-- Example 7e: a genus 7 graph curve
S=QQ[x_13,x_24,x_25,x_34,x_45,x_1235,x_1345];
x_0=-x_25+x_45;
x_12=x_13;
x_14=0;
x_15=-x_25+x_45;
x_23=x_25;
x_35=0;
x_1234=0;
x_1245=0;
x_2345=0;
LGraphCurve7={x_2345, x_1245, x_1234, x_35, x_23-x_25, x_15+x_25-x_35-x_45, x_14, x_12-x_13, x_0+x_25-x_35-x_45};
all(LGraphCurve7, 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_6];
GraphCurve7 = {y_2*y_6,y_1*y_6,y_3*y_5-y_4*y_5+y_4*y_6,y_1*y_5,y_0*y_5,y_2*y_4-y_3*y_4+y_4*y_5-y_4*y_6,y_0*y_4,y_1*y_3-y_2*y_3+y_3*y_4-y_4*y_5+y_4*y_6,y_0*y_3-y_2*y_3+y_3^2-y_4*y_5+y_3*y_6+y_4*y_6,y_0*y_2-y_1*y_2+y_2*y_3-y_3*y_4+y_4*y_5-y_4*y_6};
F=map(R,S,{-y_2, y_1, y_4, y_0+y_3-y_4, -y_3+y_4, y_5, -y_6});
F(ideal(PcapOG510))==ideal(GraphCurve7)