chern(AbstractSheaf) -- compute the total Chern class of a sheaf

i1 : base(3, Bundle => (A,2,a), Bundle => (B,3,b))

o1 = a variety

o1 : an abstract variety of dimension 3

i2 : chern B

o2 = 1 + b  + b  + b
          1    2    3

o2 : QQ[a , a , b , b , b ]
         1   2   1   2   3

i3 : chern(-A)

                2             3
o3 = 1 - a  + (a  - a ) + (- a  + 2a a )
          1     1    2        1     1 2

o3 : QQ[a , a , b , b , b ]
         1   2   1   2   3

i4 : pt = base(n,p,q)

o4 = pt

o4 : an abstract variety of dimension 0

i5 : P2 = projectiveSpace'_2 pt

o5 = P2

o5 : a flag bundle with ranks {2, 1}

i6 : E = abstractSheaf(P2, Rank=>2, ChernClass=>1+p*h+q*h^2)

o6 = E

o6 : an abstract sheaf of rank 2 on P2

i7 : chern E(n*h)

                       2            2
o7 = 1 + (2n + p)h + (n  + n*p + q)h

        QQ[n, p, q][H   , H   , h]
                     1,1   1,2
o7 : -------------------------------
     (H    + h, H    + H   h, H   h)
       1,1       1,2    1,1    1,2