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D.15.3.30 chSymm2LP

Procedure from library chern.lib (see chern_lib).

Usage:
chSymm2LP(r, c); r integer, c list of polynomials

Return:
poly

Purpose:
computes the total Chern class 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)

Example:
 
LIB "chern.lib";
ring r=0, (c(1..2)), ws(1, 2);
list l=c(1..2);
// the total Chern class of the second symmetric power of a vector bundle of rank 2
print( chSymm2LP(2, l));
==> 1+3*c(1)+2*c(1)^2+4*c(2)+4*c(1)*c(2)