-- Example 8a: the genus 8 tangent developable
load "MukaiModels.m2"
S = QQ[x_12,x_13,x_14,x_15,x_16,x_26,x_36,x_46,x_56];
x_23 = (5/3)*x_14;
x_24 = 5*x_15;
x_25 = 15*x_16;
x_34 = 20*x_16;
x_35 = 5*x_26;
x_45 = (5/3)*x_36;
LTD8 = {x_23-(5/3)*x_14, x_24-5*x_15, x_25-15*x_16, x_34-20*x_16, x_35-5*x_26, x_45-(5/3)*x_36};
all(LTD8, i -> i==0)
PcapGr26 = {x_12*x_34-x_13*x_24+x_14*x_23,
x_12*x_35-x_13*x_25+x_15*x_23,
x_12*x_36-x_13*x_26+x_16*x_23,
x_12*x_45-x_14*x_25+x_15*x_24,
x_12*x_46-x_14*x_26+x_16*x_24,
x_12*x_56-x_15*x_26+x_16*x_25,
x_13*x_45-x_14*x_35+x_15*x_34,
x_13*x_46-x_14*x_36+x_16*x_34,
x_13*x_56-x_15*x_36+x_16*x_35,
x_14*x_56-x_15*x_46+x_16*x_45,
x_23*x_45-x_24*x_35+x_25*x_34,
x_23*x_46-x_24*x_36+x_26*x_34,
x_23*x_56-x_25*x_36+x_26*x_35,
x_24*x_56-x_25*x_46+x_26*x_45,
x_34*x_56-x_35*x_46+x_36*x_45};
R=QQ[y_0..y_8];
TD8 = schreyerTangentDevelopableQuadrics(gens R);
F = map(R,S,{y_0, 4*y_1, 6*y_2, 4*y_3, y_4, 4*y_5, 6*y_6, 4*y_7, y_8});
F(ideal(PcapGr26))==ideal(TD8)