Type "help" to see useful commands

i1 : -- Example 10b: the genus 10 cuspidal cubic with 10-gonal symmetry
     load "MukaiModels.m2";

i2 : S = QQ[H_2,X_1,X_2,X_4,X_6,Y_1,Y_2,Y_4,Y_5,Y_6];

i3 : H_1 = 4/9*H_2;

i4 : X_3 = 4/27*Y_6;

i5 : Y_3 = 5/4*X_6;

i6 : X_5 = -8/75*Y_5;

i7 : 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};

i8 : all(LCusp10, i -> i==0)

o8 = true

i9 : PcapG2AdjVar = {Y_4^2+Y_3*Y_5-Y_1*Y_6,
     Y_3*Y_4+Y_2*Y_5+2*H_1*Y_6-H_2*Y_6,
     Y_1*Y_4-H_1*Y_5+H_2*Y_5+X_2*Y_6,
     H_1*Y_4+X_1*Y_5+X_3*Y_6,
     Y_3^2-Y_2*Y_4+X_1*Y_6,
     Y_1*Y_3-H_2*Y_4-X_1*Y_5-2*X_3*Y_6,
     H_1*Y_3-X_1*Y_4-X_4*Y_6,
     Y_1*Y_2-H_2*Y_3+X_1*Y_4+2*X_4*Y_6,
     H_1*Y_2-X_1*Y_3-X_5*Y_6,
     Y_1^2+X_2*Y_4-X_3*Y_5,
     X_1*Y_1+X_3*Y_3+X_4*Y_4,
     H_2*Y_1+X_2*Y_3+2*X_3*Y_4-X_4*Y_5,
     H_1*Y_1+X_3*Y_4-X_4*Y_5,
     X_4^2+X_3*X_5-X_1*X_6,
     X_3*X_4+X_2*X_5+2*H_1*X_6-H_2*X_6,
     X_1*X_4-H_1*X_5+H_2*X_5+X_6*Y_2,
     H_1*X_4+X_5*Y_1+X_6*Y_3,
     X_3^2-X_2*X_4+X_6*Y_1,
     X_1*X_3-H_2*X_4-X_5*Y_1-2*X_6*Y_3,
     H_1*X_3-X_4*Y_1-X_6*Y_4,
     X_1*X_2-H_2*X_3+X_4*Y_1+2*X_6*Y_4,
     H_1*X_2-X_3*Y_1-X_6*Y_5,
     X_1^2+X_4*Y_2-X_5*Y_3,
     H_2*X_1+X_3*Y_2+2*X_4*Y_3-X_5*Y_4,
     H_1*X_1+X_4*Y_3-X_5*Y_4,
     H_2^2+X_2*Y_2+3*X_3*Y_3+3*X_4*Y_4+X_5*Y_5+4*X_6*Y_6,
     H_1*H_2+X_3*Y_3+2*X_4*Y_4+X_5*Y_5+2*X_6*Y_6,
     H_1^2+X_4*Y_4+X_5*Y_5+X_6*Y_6};

i10 : R=QQ[y_0..y_9];

i11 : Cusp10 = schreyerCuspidalCurveQuadrics(gens R);

i12 : F = map(R,S,{-(9/5)*y_5, (1/5)*y_8, -(1/3)*y_1, (4/15)*y_7, (2/5)*y_6, -(1/2)*y_2, -(1/5)*y_9, y_3, (1/4)*y_0, -(9/4)*y_4});

o12 : RingMap R <-- S

i13 : F(ideal PcapG2AdjVar)==ideal(Cusp10)

o13 = true

i14 :