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D.5.2.6 chNum

Procedure from library chern.lib (see chern_lib).

Usage:
chNum(N, c); N 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 N,
the zeroes corresponding to the higher zero Chern classes are ignored

Note:
computes basically the partitions of N
in summands not greater than the length of c

Example:
 
LIB "chern.lib";
ring r = 0, (c(1..2)), dp;
list l=c(1..2);
// Let c(1) be a variable of degree 1, let c(2) be a variable of degree 2.
// The monomials in c(1) and c(2) of weighted degree 5 are:
print( chNum( 5, l ) );
==> [1]:
==>    c(1)^5
==> [2]:
==>    c(1)^3*c(2)
==> [3]:
==>    c(1)*c(2)^2
// Compare the result to the output of chNumbers(...):
print( chNumbers(5, l) );
==> [1]:
==>    c(1)^5
==> [2]:
==>    c(1)^3*c(2)
==> [3]:
==>    c(1)*c(2)^2
==> [4]:
==>    0
==> [5]:
==>    0
==> [6]:
==>    0
==> [7]:
==>    0