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D.15.3.48 SchurS

Procedure from library chern.lib (see chern_lib).

Usage:
SchurS(I, S); I list of integers representing a partition, S list of polynomials

Return:
poly

Purpose:
computes the Schur polynomial in the Segre classes S, i.e., in the complete homogeneous symmetric polynomials, with respect to the partition I

Note:
if S are the Segre classes of the tautological bundle on a grassmanian, this gives the cohomology class of a Schubert cycle

Example:
 
LIB "chern.lib";
// The Schur polynomial corresponding to the partition 1,2,3
// and the Segre classes 1, s(1), s(2),..., s(5)
ring r=0,(s(1..5)), dp;
list I=1,2,3;
list S=s(1..5);
print( SchurS(I, S) );
==> s(1)*s(2)*s(3)-s(1)^2*s(4)-s(3)^2+s(1)*s(5)
// compare this with the Schur polynomial computed using Chern classes
list C=chern(S);
print( SchurCh(I, C) );
==> s(1)*s(2)*s(3)-s(1)^2*s(4)-s(3)^2+s(1)*s(5)


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