+ 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 : ------------------------------------------------------------------
     -- Table 5.2                                                    --
     -- The linear systems reported in Table 5.2 yield curve of the  --
     -- desired genus and degree on the Alexander surface            --
     ------------------------------------------------------------------
     --
     p=32009; -- a prime number

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

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

i5 : -- We construct the Alexander surface Y
     time (Y,pts)=alexanderSurface(S); -- takes 9 sec
     -- used 9.49771 seconds

i6 : -- For every linear system listed in Table 5.2, we compute the
     -- proper transform on Y
     (g,d)=(16,17)

o6 = (16, 17)

o6 : Sequence

i7 : L=linSysAlexander(g,d)

o7 = {21, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6}

o7 : List

i8 : time IC=properTransformAlexander(S,L,pts); -- takes 17 sec
     -- used 16.5189 seconds

o8 : Ideal of S

i9 : (codim IC, genus IC, degree IC) == (3,g,d)

o9 = true

i10 : isSmoothCurve(IC)

o10 = true

i11 : betti res IC

             0  1  2  3 4
o11 = total: 1 17 29 14 1
          0: 1  .  .  . .
          1: .  .  .  . .
          2: .  .  .  . .
          3: . 17 29 13 .
          4: .  .  .  1 1

o11 : BettiTally

i12 : --
      (g,d)=(17,18)

o12 = (17, 18)

o12 : Sequence

i13 : L=linSysAlexander(g,d)

o13 = {22, 7, 7, 7, 7, 7, 7, 7, 7, 6, 5}

o13 : List

i14 : time IC=properTransformAlexander(S,L,pts); -- takes 19 sec
     -- used 18.6634 seconds

o14 : Ideal of S

i15 : (codim IC, genus IC, degree IC) == (3,g,d)

o15 = true

i16 : isSmoothCurve(IC)

o16 = true

i17 : betti res IC

             0  1  2  3 4
o17 = total: 1 14 20 10 3
          0: 1  .  .  . .
          1: .  .  .  . .
          2: .  .  .  . .
          3: . 14 18  . .
          4: .  .  2 10 3

o17 : BettiTally

i18 : --
      (g,d)=(18,19)

o18 = (18, 19)

o18 : Sequence

i19 : L=linSysAlexander(g,d)

o19 = {19, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5}

o19 : List

i20 : time IC=properTransformAlexander(S,L,pts); -- takes 13 sec
     -- used 13.0633 seconds

o20 : Ideal of S

i21 : (codim IC, genus IC, degree IC) == (3,g,d)

o21 = true

i22 : isSmoothCurve(IC)

o22 = true

i23 : betti res IC

             0  1  2  3 4
o23 = total: 1 11 24 19 5
          0: 1  .  .  . .
          1: .  .  .  . .
          2: .  .  .  . .
          3: . 11  7  . .
          4: .  . 17 19 5

o23 : BettiTally

i24 : --
      (g,d)=(19,20)

o24 = (19, 20)

o24 : Sequence

i25 : L=linSysAlexander(g,d)

o25 = {20, 7, 7, 6, 6, 6, 6, 6, 6, 5, 5}

o25 : List

i26 : time IC=properTransformAlexander(S,L,pts); -- takes 15 sec
     -- used 14.7473 seconds

o26 : Ideal of S

i27 : (codim IC, genus IC, degree IC) == (3,g,d)

o27 = true

i28 : isSmoothCurve(IC)

o28 = true

i29 : betti res IC

             0  1  2  3 4
o29 = total: 1 12 32 28 7
          0: 1  .  .  . .
          1: .  .  .  . .
          2: .  .  .  . .
          3: .  8  .  . .
          4: .  4 32 28 7

o29 : BettiTally

i30 : --
      (g,d)=(20,20)

o30 = (20, 20)

o30 : Sequence

i31 : L=linSysAlexander(g,d)

o31 = {20, 7, 6, 6, 6, 6, 6, 6, 6, 6, 5}

o31 : List

i32 : time IC=properTransformAlexander(S,L,pts); -- takes 15 sec
     -- used 15.2199 seconds

o32 : Ideal of S

i33 : (codim IC, genus IC, degree IC) == (3,g,d)

o33 = true

i34 : isSmoothCurve(IC)

o34 = true

i35 : betti res IC

             0 1  2  3 4
o35 = total: 1 9 26 24 6
          0: 1 .  .  . .
          1: . .  .  . .
          2: . .  .  . .
          3: . 9  .  . .
          4: . . 26 24 6

o35 : BettiTally

i36 :