D.5.2.51 SchurCh

Usage:

SchurCh(I, C); I list of integers representing a partition, C list of polynomials

Return:

poly

Purpose:

computes the Schur polynomial in the Chern classes C, i.e., in the elementary symmetric polynomials, with respect to the partition I

Note:

if C are the Chern classes of the tautological bundle on a grassmanian, this gives the cohomology class of a Schubert cycle

LIB "chern.lib";
// The Schur polynomial corresponding to the partition 1,2,4
// and the Chern classes c(1), c(2), c(3)
ring r=0,(c(1..3)), dp;
list I=1,2,4;
list C=c(1..3);
print( SchurCh(I, C) );
// Compare this with the Schur polynomial computed using Segre classes
list S=segre( chDual( list(c(1..3)) ), 6 );
print(SchurS(I,S));