This function computes the ramification divisor on C under the natural projection map of C to P1, and checks whether it intersects the preimage of the singular locus of the plane model of C under the second projection map.
i1 : p=101; |
i2 : Fp=ZZ/p; |
i3 : S=Fp[x_0,x_1,y_0..y_2,Degrees=>{2:{1,0},3:{0,1}}];
|
i4 : pt=ideal random(S^1,S^{{-1,0},{0,-1},{0,-1}});
o4 : Ideal of S
|
i5 : Y1=ideal(gens pt * random(source gens pt,S^{{-1,-1},{-1,-1}}));
o5 : Ideal of S
|
i6 : Y2=ideal(gens pt * random(source gens pt,S^{{-1,0},{0,-1}}));
o6 : Ideal of S
|
i7 : Y3=ideal(gens pt * random(source gens pt,S^{{-1,-1},{-2,-1}}));
o7 : Ideal of S
|
i8 : isSmooth(Y1) o8 = true |
i9 : isSmooth(Y2) o9 = true |
i10 : isSmooth(Y3) o10 = true |
i11 : isSmooth(intersect({Y1,Y2}))
o11 = false
|
i12 : isSmooth(intersect({Y1,Y2,Y3}))
o12 = false
|