Singular

D.15.4.29 chSymm2L

Usage:

chSymm2L(r, c); r integer, c list of polynomials

Return:

list of polynomials

Purpose:

computes the Chern classes of the second symmetric power of a vector bundle

Note:

Implementation of the formula of Lascoux, the Schur polynomials are computed using the second Jacobi-Trudi formula (in terms of the Chern classes)

LIB "chern.lib";
ring r=0, (c(1..2)), dp;
list l=c(1..2);
// the Chern classes of the second symmetric power of a vector bundle of rank 2
print( chSymm2L(2, l));
==> [1]:
==>    3
==> [2]:
==>    [1]:
==>       3*c(1)
==>    [2]:
==>       2*c(1)^2+4*c(2)
==>    [3]:
==>       4*c(1)*c(2)