-- Example 9a: the genus 9 tangent developable
load "MukaiModels.m2";
S = QQ[z_0,z_1,z_2,z_4,z_7,z_8,z_10,z_11,z_12,z_13];
z_3 = (135/2)*z_4;
z_9 = (1/432)*z_10;
z_5 = 45*z_12;
z_6 = -36*z_11;
LTD9 = {z_3-(135/2)*z_4,z_9-(1/432)*z_10,z_5-45*z_12,z_6 + 36*z_11};
all(LTD9, i -> i==0)
I1 = {-z_5^2+z_4*z_6-z_0*z_7, z_3*z_5-z_2*z_6-z_0*z_8, -z_3*z_4+z_2*z_5-z_0*z_9, -z_3^2+z_1*z_6-z_0*z_10, z_2*z_3-z_1*z_5-z_0*z_11, -z_2^2+z_1*z_4-z_0*z_12};
I2 = {-z_11^2+z_10*z_12-z_1*z_13, z_9*z_11-z_8*z_12-z_2*z_13, -z_9*z_10+z_8*z_11-z_3*z_13, -z_9^2+z_7*z_12-z_4*z_13, z_8*z_9-z_7*z_11-z_5*z_13, -z_8^2+z_7*z_10-z_6*z_13};
I3 = {z_1*z_7+z_2*z_8+z_3*z_9-z_0*z_13, z_1*z_8+z_2*z_10+z_3*z_11, z_1*z_9+z_2*z_11+z_3*z_12, z_2*z_7+z_4*z_8+z_5*z_9, z_2*z_8+z_4*z_10+z_5*z_11-z_0*z_13, z_2*z_9+z_4*z_11+z_5*z_12, z_3*z_7+z_5*z_8+z_6*z_9, z_3*z_8+z_5*z_10+z_6*z_11, z_3*z_9+z_5*z_11+z_6*z_12-z_0*z_13};
PcapSpGr36 = flatten {I1,I2,I3};
R=QQ[y_0..y_9];
TD9 = schreyerTangentDevelopableQuadrics(gens R);
F = map(R,S,{y_0, -3*y_1, y_2, -4/9*y_3, 15*y_8, 90*y_7, 720*y_6, 15*y_5, 1/3*y_4, -5*y_9});
F(ideal(PcapSpGr36))==ideal(TD9)