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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
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