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D.5.2.28 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]:
==> 5*c(1)^2+5*c(2)
==> [3]:
==> 2*c(1)^3+11*c(1)*c(2)+7*c(3)
==> [4]:
==> 6*c(1)^2*c(2)+4*c(2)^2+14*c(1)*c(3)
==> [5]:
==> 4*c(1)*c(2)^2+8*c(1)^2*c(3)+4*c(2)*c(3)
==> [6]:
==> 8*c(1)*c(2)*c(3)-8*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]:
==> 14*c(1)^2+7*c(2)
==> [3]:
==> 16*c(1)^3+31*c(1)*c(2)+9*c(3)
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