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i1 : -- Example 7e: a genus 7 graph curve
     S=QQ[x_13,x_24,x_25,x_34,x_45,x_1235,x_1345];

i2 : x_0=-x_25+x_45;

i3 : x_12=x_13;

i4 : x_14=0;

i5 : x_15=-x_25+x_45;

i6 : x_23=x_25;

i7 : x_35=0;

i8 : x_1234=0;

i9 : x_1245=0;

i10 : x_2345=0;

i11 : 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};

i12 : all(LGraphCurve7, i -> i==0)

o12 = true

i13 : 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};

i14 : R=QQ[y_0..y_6];

i15 : 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};

i16 : F=map(R,S,{-y_2, y_1, y_4, y_0+y_3-y_4, -y_3+y_4, y_5, -y_6});

o16 : RingMap R <-- S

i17 : F(ideal(PcapOG510))==ideal(GraphCurve7)

o17 = true

i18 :