-- Realization space of 01111111110111111110111111110111111011111111111011111101111101111011111111011111 R = QQ[b12,b13,b14,b15,b23,b24,b25,b34,b35,b45]; positivePolynomials = {-b12^2 + 1, -b13^2 + 1, -b14^2 + 1, -b15^2 + 1, -b23^2 + 1, -b24^2 + 1, -b25^2 + 1, -b34^2 + 1, -b35^2 + 1, -b45^2 + 1, 2*b12*b13*b23 - b12^2 - b13^2 - b23^2 + 1, 2*b12*b14*b24 - b12^2 - b14^2 - b24^2 + 1, 2*b12*b15*b25 - b12^2 - b15^2 - b25^2 + 1, 2*b13*b14*b34 - b13^2 - b14^2 - b34^2 + 1, 2*b13*b15*b35 - b13^2 - b15^2 - b35^2 + 1, 2*b14*b15*b45 - b14^2 - b15^2 - b45^2 + 1, 2*b23*b24*b34 - b23^2 - b24^2 - b34^2 + 1, 2*b23*b25*b35 - b23^2 - b25^2 - b35^2 + 1, 2*b24*b25*b45 - b24^2 - b25^2 - b45^2 + 1, 2*b34*b35*b45 - b34^2 - b35^2 - b45^2 + 1, b14^2*b23^2 - 2*b13*b14*b23*b24 + b13^2*b24^2 - 2*b12*b14*b23*b34 - 2*b12*b13*b24*b34 + b12^2*b34^2 + 2*b12*b13*b23 + 2*b12*b14*b24 + 2*b13*b14*b34 + 2*b23*b24*b34 - b12^2 - b13^2 - b14^2 - b23^2 - b24^2 - b34^2 + 1, b15^2*b23^2 - 2*b13*b15*b23*b25 + b13^2*b25^2 - 2*b12*b15*b23*b35 - 2*b12*b13*b25*b35 + b12^2*b35^2 + 2*b12*b13*b23 + 2*b12*b15*b25 + 2*b13*b15*b35 + 2*b23*b25*b35 - b12^2 - b13^2 - b15^2 - b23^2 - b25^2 - b35^2 + 1, b15^2*b24^2 - 2*b14*b15*b24*b25 + b14^2*b25^2 - 2*b12*b15*b24*b45 - 2*b12*b14*b25*b45 + b12^2*b45^2 + 2*b12*b14*b24 + 2*b12*b15*b25 + 2*b14*b15*b45 + 2*b24*b25*b45 - b12^2 - b14^2 - b15^2 - b24^2 - b25^2 - b45^2 + 1, b15^2*b34^2 - 2*b14*b15*b34*b35 + b14^2*b35^2 - 2*b13*b15*b34*b45 - 2*b13*b14*b35*b45 + b13^2*b45^2 + 2*b13*b14*b34 + 2*b13*b15*b35 + 2*b14*b15*b45 + 2*b34*b35*b45 - b13^2 - b14^2 - b15^2 - b34^2 - b35^2 - b45^2 + 1, b25^2*b34^2 - 2*b24*b25*b34*b35 + b24^2*b35^2 - 2*b23*b25*b34*b45 - 2*b23*b24*b35*b45 + b23^2*b45^2 + 2*b23*b24*b34 + 2*b23*b25*b35 + 2*b24*b25*b45 + 2*b34*b35*b45 - b23^2 - b24^2 - b25^2 - b34^2 - b35^2 - b45^2 + 1, -2*b15^2*b23*b24*b34 + 2*b14*b15*b23*b25*b34 + 2*b13*b15*b24*b25*b34 - 2*b13*b14*b25^2*b34 - 2*b12*b15*b25*b34^2 + 2*b14*b15*b23*b24*b35 - 2*b13*b15*b24^2*b35 - 2*b14^2*b23*b25*b35 + 2*b13*b14*b24*b25*b35 + 2*b12*b15*b24*b34*b35 + 2*b12*b14*b25*b34*b35 - 2*b12*b14*b24*b35^2 - 2*b14*b15*b23^2*b45 + 2*b13*b15*b23*b24*b45 + 2*b13*b14*b23*b25*b45 - 2*b13^2*b24*b25*b45 + 2*b12*b15*b23*b34*b45 + 2*b12*b13*b25*b34*b45 + 2*b12*b14*b23*b35*b45 + 2*b12*b13*b24*b35*b45 - 2*b12^2*b34*b35*b45 - 2*b12*b13*b23*b45^2 + b14^2*b23^2 + b15^2*b23^2 - 2*b13*b14*b23*b24 + b13^2*b24^2 + b15^2*b24^2 - 2*b13*b15*b23*b25 - 2*b14*b15*b24*b25 + b13^2*b25^2 + b14^2*b25^2 - 2*b12*b14*b23*b34 - 2*b12*b13*b24*b34 + b12^2*b34^2 + b15^2*b34^2 + b25^2*b34^2 - 2*b12*b15*b23*b35 - 2*b12*b13*b25*b35 - 2*b14*b15*b34*b35 - 2*b24*b25*b34*b35 + b12^2*b35^2 + b14^2*b35^2 + b24^2*b35^2 - 2*b12*b15*b24*b45 - 2*b12*b14*b25*b45 - 2*b13*b15*b34*b45 - 2*b23*b25*b34*b45 - 2*b13*b14*b35*b45 - 2*b23*b24*b35*b45 + b12^2*b45^2 + b13^2*b45^2 + b23^2*b45^2 + 2*b12*b13*b23 + 2*b12*b14*b24 + 2*b12*b15*b25 + 2*b13*b14*b34 + 2*b23*b24*b34 + 2*b13*b15*b35 + 2*b23*b25*b35 + 2*b14*b15*b45 + 2*b24*b25*b45 + 2*b34*b35*b45 - b12^2 - b13^2 - b14^2 - b15^2 - b23^2 - b24^2 - b25^2 - b34^2 - b35^2 - b45^2 + 1}; zeroPolynomials = { b12, -b14*b34 + b13, -b15*b45 + b14, -b15*b23^2 + b13*b23*b25 + b12*b23*b35 - b12*b25 - b13*b35 + b15, -b25*b35 + b23, b15^2*b23*b34 - b13*b15*b25*b34 - b14*b15*b23*b35 + 2*b13*b15*b24*b35 - b13*b14*b25*b35 - b12*b15*b34*b35 + b12*b14*b35^2 - b13*b15*b23*b45 + b13^2*b25*b45 - b12*b13*b35*b45 + b13*b14*b23 - b13^2*b24 - b15^2*b24 + b14*b15*b25 + b12*b13*b34 + b25*b34*b35 - b24*b35^2 + b12*b15*b45 + b23*b35*b45 - b12*b14 - b23*b34 - b25*b45 + b24, -b25*b34^2 + b24*b34*b35 + b23*b34*b45 - b23*b35 - b24*b45 + b25, b12*b14*b23 + b12*b13*b24 - b12^2*b34 - b13*b14 - b23*b24 + b34, -b13*b15 + b35, -b24*b25 + b45}; nonzeroPolynomials = {-b13*b23 + b12, -b14*b24 + b12, -b15*b25 + b12, b14*b23*b34 + b13*b24*b34 - b12*b34^2 - b13*b23 - b14*b24 + b12, b15*b23*b35 + b13*b25*b35 - b12*b35^2 - b13*b23 - b15*b25 + b12, b15*b24*b45 + b14*b25*b45 - b12*b45^2 - b14*b24 - b15*b25 + b12, b15*b25*b34^2 - b15*b24*b34*b35 - b14*b25*b34*b35 + b14*b24*b35^2 - b15*b23*b34*b45 - b13*b25*b34*b45 - b14*b23*b35*b45 - b13*b24*b35*b45 + 2*b12*b34*b35*b45 + b13*b23*b45^2 + b14*b23*b34 + b13*b24*b34 - b12*b34^2 + b15*b23*b35 + b13*b25*b35 - b12*b35^2 + b15*b24*b45 + b14*b25*b45 - b12*b45^2 - b13*b23 - b14*b24 - b15*b25 + b12, b13, -b12*b23 + b13, -b15*b35 + b13, b14*b23*b24 - b13*b24^2 + b12*b24*b34 - b12*b23 - b14*b34 + b13, b15*b23*b25 - b13*b25^2 + b12*b25*b35 - b12*b23 - b15*b35 + b13, b15*b34*b45 + b14*b35*b45 - b13*b45^2 - b14*b34 - b15*b35 + b13, -b15*b24*b25*b34 + b14*b25^2*b34 + b15*b24^2*b35 - b14*b24*b25*b35 - b15*b23*b24*b45 - b14*b23*b25*b45 + 2*b13*b24*b25*b45 - b12*b25*b34*b45 - b12*b24*b35*b45 + b12*b23*b45^2 + b14*b23*b24 - b13*b24^2 + b15*b23*b25 - b13*b25^2 + b12*b24*b34 + b12*b25*b35 + b15*b34*b45 + b14*b35*b45 - b13*b45^2 - b12*b23 - b14*b34 - b15*b35 + b13, b14, -b12*b24 + b14, -b13*b34 + b14, -b14*b23^2 + b13*b23*b24 + b12*b23*b34 - b12*b24 - b13*b34 + b14, b15*b24*b25 - b14*b25^2 + b12*b25*b45 - b12*b24 - b15*b45 + b14, b15*b34*b35 - b14*b35^2 + b13*b35*b45 - b13*b34 - b15*b45 + b14, -b15*b23*b25*b34 + b13*b25^2*b34 - b15*b23*b24*b35 + 2*b14*b23*b25*b35 - b13*b24*b25*b35 - b12*b25*b34*b35 + b12*b24*b35^2 + b15*b23^2*b45 - b13*b23*b25*b45 - b12*b23*b35*b45 - b14*b23^2 + b13*b23*b24 + b15*b24*b25 - b14*b25^2 + b12*b23*b34 + b15*b34*b35 - b14*b35^2 + b12*b25*b45 + b13*b35*b45 - b12*b24 - b13*b34 - b15*b45 + b14, b15, -b12*b25 + b15, -b13*b35 + b15, -b14*b45 + b15, -b15*b24^2 + b14*b24*b25 + b12*b24*b45 - b12*b25 - b14*b45 + b15, -b15*b34^2 + b14*b34*b35 + b13*b34*b45 - b13*b35 - b14*b45 + b15, 2*b15*b23*b24*b34 - b14*b23*b25*b34 - b13*b24*b25*b34 + b12*b25*b34^2 - b14*b23*b24*b35 + b13*b24^2*b35 - b12*b24*b34*b35 + b14*b23^2*b45 - b13*b23*b24*b45 - b12*b23*b34*b45 - b15*b23^2 - b15*b24^2 + b13*b23*b25 + b14*b24*b25 - b15*b34^2 + b12*b23*b35 + b14*b34*b35 + b12*b24*b45 + b13*b34*b45 - b12*b25 - b13*b35 - b14*b45 + b15, b23, -b12*b13 + b23, -b24*b34 + b23, -b14^2*b23 + b13*b14*b24 + b12*b14*b34 - b12*b13 - b24*b34 + b23, -b15^2*b23 + b13*b15*b25 + b12*b15*b35 - b12*b13 - b25*b35 + b23, b25*b34*b45 + b24*b35*b45 - b23*b45^2 - b24*b34 - b25*b35 + b23, b15^2*b24*b34 - b14*b15*b25*b34 - b14*b15*b24*b35 + b14^2*b25*b35 + 2*b14*b15*b23*b45 - b13*b15*b24*b45 - b13*b14*b25*b45 - b12*b15*b34*b45 - b12*b14*b35*b45 + b12*b13*b45^2 - b14^2*b23 - b15^2*b23 + b13*b14*b24 + b13*b15*b25 + b12*b14*b34 + b12*b15*b35 + b25*b34*b45 + b24*b35*b45 - b23*b45^2 - b12*b13 - b24*b34 - b25*b35 + b23, b24, -b12*b14 + b24, -b23*b34 + b24, -b25*b45 + b24, b13*b14*b23 - b13^2*b24 + b12*b13*b34 - b12*b14 - b23*b34 + b24, -b15^2*b24 + b14*b15*b25 + b12*b15*b45 - b12*b14 - b25*b45 + b24, b25*b34*b35 - b24*b35^2 + b23*b35*b45 - b23*b34 - b25*b45 + b24, b25, -b12*b15 + b25, -b23*b35 + b25, -b24*b45 + b25, b13*b15*b23 - b13^2*b25 + b12*b13*b35 - b12*b15 - b23*b35 + b25, b14*b15*b24 - b14^2*b25 + b12*b14*b45 - b12*b15 - b24*b45 + b25, -b14*b15*b23*b34 - b13*b15*b24*b34 + 2*b13*b14*b25*b34 + b12*b15*b34^2 + b14^2*b23*b35 - b13*b14*b24*b35 - b12*b14*b34*b35 - b13*b14*b23*b45 + b13^2*b24*b45 - b12*b13*b34*b45 + b13*b15*b23 + b14*b15*b24 - b13^2*b25 - b14^2*b25 - b25*b34^2 + b12*b13*b35 + b24*b34*b35 + b12*b14*b45 + b23*b34*b45 - b12*b15 - b23*b35 - b24*b45 + b25, b34, -b13*b14 + b34, -b23*b24 + b34, -b35*b45 + b34, -b15^2*b34 + b14*b15*b35 + b13*b15*b45 - b13*b14 - b35*b45 + b34, -b25^2*b34 + b24*b25*b35 + b23*b25*b45 - b23*b24 - b35*b45 + b34, b15^2*b23*b24 - b14*b15*b23*b25 - b13*b15*b24*b25 + b13*b14*b25^2 + 2*b12*b15*b25*b34 - b12*b15*b24*b35 - b12*b14*b25*b35 - b12*b15*b23*b45 - b12*b13*b25*b45 + b12^2*b35*b45 + b12*b14*b23 + b12*b13*b24 - b12^2*b34 - b15^2*b34 - b25^2*b34 + b14*b15*b35 + b24*b25*b35 + b13*b15*b45 + b23*b25*b45 - b13*b14 - b23*b24 - b35*b45 + b34, b35, -b23*b25 + b35, -b34*b45 + b35, b12*b15*b23 + b12*b13*b25 - b12^2*b35 - b13*b15 - b23*b25 + b35, b14*b15*b34 - b14^2*b35 + b13*b14*b45 - b13*b15 - b34*b45 + b35, b24*b25*b34 - b24^2*b35 + b23*b24*b45 - b23*b25 - b34*b45 + b35, -b14*b15*b23*b24 + b13*b15*b24^2 + b14^2*b23*b25 - b13*b14*b24*b25 - b12*b15*b24*b34 - b12*b14*b25*b34 + 2*b12*b14*b24*b35 - b12*b14*b23*b45 - b12*b13*b24*b45 + b12^2*b34*b45 + b12*b15*b23 + b12*b13*b25 + b14*b15*b34 + b24*b25*b34 - b12^2*b35 - b14^2*b35 - b24^2*b35 + b13*b14*b45 + b23*b24*b45 - b13*b15 - b23*b25 - b34*b45 + b35, b45, -b14*b15 + b45, -b34*b35 + b45, b12*b15*b24 + b12*b14*b25 - b12^2*b45 - b14*b15 - b24*b25 + b45, b13*b15*b34 + b13*b14*b35 - b13^2*b45 - b14*b15 - b34*b35 + b45, b23*b25*b34 + b23*b24*b35 - b23^2*b45 - b24*b25 - b34*b35 + b45, b14*b15*b23^2 - b13*b15*b23*b24 - b13*b14*b23*b25 + b13^2*b24*b25 - b12*b15*b23*b34 - b12*b13*b25*b34 - b12*b14*b23*b35 - b12*b13*b24*b35 + b12^2*b34*b35 + 2*b12*b13*b23*b45 + b12*b15*b24 + b12*b14*b25 + b13*b15*b34 + b23*b25*b34 + b13*b14*b35 + b23*b24*b35 - b12^2*b45 - b13^2*b45 - b23^2*b45 - b14*b15 - b24*b25 - b34*b35 + b45}; I = ideal zeroPolynomials; I' = (I : positivePolynomials#5) -- colons some principal minor is -- monomial already print (I':b45)