+ M2 Macaulay2, version 1.9.2
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition,
ReesAlgebra, TangentCone
i1 : loadPackage("MatFacCurvesP4")
o1 = MatFacCurvesP4
o1 : Package
i2 : p=32009;
i3 : Fp=ZZ/p;
i4 : S=Fp[x_0..x_4];
i5 : time (Y,pts)=alexanderSurface(S);
i6 : (g,d)=(16,17)
o6 = (16, 17)
o6 : Sequence
i7 : L=linSysAlexander(g,d)
o7 = {21, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6}
o7 : List
i8 : time IC=properTransformAlexander(S,L,pts);
o8 : Ideal of S
i9 : (codim IC, genus IC, degree IC) == (3,g,d)
o9 = true
i10 : isSmoothCurve(IC)
o10 = true
i11 : betti res IC
0 1 2 3 4
o11 = total: 1 17 29 14 1
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 17 29 13 .
4: . . . 1 1
o11 : BettiTally
i12 : (g,d)=(17,18)
o12 = (17, 18)
o12 : Sequence
i13 : L=linSysAlexander(g,d)
o13 = {22, 7, 7, 7, 7, 7, 7, 7, 7, 6, 5}
o13 : List
i14 : time IC=properTransformAlexander(S,L,pts);
o14 : Ideal of S
i15 : (codim IC, genus IC, degree IC) == (3,g,d)
o15 = true
i16 : isSmoothCurve(IC)
o16 = true
i17 : betti res IC
0 1 2 3 4
o17 = total: 1 14 20 10 3
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 14 18 . .
4: . . 2 10 3
o17 : BettiTally
i18 : (g,d)=(18,19)
o18 = (18, 19)
o18 : Sequence
i19 : L=linSysAlexander(g,d)
o19 = {19, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5}
o19 : List
i20 : time IC=properTransformAlexander(S,L,pts);
o20 : Ideal of S
i21 : (codim IC, genus IC, degree IC) == (3,g,d)
o21 = true
i22 : isSmoothCurve(IC)
o22 = true
i23 : betti res IC
0 1 2 3 4
o23 = total: 1 11 24 19 5
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 11 7 . .
4: . . 17 19 5
o23 : BettiTally
i24 : (g,d)=(19,20)
o24 = (19, 20)
o24 : Sequence
i25 : L=linSysAlexander(g,d)
o25 = {20, 7, 7, 6, 6, 6, 6, 6, 6, 5, 5}
o25 : List
i26 : time IC=properTransformAlexander(S,L,pts);
o26 : Ideal of S
i27 : (codim IC, genus IC, degree IC) == (3,g,d)
o27 = true
i28 : isSmoothCurve(IC)
o28 = true
i29 : betti res IC
0 1 2 3 4
o29 = total: 1 12 32 28 7
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 8 . . .
4: . 4 32 28 7
o29 : BettiTally
i30 : (g,d)=(20,20)
o30 = (20, 20)
o30 : Sequence
i31 : L=linSysAlexander(g,d)
o31 = {20, 7, 6, 6, 6, 6, 6, 6, 6, 6, 5}
o31 : List
i32 : time IC=properTransformAlexander(S,L,pts);
o32 : Ideal of S
i33 : (codim IC, genus IC, degree IC) == (3,g,d)
o33 = true
i34 : isSmoothCurve(IC)
o34 = true
i35 : betti res IC
0 1 2 3 4
o35 = total: 1 9 26 24 6
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 9 . . .
4: . . 26 24 6
o35 : BettiTally
i36 :