Singular

LIB "chern.lib";
ring r=0, (c(1..5)), dp;
list l=c(1..5);
// the rank and the Chern classes of the second symmetric power of a vector bundle of rank 3
print( chSymm(2, 3, l) );
==> [1]:
==>    6
==> [2]:
==>    [1]:
==>       4*c(1)
==>    [2]:
==>       -c(1)^2-c(2)
==>    [3]:
==>       -c(1)^3-11/2*c(1)*c(2)-7/2*c(3)
==>    [4]:
==>       -c(1)^2*c(2)-2/3*c(2)^2-7/3*c(1)*c(3)
==>    [5]:
==>       -c(1)*c(2)^2-2*c(1)^2*c(3)-c(2)*c(3)
==>    [6]:
==>       -c(1)*c(2)*c(3)+c(3)^2
// the rank and the first 3 Chern classes
// of the second symmetric power of a vector bundle of rank 5
print( chSymm(2, 5, l, 1, 2, 3) );
==> [1]:
==>    15
==> [2]:
==>    [1]:
==>       6*c(1)
==>    [2]:
==>       -c(1)^2-1/2*c(2)
==>    [3]:
==>       -c(1)^3-31/16*c(1)*c(2)-9/16*c(3)