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D.15.2.7 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)