-- -*- M2-comint -*- hash: 1448514238910196962

i1 : d=7

o1 = 7

i2 : L=toList(8:2)|toList(5:1)

o2 = {2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1}

o2 : List

i3 : n=expectedDimension(d,L)-1

o3 = 6

i4 : kk=ZZ/nextPrime(10^3)

o4 = kk

o4 : QuotientRing

i5 : t=symbol t, x= symbol x

o5 = (t, x)

o5 : Sequence

i6 : P2=kk[t_0..t_2]

o6 = P2

o6 : PolynomialRing

i7 : Pn=kk[x_0..x_n]

o7 = Pn

o7 : PolynomialRing

i8 : betti(I=rationalSurface(P2,d,L,Pn))

            0  1
o8 = total: 1 11
         0: 1  .
         1: .  3
         2: .  8

o8 : BettiTally

i9 : minimalBetti I

            0  1  2  3 4
o9 = total: 1 11 27 24 7
         0: 1  .  .  . .
         1: .  3  .  . .
         2: .  8 27 24 7

o9 : BettiTally

i10 : (numList,adjList,ptsList,J)=adjunctionProcess(I);

i11 : numList

o11 = {(6, 12, 7), 5, (6, 8, 3), 8, (2, 1, 0)}

o11 : List

i12 : P2=ring J

o12 = P2

o12 : PolynomialRing

i13 : betti(H=parametrization(P2,adjList))

             0 1
o13 = total: 1 7
          0: 1 .
          1: . .
          2: . .
          3: . .
          4: . .
          5: . .
          6: . 7

o13 : BettiTally

i14 : phi=map(P2,Pn,H);

o14 : RingMap P2 <-- Pn

i15 : elapsedTime betti(I'=trim ker phi)
 -- .610907s elapsed

             0  1
o15 = total: 1 11
          0: 1  .
          1: .  3
          2: .  8

o15 : BettiTally

i16 : I'== I

o16 = true

i17 : elapsedTime basePts=primaryDecomposition ideal H;
 -- 5.10577s elapsed

i18 : tally apply(basePts,c->(dim c, degree c, betti c))

                          0 1
o18 = Tally{(1, 1, total: 1 2) => 5}
                       0: 1 2
                          0 1
            (1, 3, total: 1 3) => 8
                       0: 1 .
                       1: . 3

o18 : Tally

i19 : 
