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D.15.3.21 chProdLP
Procedure from library chern.lib (see chern_lib).
- 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)
Example:
| | 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
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