+ 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 : H={13,4,4,4,4,4,4,4,4,4,4};
i6 : (Y,pts)=alexanderSurface(S);
i7 : Z={31,10,10,10,10,10,10,9,9,9,9}
o7 = {31, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9}
o7 : List
i8 : time IZ=properTransformAlexander(S,Z,pts);
o8 : Ideal of S
i9 : N=auxiliarLineBundle(Y,IZ);
i10 : betti res N
0 1 2 3 4
o10 = total: 6 14 16 9 1
1: 6 10 3 . .
2: . 3 . . .
3: . 1 13 9 1
o10 : BettiTally
i11 : (phi,psi)=matrixFactorizationFromModule(N);
i12 : betti dual psi
0 1
o12 = total: 23 23
-6: 19 1
-5: . 3
-4: 4 19
o12 : BettiTally
i13 : monadShape=betti map(S^{4:-2},S^{3:-2,1:-1},0)
0 1
o13 = total: 4 4
0: . 1
1: . 3
2: 4 .
o13 : BettiTally
i14 : time IC=idealFromMatFac(dual psi, monadShape);
o14 : Ideal of S
i15 : (codim IC, genus IC, degree IC) == (3, 16, 17)
o15 = true
i16 : isSmoothCurve(IC)
o16 = true
i17 : betti res IC
0 1 2 3 4
o17 = total: 1 17 29 14 1
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 17 29 13 .
4: . . . 1 1
o17 : BettiTally
i18 : omegaC=Ext^2(IC,S^
i19 : fomega=res omegaC;
i20 : sM=S^{1:-5}**coker transpose fomega.dd_3;
i21 : betti res sM
0 1 2 3
o21 = total: 5 19 18 4
0: 1 . . .
1: . . . .
2: 4 19 18 1
3: . . . 3
o21 : BettiTally
i22 : gIC=gens IC;
1 17
o22 : Matrix S <
i23 : betti res (sM**(S/(ideal(gIC * random(source gIC,S^
0 1 2 3 4 5 6
o23 = total: 5 19 23 23 23 23 23
0: 1 . . . . . .
1: . . . . . . .
2: 4 19 19 1 . . .
3: . . . 3 . . .
4: . . 4 19 19 1 .
5: . . . . . 3 .
6: . . . . 4 19 19
7: . . . . . . .
8: . . . . . . 4
o23 : BettiTally
i24 : X=ideal ring psi;
o24 : Ideal of S
i25 : YpX=Y+X;
o25 : Ideal of S
i26 : CiZ=intersect(IZ,IC);
o26 : Ideal of S
i27 : saturate YpX == CiZ
o27 = true
i28 :