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D.15.3.51 SchurCh
Procedure from library chern.lib (see chern_lib).
- 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
Example:
| | 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) );
==> c(1)^2*c(2)*c(3)-c(2)^2*c(3)-c(1)*c(3)^2
// Compare this with the Schur polynomial computed using Segre classes
list S=segre( chDual( list(c(1..3)) ), 6 );
print(SchurS(I,S));
==> c(1)^2*c(2)*c(3)-c(2)^2*c(3)-c(1)*c(3)^2
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