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D.15.3.28 chSymm
Procedure from library chern.lib (see chern_lib).
- Usage:
- chSymm(k, r, c[, pos]); k, r integers, c list of polynomials, pos list of integers
- Return:
- list with entries: int N, list of polynomials l
- Purpose:
- computes the rank and the Chern classes of the symmetric power of a vector bundle
- Note:
- for the second symmetric power chSymm2L(...) could be faster
Example:
| LIB "chern.lib";
ring r=0, (c(1..5)), dp;
list l=c(1..5);
// the rank and the Chern classes of the second symmetric power of a vector bundle of rank 3
print( chSymm(2, 3, l) );
==> [1]:
==> 6
==> [2]:
==> [1]:
==> 4*c(1)
==> [2]:
==> -c(1)^2-c(2)
==> [3]:
==> -c(1)^3-11/2*c(1)*c(2)-7/2*c(3)
==> [4]:
==> -c(1)^2*c(2)-2/3*c(2)^2-7/3*c(1)*c(3)
==> [5]:
==> -c(1)*c(2)^2-2*c(1)^2*c(3)-c(2)*c(3)
==> [6]:
==> -c(1)*c(2)*c(3)+c(3)^2
// the rank and the first 3 Chern classes
// of the second symmetric power of a vector bundle of rank 5
print( chSymm(2, 5, l, 1, 2, 3) );
==> [1]:
==> 15
==> [2]:
==> [1]:
==> 6*c(1)
==> [2]:
==> -c(1)^2-1/2*c(2)
==> [3]:
==> -c(1)^3-31/16*c(1)*c(2)-9/16*c(3)
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