Singular

D.5.2.21 chProdLP

Usage:

chProdLP(r, c, R, C); r, R integers; c, C lists of polynomials

Return:

polynomial

Purpose:

computes the total Chern class of the product of two vector bundles in terms of their ranks and Chern clases

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";
// The total Chern class of the tensor product of a vector bundle of rank 3
// with Chern classes c(1), c(2), c(3) and a vector bundle of rank 1 with
// Chern class C(1)
ring r = 0, ( c(1..3), C(1)), ws(1,2,3, 1);
list c=c(1..3);
list C=C(1);
print( chProdLP(3,c,1,C) );
==> 1+c(1)+3*C(1)+c(2)+2*c(1)*C(1)+3*C(1)^2+c(3)+c(2)*C(1)+c(1)*C(1)^2+C(1)^3