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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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