Example from Schubert: Lines on a quintic threefold

# Lines on a quintic threefold.  This is the top Chern class of the
# 5th symmetric power of the universal quotient bundle on the Grassmannian
# of lines.
>
> grass(2,5,c):        # Lines in P^4.

i1 : Gc = flagBundle({3,2}, VariableNames => {,c})

o1 = Gc

o1 : a flag bundle with subquotient ranks {3, 2}

i2 : (Sc,Qc) = bundles Gc

o2 = (Sc, Qc)

o2 : Sequence

> B:=symm(5,Qc):       # Qc is the rank 2 quotient bundle, B its 5th
>                      # symmetric power.

i3 : B = symmetricPower(5,Qc)

o3 = B

o3 : an abstract sheaf of rank 6 on Gc

> c6:=chern(rank(B),B):# the 6th Chern class of this rank 6 bundle.

i4 : c6 = chern(rank B,B)

          3
o4 = 2875c
          2

                                      QQ[][H   ..H   , c ..c ]
                                            1,1   1,3   1   2
o4 : -----------------------------------------------------------------------------------------
     (- H    - c , - H    - H   c  - c , - H    - H   c  - H   c , - H   c  - H   c , -H   c )
         1,1    1     1,2    1,1 1    2     1,3    1,2 1    1,1 2     1,3 1    1,2 2    1,3 2

> integral(c6);
                                      2875

i5 : integral c6

o5 = 2875