slowAdjunctionCalculation -- compute the adjoint variety and the presentation of O(1)

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

i2 : P2=kk[x_0..x_2]

o2 = P2

o2 : PolynomialRing

i3 : betti(Y=rationalSurface(P2,8,toList(4:3)|toList(4:2)|{1,1},symbol z))

            0 1
o3 = total: 1 7
         0: 1 .
         1: . 5
         2: . 2

o3 : BettiTally

i4 : P6=ring Y, dim P6==7

o4 = (P6, true)

o4 : Sequence

i5 : betti(fY=res Y)

            0 1  2  3 4
o5 = total: 1 7 17 16 5
         0: 1 .  .  . .
         1: . 5  2  . .
         2: . 2 15 16 5

o5 : BettiTally

i6 : betti(omegaY=coker transpose fY.dd_4**P6^{-dim P6})

            0  1
o6 = total: 5 16
         1: 5 16

o6 : BettiTally

i7 : betti(D=transpose presentation omegaY)

             0 1
o7 = total: 16 5
        -2: 16 5

o7 : BettiTally

i8 : (I,adj)=slowAdjunctionCalculation(Y,D,symbol x);

i9 : betti adj

            0  1
o9 = total: 7 16
         0: 7 16

o9 : BettiTally

i10 : P4=ring I, dim P4==5

o10 = (P4, true)

o10 : Sequence

i11 : PI=P4/I

o11 = PI

o11 : QuotientRing

i12 : m=adj**PI;

               7       16
o12 : Matrix PI  <-- PI

i13 : betti(sm=syz transpose m)

             0 1
o13 = total: 7 2
          0: 7 .
          1: . 2

o13 : BettiTally

i14 : rank sm==1

o14 = true

i15 : (numList,adjList,ptsList,I)=adjunctionProcess Y;

i16 : numList, minimalBetti I

                                          0 1 2
o16 = ({(6, 10, 5), 2, (4, 5, 2)}, total: 1 3 2)
                                       0: 1 . .
                                       1: . 1 .
                                       2: . 2 2

o16 : Sequence