Singular Manual: chNumbers

| #### D.5.2.7 chNumbers Procedure from library `chern.lib` (see chern_lib). Usage: chNumbers(r, c); r integer, c list Return: list Purpose: computes the Chern numbers of a vector bundle with Chern classes c on a complex manifold (variety) of dimension r Note: computes basically the partitions of r Example:
    LIB "chern.lib";
    ring r = 0, (c(1..3)), dp;
    list l=c(1..3);
    // The Chern numbers of a vector bundle with Chern classes c(1), c(2), c(3)
    // on a 3-fold:
    print( chNumbers( 3, l ) );
    ==> [1]:
    ==>    c(1)^3
    ==> [2]:
    ==>    c(1)*c(2)
    ==> [3]:
    ==>    c(3)
    // If the highest Chern class is zero, the Chern numbers are:
    l=c(1..2);
    print( chNumbers( 3, l ) );
    ==> [1]:
    ==>    c(1)^3
    ==> [2]:
    ==>    c(1)*c(2)
    ==> [3]:
    ==>    0
    // Compare this to the output of chNum(...):
    print( chNum( 3, l ) );
    ==> [1]:
    ==>    c(1)^3
    ==> [2]:
    ==>    c(1)*c(2)

User manual for Singular version 4.4.1, 2025, generated by texi2html.