^2   1         1   0     x1^2 - 3*x1 + 1]
  [0   1   1   3*x1^2 - 4*x1 + 1   0   0              0   1   -x1 + 1   1   3*x1^2 - 4*x1 + 1]
  [0   0   0                   0   1   1   -3*x1^2 + x1   1        x1   1        -3*x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 1 generator
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, 2*x1 - 1, 5*x1 - 2, 7*x1^2 - 8*x1 + 2, x1 - 1, x1^2 - 3*x1 + 1, 2, 2*x1^2 - 4*x1 + 1, 4*x1 - 1, 4*x1^2 - 7*x1 + 2]