+ 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 IC=randomCurveGenus12Degree14InP4(S);
o5 : Ideal of S
i6 : omegaC=Ext^2(IC,S^
i7 : fomega=res omegaC;
i8 : sM=S^{1:-5}**coker transpose fomega.dd_3;
i9 : (psi,phi)=matrixFactorizationFromModule(sM);
i10 : SX=ring phi;
i11 : A1=((psi_{0,1}))^{0..14};
15 2
o11 : Matrix SX <
i12 : A2=syz transpose A1;
15 27
o12 : Matrix SX <
i13 : q=transpose(A2*random(source A2, SX^{4:0}));
4 15
o13 : Matrix SX <
i14 : q*A1==0
o14 = true
i15 : incl=id_(source A1)||map(source q,source A1,0);
17 2
o15 : Matrix SX <
i16 : alpha=inducedMap(target(q++id_(S^{2:-1})),coker phi,(q++id_(S^{2:-1}))*psi);
o16 : Matrix
i17 : beta=inducedMap(coker phi,source A1,incl);
o17 : Matrix
i18 : prune(ker(alpha)/image(beta)) == 0
o18 = true
i19 : prune ker(beta) == 0
o19 = true
i20 : hom=Hom(coker ((q++id_(S^{2:-1}))*psi_{2..16}),SX);
i21 : f=homomorphism hom_{0};
o21 : Matrix
i22 : ICX = ann coker f;
o22 : Ideal of SX
i23 : pr=map(SX,S);
o23 : RingMap SX <
i24 : IC=preimage(pr,ICX);
o24 : Ideal of S
i25 : betti res IC
0 1 2 3 4
o25 = total: 1 7 15 11 2
0: 1 . . . .
1: . . . . .
2: . 5 . . .
3: . 2 15 11 2
o25 : BettiTally
i26 : (codim IC, genus IC, degree IC)==(3,10,13)
o26 = true
i27 : isSmoothCurve(IC)
o27 = true
i28 :