+ M2 --no-readline --print-width 99
Macaulay2, version 1.9.2
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition,
               ReesAlgebra, TangentCone

i1 : loadPackage("MatFacCurvesP4")

o1 = MatFacCurvesP4

o1 : Package

i2 : ------------------------------------------------------------------
     -- Theorem 5.2                                                      --
     -- We compute h^1(N), where N is the normal sheaf of a curve C  --
     -- with respect to a general supporting threefold of minimal    --
     -- degree, and we check that it is zero for the general C       --
     ------------------------------------------------------------------
     --
     p=32009; -- a prime number

i3 : Fp=ZZ/p; -- a prime field

i4 : S=Fp[x_0..x_4];

i5 : -- (g,d)=(12,14)
     IC=randomCurveGenus12Degree14InP4(S);

o5 : Ideal of S

i6 : gIC=gens IC;     

             1       9
o6 : Matrix S  <--- S

i7 : X=ideal(gIC * random(source gIC,S^{-min(degrees source gIC)}));

o7 : Ideal of S

i8 : time h1NormalBundle(IC,X) == 0 -- takes 13 sec
     -- used 12.8239 seconds

o8 = true

i9 : -- (g,d)=(13,15)
     IC=curveGenus13Degree15InP4(S);

o9 : Ideal of S

i10 : gIC=gens IC;     

              1       14
o10 : Matrix S  <--- S

i11 : X=ideal(gIC * random(source gIC,S^{-min(degrees source gIC)}));

o11 : Ideal of S

i12 : time h1NormalBundle(IC,X) == 0 -- takes 161 sec
     -- used 161.118 seconds

o12 = true

i13 : -- (g,d)=(16,17)
      (g,d)=(16,17);

i14 : IC=first curveOnAlexanderSurface(S,g,d);

o14 : Ideal of S

i15 : gIC=gens IC;     

              1       18
o15 : Matrix S  <--- S

i16 : X=ideal(gIC * random(source gIC,S^{-min(degrees source gIC)}));

o16 : Ideal of S

i17 : time h1NormalBundle(IC,X) == 0 -- takes 1089 sec 
     -- used 1089.45 seconds

o17 = true

i18 : -- (g,d)=(17,18)
      (g,d)=(17,18);

i19 : IC=first curveOnAlexanderSurface(S,g,d);

o19 : Ideal of S

i20 : gIC=gens IC;     

              1       18
o20 : Matrix S  <--- S

i21 : X=ideal(gIC * random(source gIC,S^{-min(degrees source gIC)}));

o21 : Ideal of S

i22 : time h1NormalBundle(IC,X) == 0 -- takes 1239 sec
     -- used 1239.18 seconds

o22 = true

i23 : -- (g,d)=(18,19)
      (g,d)=(18,19);

i24 : IC=first curveOnAlexanderSurface(S,g,d);

o24 : Ideal of S

i25 : gIC=gens IC;     

              1       20
o25 : Matrix S  <--- S

i26 : X=ideal(gIC * random(source gIC,S^{-min(degrees source gIC)}));

o26 : Ideal of S

i27 : time h1NormalBundle(IC,X) == 0 -- takes 435 sec
     -- used 435.426 seconds

o27 = true

i28 : -- (g,d)=(19,20)
      (g,d)=(19,20);

i29 : IC=first curveOnAlexanderSurface(S,g,d);

o29 : Ideal of S

i30 : gIC=gens IC;     

              1       22
o30 : Matrix S  <--- S

i31 : X=ideal(gIC * random(source gIC,S^{-min(degrees source gIC)}));

o31 : Ideal of S

i32 : time h1NormalBundle(IC,X) == 0 -- takes 362 sec
     -- used 361.564 seconds

o32 = true

i33 : -- (g,d)=(20,20)
      (g,d)=(20,20);

i34 : IC=first curveOnAlexanderSurface(S,g,d);

o34 : Ideal of S

i35 : gIC=gens IC;     

              1       21
o35 : Matrix S  <--- S

i36 : X=ideal(gIC * random(source gIC,S^{-min(degrees source gIC)}));

o36 : Ideal of S

i37 : time h1NormalBundle(IC,X) == 0 -- takes 242 sec
     -- used 241.957 seconds

o37 = true

i38 :