Singular

D.15.4.32 chWedge2L

Usage:

chWedge2L(r, c ); r integer, c list of polynomials

Return:

list of polynomials

Purpose:

computes the Chern classes of the second exterior 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..3)), dp;
list l=c(1..3);
// the Chern classes of the second exterior power of a vector bundle of rank 3
print(chWedge2L(3, l));
==> [1]:
==>    3
==> [2]:
==>    [1]:
==>       2*c(1)
==>    [2]:
==>       c(1)^2+c(2)
==>    [3]:
==>       c(1)*c(2)-c(3)