Singular Manual: SchurCh

| #### D.5.2.51 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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