-- Example 7a: the genus 7 tangent developable
load "MukaiModels.m2"
S=QQ[x_0, x_12, x_14, x_15, x_25, x_35, x_1234, x_1235];
x_13=0;
x_23=-(5/3)*x_15;
x_24=0;
x_34=5*x_25;
x_45=(4/3)*x_35;
x_1245=(9/8)*x_1235;
x_1345=-(1/2)*x_12;
x_2345=-(2/15)*x_14;
LTD7 = {x_13, x_23+(5/3)*x_15, x_24, x_34-5*x_25, x_45-(4/3)*x_35, x_1245-(9/8)*x_1235, x_1345+(1/2)*x_12, x_2345+(2/15)*x_14};
all(LTD7, i -> i==0)
PcapOG510 = {x_0*x_2345-x_23*x_45+x_24*x_35-x_25*x_34,
x_12*x_1345-x_13*x_1245+x_14*x_1235-x_15*x_1234,
x_0*x_1345-x_13*x_45+x_14*x_35-x_15*x_34,
x_12*x_2345-x_23*x_1245+x_24*x_1235-x_25*x_1234,
x_0*x_1245-x_12*x_45+x_14*x_25-x_15*x_24,
x_13*x_2345-x_23*x_1345+x_34*x_1235-x_35*x_1234,
x_0*x_1235-x_12*x_35+x_13*x_25-x_15*x_23,
x_14*x_2345-x_24*x_1345+x_34*x_1245-x_45*x_1234,
x_0*x_1234-x_12*x_34+x_13*x_24-x_14*x_23,
x_15*x_2345-x_25*x_1345+x_35*x_1245-x_45*x_1235};
R=QQ[y_0..y_7];
TD7 = schreyerTangentDevelopableQuadrics(gens R);
F = map(R,S,{5*y_7, y_2, (5/2)*y_3, y_4, y_5, 3*y_6, 1/6*y_0,(4/15)*y_1});
F(ideal(PcapOG510))==ideal(TD7)