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D.5.2.20 chProdL
Procedure from library chern.lib (see chern_lib).
- Usage:
- chProdL(r, c, R, C); r, R integers; c, C lists of polynomials
- Return:
- list
- Purpose:
- computes the list of Chern classes of the product of two vector bundles
in terms of their 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)
Example:
| | LIB "chern.lib";
// The Chern classes 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)), dp;
list c=c(1..3);
list C=C(1);
print( chProdL(3,c,1,C) );
==> [1]:
==> c(1)+3*C(1)
==> [2]:
==> 2*c(1)*C(1)+3*C(1)^2+c(2)
==> [3]:
==> c(1)*C(1)^2+C(1)^3+c(2)*C(1)+c(3)
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