+ 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 singC=singularCurveInP4(S,12,14);
o5 : Ideal of S
i6 : isSmoothCurve(singC) == false
bad
projection center
o6 = true
i7 : omegaSingC=Ext^2(singC,S^{ -5});
i8 : fomegaSing=res omegaSingC;
i9 : sM=S^{ -5}**coker transpose fomegaSing.dd_3;
i10 : (psi,phi)=matrixFactorizationFromModule(sM);
i11 : X=ideal ring phi;
o11 : Ideal of S
i12 : codim X, degree X
o12 = (1, 3)
o12 : Sequence
i13 : prune ((ker psi) / (image phi)) == 0
o13 = true
i14 : betti res (coker psi ** S)
0 1
o14 = total: 17 17
0: 15 2
1: 2 15
o14 : BettiTally
i15 : betti psi
0 1
o15 = total: 17 17
0: 15 2
1: 2 15
o15 : BettiTally
i16 : betti syz((psi_{2..16})^{15,16},DegreeLimit=>2)
0 1
o16 = total: 15 5
1: . 5
2: 15 .
o16 : BettiTally
i17 : monadShape=betti map(S^{2:-1},S^{2:-1,2:-2},0);
i18 : IC=idealFromMatFac(psi, monadShape);
o18 : Ideal of S
i19 : (codim IC, genus IC, degree IC) == (3, 12, 14)
o19 = true
i20 : isSmoothCurve(IC)
o20 = true
i21 : betti res IC
0 1 2 3 4
o21 = total: 1 9 18 12 2
0: 1 . . . .
1: . . . . .
2: . 4 . . .
3: . 5 18 12 2
o21 : BettiTally
i22 : omegaC=Ext^2(IC,S^{ -5});
i23 : fomega=res omegaC;
i24 : sM=S^{ -5}**coker transpose fomega.dd_3;
i25 : betti res sM
0 1 2 3
o25 = total: 3 14 15 4
0: 1 . . .
1: . . . .
2: 2 14 15 2
3: . . . 2
o25 : BettiTally
i26 : gIE=gens IC;
1 9
o26 : Matrix S <
i27 : Y=ideal(gIE * random(source gIE,S^
o27 : Ideal of S
i28 : betti res (sM**(S/Y))
0 1 2 3 4 5 6
o28 = total: 3 14 18 17 17 17 17
0: 1 . . . . . .
1: . . 1 . . . .
2: 2 14 15 2 . . .
3: . . 2 15 15 2 .
4: . . . . 2 15 15
5: . . . . . . 2
o28 : BettiTally
i29 : betti res prune (sM**(S/Y))
0 1 2 3 4 5 6
o29 = total: 3 13 17 17 17 17 17
0: 1 . . . . . .
1: . . . . . . .
2: 2 13 15 2 . . .
3: . . 2 15 15 2 .
4: . . . . 2 15 15
5: . . . . . . 2
o29 : BettiTally
i30 : time singC=singularCurveInP4(S,13,15);
o30 : Ideal of S
i31 : isSmoothCurve(singC) == false
bad
projection center
o31 = true
i32 : omegaSingC=Ext^2(singC,S^{ -5});
i33 : fomegaSing=res omegaSingC;
i34 : sM=S^{ -5}**coker transpose fomegaSing.dd_3;
i35 : (psi,phi)=matrixFactorizationFromModule(sM);
i36 : X=ideal ring phi;
o36 : Ideal of S
i37 : codim X, degree X
o37 = (1, 3)
o37 : Sequence
i38 : prune ((ker psi) / (image phi)) == 0
o38 = true
i39 : betti res (coker psi ** S)
0 1
o39 = total: 21 21
0: 18 3
1: 3 18
o39 : BettiTally
i40 : betti psi
0 1
o40 = total: 21 21
0: 18 3
1: 3 18
o40 : BettiTally
i41 : betti syz((psi_{3..20})^{18,19,20},DegreeLimit=>2)
0 1
o41 = total: 18 3
1: . 3
2: 18 .
o41 : BettiTally
i42 : monadShape=betti map(S^{3:-1},S^{3:-1,2:-2},0);
i43 : IC=idealFromMatFac(psi, monadShape);
o43 : Ideal of S
i44 : (codim IC, genus IC, degree IC) == (3, 13, 15)
o44 = true
i45 : isSmoothCurve(IC)
o45 = true
i46 : betti res IC
0 1 2 3 4
o46 = total: 1 14 27 17 3
0: 1 . . . .
1: . . . . .
2: . 2 . . .
3: . 12 27 17 3
o46 : BettiTally
i47 : omegaC=Ext^2(IC,S^{1:-5});
i48 : fomega=res omegaC;
i49 : sM=S^{ -5}**coker transpose fomega.dd_3;
i50 : betti res sM
0 1 2 3
o50 = total: 4 17 18 5
0: 1 . . .
1: . . . .
2: 3 17 18 3
3: . . . 2
o50 : BettiTally
i51 : gIE=gens IC;
1 14
o51 : Matrix S <
i52 : Y=ideal(gIE * random(source gIE,S^{1:-3}));
o52 : Ideal of S
i53 : betti res (sM**(S/Y))
0 1 2 3 4 5 6
o53 = total: 4 17 22 21 21 21 21
0: 1 . . . . . .
1: . . 1 . . . .
2: 3 17 18 3 . . .
3: . . 3 18 18 3 .
4: . . . . 3 18 18
5: . . . . . . 3
o53 : BettiTally
i54 : betti res prune (sM**(S/Y))
0 1 2 3 4 5 6
o54 = total: 4 16 21 21 21 21 21
0: 1 . . . . . .
1: . . . . . . .
2: 3 16 18 3 . . .
3: . . 3 18 18 3 .
4: . . . . 3 18 18
5: . . . . . . 3
o54 : BettiTally
i55 : time alexC=first curveOnAlexanderSurface(S,16,17);
o55 : Ideal of S
i56 : omegaAlexC=Ext^2(alexC,S^{1:-5});
i57 : fomegaAlex=res omegaAlexC;
i58 : sM=S^{1:-5}**coker transpose fomegaAlex.dd_3;
i59 : (psi,phi)=matrixFactorizationFromModule(sM);
i60 : X=ideal ring phi;
o60 : Ideal of S
i61 : codim X, degree X
o61 = (1, 4)
o61 : Sequence
i62 : time prune ((ker psi) / (image phi)) == 0
o62 = true
i63 : betti res (coker psi ** S)
0 1
o63 = total: 23 23
0: 19 1
1: . 3
2: 4 19
o63 : BettiTally
i64 : monadShape=betti map(S^{4:-2},S^{3:-2,1:-1},0);
i65 : time IC=idealFromMatFac(psi, monadShape);
o65 : Ideal of S
i66 : (codim IC, genus IC, degree IC) == (3, 16, 17)
o66 = true
i67 : isSmoothCurve(IC)
o67 = true
i68 : betti res IC
0 1 2 3 4
o68 = total: 1 17 29 14 1
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 17 29 13 .
4: . . . 1 1
o68 : BettiTally
i69 : omegaC=Ext^2(IC,S^{1:-5});
i70 : fomega=res omegaC;
i71 : sM=S^{1:-5}**coker transpose fomega.dd_3;
i72 : betti res sM
0 1 2 3
o72 = total: 5 19 18 4
0: 1 . . .
1: . . . .
2: 4 19 18 1
3: . . . 3
o72 : BettiTally
i73 : gIE=gens IC;
1 17
o73 : Matrix S <
i74 : Y=ideal(gIE * random(source gIE,S^
o74 : Ideal of S
i75 : betti res (sM**(S/Y))
0 1 2 3 4 5 6
o75 = 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
o75 : BettiTally
i76 : time alexC=first curveOnAlexanderSurface(S,17,18);
o76 : Ideal of S
i77 : omegaAlexC=Ext^2(alexC,S^
i78 : fomegaAlex=res omegaAlexC;
i79 : sM=S^{1:-5}**coker transpose fomegaAlex.dd_3;
i80 : (psi,phi)=matrixFactorizationFromModule(sM);
i81 : X=ideal ring phi;
o81 : Ideal of S
i82 : codim X, degree X
o82 = (1, 4)
o82 : Sequence
i83 : time prune ((ker psi) / (image phi)) == 0
o83 = true
i84 : betti res (coker psi ** S)
0 1
o84 = total: 27 27
0: 22 2
1: . 3
2: 5 22
o84 : BettiTally
i85 : monadShape=betti map(S^{5:-2},S^{3:-2,2:-1},0);
i86 : time IC=idealFromMatFac(psi, monadShape);
o86 : Ideal of S
i87 : (codim IC, genus IC, degree IC) == (3, 17, 18)
o87 = true
i88 : isSmoothCurve(IC)
o88 = true
i89 : betti res IC
0 1 2 3 4
o89 = total: 1 14 20 10 3
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 14 18 . .
4: . . 2 10 3
o89 : BettiTally
i90 : omegaC=Ext^2(IC,S^
i91 : fomega=res omegaC;
i92 : sM=S^{1:-5}**coker transpose fomega.dd_3;
i93 : betti res sM
0 1 2 3
o93 = total: 6 22 21 5
0: 1 . . .
1: . . . .
2: 5 22 21 2
3: . . . 3
o93 : BettiTally
i94 : gIE=gens IC;
1 14
o94 : Matrix S <
i95 : Y=ideal(gIE * random(source gIE,S^
o95 : Ideal of S
i96 : betti res (sM**(S/Y))
0 1 2 3 4 5 6
o96 = total: 6 22 27 27 27 27 27
0: 1 . . . . . .
1: . . . . . . .
2: 5 22 22 2 . . .
3: . . . 3 . . .
4: . . 5 22 22 2 .
5: . . . . . 3 .
6: . . . . 5 22 22
7: . . . . . . .
8: . . . . . . 5
o96 : BettiTally
i97 : time alexC=first curveOnAlexanderSurface(S,18,19);
o97 : Ideal of S
i98 : omegaAlexC=Ext^2(alexC,S^
i99 : fomegaAlex=res omegaAlexC;
i100 : sM=S^{1:-5}**coker transpose fomegaAlex.dd_3;
i101 : (psi,phi)=matrixFactorizationFromModule(sM);
i102 : X=ideal ring phi;
o102 : Ideal of S
i103 : codim X, degree X
o103 = (1, 4)
o103 : Sequence
i104 : time prune ((ker psi) / (image phi)) == 0
o104 = true
i105 : betti res (coker psi ** S)
0 1
o105 = total: 31 31
0: 25 3
1: . 3
2: 6 25
o105 : BettiTally
i106 : monadShape=betti map(S^{6:-2},S^{3:-2,3:-1},0);
i107 : time IC=idealFromMatFac(psi, monadShape);
o107 : Ideal of S
i108 : (codim IC, genus IC, degree IC) == (3, 18, 19)
o108 = true
i109 : isSmoothCurve(IC)
o109 = true
i110 : betti res IC
0 1 2 3 4
o110 = total: 1 11 24 19 5
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 11 7 . .
4: . . 17 19 5
o110 : BettiTally
i111 : omegaC=Ext^2(IC,S^
i112 : fomega=res omegaC;
i113 : sM=S^{1:-5}**coker transpose fomega.dd_3;
i114 : betti res sM
0 1 2 3
o114 = total: 7 25 24 6
0: 1 . . .
1: . . . .
2: 6 25 24 3
3: . . . 3
o114 : BettiTally
i115 : gIE=gens IC;
1 11
o115 : Matrix S <
i116 : Y=ideal(gIE * random(source gIE,S^
o116 : Ideal of S
i117 : betti res (sM**(S/Y))
0 1 2 3 4 5 6
o117 = total: 7 25 31 31 31 31 31
0: 1 . . . . . .
1: . . . . . . .
2: 6 25 25 3 . . .
3: . . . 3 . . .
4: . . 6 25 25 3 .
5: . . . . . 3 .
6: . . . . 6 25 25
7: . . . . . . .
8: . . . . . . 6
o117 : BettiTally
i118 : time alexC=first curveOnAlexanderSurface(S,19,20);
o118 : Ideal of S
i119 : omegaAlexC=Ext^2(alexC,S^
i120 : fomegaAlex=res omegaAlexC;
i121 : sM=S^{1:-5}**coker transpose fomegaAlex.dd_3;
i122 : (psi,phi)=matrixFactorizationFromModule(sM);
i123 : X=ideal ring phi;
o123 : Ideal of S
i124 : codim X, degree X
o124 = (1, 4)
o124 : Sequence
i125 : time prune ((ker psi) / (image phi)) == 0
o125 = true
i126 : betti res (coker psi ** S)
0 1
o126 = total: 35 35
0: 28 4
1: . 3
2: 7 28
o126 : BettiTally
i127 : monadShape=betti map(S^{7:-2},S^{3:-2,4:-1},0);
i128 : time IC=idealFromMatFac(psi, monadShape);
o128 : Ideal of S
i129 : (codim IC, genus IC, degree IC) == (3, 19, 20)
o129 = true
i130 : isSmoothCurve(IC)
o130 = true
i131 : betti res IC
0 1 2 3 4
o131 = total: 1 12 32 28 7
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 8 . . .
4: . 4 32 28 7
o131 : BettiTally
i132 : omegaC=Ext^2(IC,S^
i133 : fomega=res omegaC;
i134 : sM=S^{1:-5}**coker transpose fomega.dd_3;
i135 : betti res sM
0 1 2 3
o135 = total: 8 28 27 7
0: 1 . . .
1: . . . .
2: 7 28 27 4
3: . . . 3
o135 : BettiTally
i136 : gIE=gens IC;
1 12
o136 : Matrix S <
i137 : Y=ideal(gIE * random(source gIE,S^
o137 : Ideal of S
i138 : betti res (sM**(S/Y))
0 1 2 3 4 5 6
o138 = total: 8 28 35 35 35 35 35
0: 1 . . . . . .
1: . . . . . . .
2: 7 28 28 4 . . .
3: . . . 3 . . .
4: . . 7 28 28 4 .
5: . . . . . 3 .
6: . . . . 7 28 28
7: . . . . . . .
8: . . . . . . 7
o138 : BettiTally
i139 : time alexC=first curveOnAlexanderSurface(S,20,20);
o139 : Ideal of S
i140 : omegaAlexC=Ext^2(alexC,S^
i141 : fomegaAlex=res omegaAlexC;
i142 : sM=S^{1:-5}**coker transpose fomegaAlex.dd_3;
i143 : (psi,phi)=matrixFactorizationFromModule(sM);
i144 : X=ideal ring phi;
o144 : Ideal of S
i145 : codim X, degree X
o145 = (1, 4)
o145 : Sequence
i146 : time prune ((ker psi) / (image phi)) == 0
o146 = true
i147 : betti res (coker psi ** S)
0 1
o147 = total: 28 28
0: 22 .
1: . 4
2: 6 24
o147 : BettiTally
i148 : monadShape=betti map(S^{6:-2},S^{4:-2},0);
i149 : time IC=idealFromMatFac(psi, monadShape);
o149 : Ideal of S
i150 : (codim IC, genus IC, degree IC) == (3, 20, 20)
o150 = true
i151 : isSmoothCurve(IC)
o151 = true
i152 : betti res IC
0 1 2 3 4
o152 = total: 1 9 26 24 6
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 9 . . .
4: . . 26 24 6
o152 : BettiTally
i153 : omegaC=Ext^2(IC,S^
i154 : fomega=res omegaC;
i155 : sM=S^{1:-5}**coker transpose fomega.dd_3;
i156 : betti res sM
0 1 2 3
o156 = total: 7 24 21 4
0: 1 . . .
1: . . . .
2: 6 24 21 .
3: . . . 4
o156 : BettiTally
i157 : gIE=gens IC;
1 9
o157 : Matrix S <
i158 : Y=ideal(gIE * random(source gIE,S^
o158 : Ideal of S
i159 : betti res (sM**(S/Y))
0 1 2 3 4 5 6
o159 = total: 7 24 28 28 28 28 28
0: 1 . . . . . .
1: . . . . . . .
2: 6 24 22 . . . .
3: . . . 4 . . .
4: . . 6 24 22 . .
5: . . . . . 4 .
6: . . . . 6 24 22
7: . . . . . . .
8: . . . . . . 6
o159 : BettiTally
i160 :