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i1 : run "date";
Mon Jun  8 23:03:50 UTC 2026

i2 : load "InvariantPolynomialsforMukaiModels.m2";

i3 : matrixFromHyperplaneEquations = (L) -> (
         R:=ring(L_0);
         eqnMatrix:=matrix apply(L, f -> apply(numgens R, i -> coefficient(R_i,f)));
         transpose gens ker eqnMatrix
     );

i4 : 
     -- The ordering and numbering here match Theorem 4.1 in the preprint
     -- Genus 7
     S=QQ[x_0,x_12,x_13,x_14,x_15,x_23,x_24,x_25,x_34,x_35,x_45,x_1234,x_1235,x_1245,x_1345,x_2345];

i5 : -- Example 7a: the genus 7 tangent developable
     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};

i6 : F72(matrixFromHyperplaneEquations LTD7)

     665
o6 = ---
      2

o6 : QQ

i7 : -- Example 7b: the genus 7 cuspidal cubic with 7-gonal symmetry
     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};

i8 : F71(matrixFromHyperplaneEquations LCusp7)

     3038765625
o8 = ----------
          2

o8 : QQ

i9 : -- Example 7c: the genus 7 balanced K3 carpet
     LK3Carpet7 = {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};

i10 : F72(matrixFromHyperplaneEquations LK3Carpet7)

o10 = 1224

o10 : QQ

i11 : -- Example 7d: the genus 7 balanced ribbon
      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};

i12 : F71(matrixFromHyperplaneEquations LBalRib7)

o12 = -6415200

o12 : QQ

i13 : -- Example 7e: a genus 7 graph curve
      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};

i14 : F71(matrixFromHyperplaneEquations LGraphCurve7)

o14 = 16200

o14 : QQ

i15 : 
      
      
      -- Genus 8
      K = toField(QQ[sqrt2,Degrees=>{0}]/ideal(sqrt2^2-2));

i16 : -- The order of the variables shown here is grevlex for subsets
      -- Do this to match M2's exteriorPower function
      R = K[x_12,x_13,x_23,x_14,x_24,x_34,x_15,x_25,x_35,x_45,x_16,x_26,x_36,x_46,x_56];

i17 : -- Example 8a: the genus 8 tangent developable
      LTD8 = {x_23-(5/3)*x_14, x_24-5*x_15, x_25-15*x_16, x_34-20*x_16, x_35-5*x_26, x_45-(5/3)*x_36};

i18 : F82(matrixFromHyperplaneEquations LTD8)

o18 = -20234375

o18 : K

i19 : -- Example 8b: the genus 8 cuspidal cubic with 8-gonal symmetry
      LCusp8 = {x_23-(5/3)*x_14, x_24-5*x_15, x_25-15*x_16, x_34-20*x_16, x_35-5*x_26, x_45-(5/3)*x_36, x_12-x_56};

i20 : F81(matrixFromHyperplaneEquations LCusp8)

o20 = 29937634506483863970011085295268659200000000000000000000000000000

o20 : K

i21 : -- Example 8c: a genus 8 reducible surface with four components, each generically nonreduced
      LNonRedSurf8 = {x_12-x_34, x_12-x_13, x_14-x_45, x_16-x_23, x_24-x_35, x_26-x_36};

i22 : F82(matrixFromHyperplaneEquations LNonRedSurf8)

o22 = -1

o22 : K

i23 : -- Example 8d: a genus 8 reducible curve with five components, each generically nonreduced:
      LNonRedCurve8={x_12-x_34, x_12-x_13, x_14-x_45, x_16-x_23, x_24-x_35, x_26-x_36, x_15-x_46};

i24 : F81(matrixFromHyperplaneEquations LNonRedCurve8)

o24 = 635751225868053551064592039280640000000000000

o24 : K

i25 : -- Example 8e: a genus 8 graph curve
      LGraphCurve8 = {x_12-32*x_46, x_13+(64*sqrt2 - 96)*x_56, x_14+(1/32)*x_23, x_15-x_24, x_16+(1/32*(2*sqrt2 + 3))*x_35, x_25-x_34, x_26-x_45};

i26 : F81(matrixFromHyperplaneEquations LGraphCurve8)

o26 = 5680925929429533134445896744302475117583107610378240000000000000000

o26 : K

i27 : 
      
      
      -- Genus 9
      -- Example 9a: the genus 9 tangent developable
      K = toField(QQ[sqrt3,Degrees=>{0}]/(sqrt3^2-3));

i28 : S = K[z_0..z_13];

i29 : LTD9 = {z_3-(135/2)*z_4,z_9-(1/432)*z_10,z_5-45*z_12,z_6 + 36*z_11};

i30 : F92(matrixFromHyperplaneEquations LTD9)

o30 = -71442

o30 : K

i31 : -- Example 9b: the genus 9 cuspidal cubic with 9-gonal symmetry
      LCusp9 = {z_3-(135/2)*z_4,z_9-(1/432)*z_10,z_5-45*z_12,z_6 + 36*z_11,z_0+1/5*z_13};

i32 : F91(matrixFromHyperplaneEquations LCusp9)

o32 = 40308132324841209722880000

o32 : K

i33 : -- Example 9c: the genus 9 balanced K3 carpet
      LK3Carpet9 = {z_0,z_13,z_3+1/2*z_4,z_9+1/2*z_10};

i34 : F92(matrixFromHyperplaneEquations LK3Carpet9)

o34 = 6

o34 : K

i35 : -- Example 9d: the genus 9 balanced ribbon:
      LBalRib9 = {z_0,z_13,z_3+1/2*z_4,z_9+1/2*z_10,z_1-4*z_7};

i36 : F91(matrixFromHyperplaneEquations LBalRib9)

o36 = 573308928

o36 : K

i37 : -- Example 9e: a genus 9 graph curve
      LGraphCurve9= {z_0-(12*sqrt3 - 18)*z_13, z_4-((4/9)*sqrt3+2/3)*z_3, z_6-(12*sqrt3-21)*z_1, z_10-(-6*sqrt3 + 9)*z_9, z_12+1/3*z_7 };

i38 : F91(matrixFromHyperplaneEquations LGraphCurve9)

o38 = - 136886571995957821440sqrt3 + 237094562521203867648

o38 : K

i39 : 
      
      
      -- Genus 10
      S = QQ[H_1,H_2,X_1,X_2,X_3,X_4,X_5,X_6,Y_1,Y_2,Y_3,Y_4,Y_5,Y_6];

i40 : -- Example 10a: the genus 10 tangent developable
      LTD10={H_1-4/9*H_2, X_3-4/27*Y_6, Y_3-5/4*X_6};

i41 : F102(matrixFromHyperplaneEquations LTD10)

         56
o41 = - ---
        135

o41 : QQ

i42 : -- Example 10b: the genus 10 cuspidal cubic with 10-gonal symmetry
      LCusp10={H_1-4/9*H_2, X_3-4/27*Y_6, Y_3-5/4*X_6,X_5+8/75*Y_5};

i43 : F101(matrixFromHyperplaneEquations LCusp10)

       25088
o43 = -------
      1366875

o43 : QQ

i44 : -- Example 10c: a genus 10 reducible surface with two components, each generically nonreduced
      LNonRedSurf10 = {X_1-Y_1,Y_2-Y_3,X_4-X_5};

i45 : F102(matrixFromHyperplaneEquations LNonRedSurf10)

o45 = 2

o45 : QQ

i46 : -- Example 10d: a genus 10 reducible curve with three components, each generically nonreduced
      LNonRedCurve10 = {X_1-Y_1,Y_2-Y_3,X_4-X_5,H_1-Y_5};

i47 : F101(matrixFromHyperplaneEquations LNonRedCurve10)

      4
o47 = -
      3

o47 : QQ

i48 : run "date";
Mon Jun  8 23:15:52 UTC 2026

i49 : quit