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i1 : -- Example 7d: the genus 7 balanced K3 carpet
     load "MukaiModels.m2";

i2 : S=QQ[x_14, x_15, x_25, x_35, x_1245, x_1345, x_2345];

i3 : x_0=0;

i4 : x_12=x_1345;

i5 : x_13=x_2345;

i6 : x_24=2*x_15;

i7 : x_34=1/2*x_25;

i8 : x_45=0;

i9 : x_1234=0;

i10 : x_1235=0;

i11 : x_23=x_14;

i12 : LBalRib7 = {x_0, x_12-x_1345, x_13-x_2345, x_24-2*x_15, x_34-1/2*x_25, x_45, x_1234, x_1235, x_23-x_14};

i13 : all(LBalRib7, 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 : BalRib7 = balancedRibbon(R);

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

o17 : RingMap R <-- S

i18 : F(ideal(PcapOG510))==ideal(BalRib7)

o18 = true

i19 :