+ 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 : IE=randomCurveGenus10Degree13InP4(S);
o5 : Ideal of S
i6 : (codim IE, genus IE, degree IE) == (3,10,13)
o6 = true
i7 : isSmoothCurve(IE)
o7 = true
i8 : betti res IE
0 1 2 3 4
o8 = total: 1 7 15 11 2
0: 1 . . . .
1: . . . . .
2: . 5 . . .
3: . 2 15 11 2
o8 : BettiTally
i9 : (phi,psi)=matrixFactorizationFromModule(IE);
i10 : betti psi
0 1
o10 = total: 17 17
2: 15 2
3: 2 15
o10 : BettiTally
i11 : monadShape=betti map(S^{2:-1},S^{2:-1,2:-2},0);
i12 : IC=idealFromMatFac(psi,monadShape);
o12 : Ideal of S
i13 : (codim IC, genus IC, degree IC) == (3,12,14)
o13 = true
i14 : isSmoothCurve(IC)
o14 = true
i15 : betti res IC
0 1 2 3 4
o15 = total: 1 9 18 12 2
0: 1 . . . .
1: . . . . .
2: . 4 . . .
3: . 5 18 12 2
o15 : BettiTally
i16 :