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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)
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