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i1 : -- Example 7b: the genus 7 cuspidal cubic with 7-gonal symmetry
     load "MukaiModels.m2"

i2 : S=QQ[x_0, x_12, x_14, x_15, x_25, x_35, x_1235];

i3 : x_13=0;

i4 : x_23=-(5/3)*x_15;

i5 : x_24=0;

i6 : x_34=5*x_25;

i7 : x_45=(4/3)*x_35;

i8 : x_1245=(9/8)*x_1235;

i9 : x_1345=-(1/2)*x_12;

i10 : x_2345=-(2/15)*x_14;

i11 : x_1234=(1/30)*x_0;

i12 : LCusp7 = {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,x_1234-1/30*x_0};

i13 : all(LCusp7, i -> i==0)

o13 = true

i14 : 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};

i15 : R=QQ[y_0..y_6];

i16 : Cusp7 = schreyerCuspidalCurveQuadrics(gens R);

i17 : F = map(R,S,{5*y_0, y_2, (5/2)*y_3, y_4, y_5, 3*y_6, (4/15)*y_1});

o17 : RingMap R <-- S

i18 : F(ideal(PcapOG510))==ideal(Cusp7)

o18 = true

i19 :