The realization space is [1 1 0 x1^2 0 1 1 0 x1^2 1 x1] [0 1 1 -2*x1^4 - x1^3 + 4*x1^2 - 4*x1 + 1 0 0 1 x1^2 -2*x1^4 - x1^3 + 4*x1^2 - 4*x1 + 1 -x1 + 1 -x1^2 + 2*x1 - 1] [0 0 0 0 1 1 1 2*x1^4 + x1^3 - 3*x1^2 + 3*x1 - 1 x1 - 1 x1 x1^2] in the multivariate polynomial ring in 1 variable over ZZ within the vanishing set of the ideal Ideal (2*x1^5 - x1^4 - 3*x1^3 + 6*x1^2 - 4*x1 + 1) avoiding the zero loci of the polynomials RingElem[x1, x1 - 1, 2*x1 - 1, x1^3 + x1^2 - x1 + 1, x1^3 - x1 + 1, 2*x1^6 + x1^5 - 3*x1^4 + 3*x1^3 + x1^2 - 2*x1 + 1, 2*x1^4 - 2*x1^2 + 3*x1 - 1, 2*x1^3 - x1^2 + 1, x1^2 + x1 - 1, 2*x1^6 - x1^5 - 3*x1^4 + 5*x1^3 - 2*x1^2 - x1 + 1, 4*x1^8 + 2*x1^7 - 10*x1^6 + 9*x1^5 + 5*x1^4 - 15*x1^3 + 13*x1^2 - 6*x1 + 1, 2*x1^6 - 3*x1^5 - 2*x1^4 + 10*x1^3 - 10*x1^2 + 5*x1 - 1, 2*x1^6 - x1^5 - x1^4 + 7*x1^3 - 7*x1^2 + 4*x1 - 1, 2*x1^2 - 2*x1 + 1, 2*x1^4 + x1^3 - 2*x1^2 + 3*x1 - 1, 2*x1^6 - x1^5 - x1^4 + 6*x1^3 - 7*x1^2 + 4*x1 - 1, x1^2 - x1 + 1, 2*x1^4 + x1^3 - 4*x1^2 + 4*x1 - 1, 2*x1^4 + x1^3 - 3*x1^2 + 4*x1 - 1, 2*x1^5 + x1^4 - 4*x1^3 + 3*x1^2 + x1 - 1, 2*x1^3 + x1^2 - 3*x1 + 3, 2*x1^4 - 3*x1^2 + 4*x1 - 1, 4*x1^8 + 2*x1^7 - 12*x1^6 + 10*x1^5 + 9*x1^4 - 21*x1^3 + 17*x1^2 - 7*x1 + 1, 4*x1^8 + 2*x1^7 - 12*x1^6 + 10*x1^5 + 9*x1^4 - 22*x1^3 + 18*x1^2 - 7*x1 + 1, 2*x1^2 - x1 + 1, 2*x1^5 - x1^4 - 3*x1^3 + 7*x1^2 - 5*x1 + 1, 2*x1^2 + 3*x1 - 1, 2*x1^6 - x1^5 - 4*x1^4 + 9*x1^3 - 8*x1^2 + 4*x1 - 1, 4*x1^8 + 4*x1^7 - 11*x1^6 + 8*x1^5 + 12*x1^4 - 22*x1^3 + 17*x1^2 - 7*x1 + 1, 4*x1^8 + 4*x1^7 - 13*x1^6 + 7*x1^5 + 14*x1^4 - 25*x1^3 + 18*x1^2 - 7*x1 + 1, 4*x1^8 + 4*x1^7 - 11*x1^6 + 8*x1^5 + 11*x1^4 - 22*x1^3 + 17*x1^2 - 7*x1 + 1, 2*x1^4 + x1^3 - 4*x1^2 + 5*x1 - 2, 2*x1^4 + x1^3 - 4*x1^2 + 3*x1 - 1, 4*x1^8 + 4*x1^7 - 11*x1^6 + 8*x1^5 + 11*x1^4 - 23*x1^3 + 18*x1^2 - 7*x1 + 1, 4*x1^8 + 4*x1^7 - 13*x1^6 + 7*x1^5 + 14*x1^4 - 26*x1^3 + 19*x1^2 - 7*x1 + 1]