-- Example 10d: a genus 10 reducible curve with four components, each generically nonreduced
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];
LNonRedCurve10 = {X_1-Y_1,Y_2-Y_3,X_4-X_5,H_1-Y_5};
G2AdjVar = {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};
I = ideal join(LNonRedCurve10,G2AdjVar);
hilbertPolynomial(I,Projective=>false)
radI = radical(I);
I==radI
pdI = primaryDecomposition(I);
radpdI = apply(pdI, J -> radical J);
apply(#pdI, i -> pdI_i==radpdI_i)
apply(pdI, J -> hilbertPolynomial(J,Projective=>false))
apply(radpdI, J -> hilbertPolynomial(J,Projective=>false))
matrix apply(#pdI, i -> apply(#pdI, j -> dim(radpdI_i+radpdI_j)))