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D.5.2.10 chAll
Procedure from library chern.lib (see chern_lib).
- Usage:
- chAll(l [,N]); l a list of polynomials, N integer
- Return:
- list of polynomials
- Purpose:
- computes the list of terms of positive degree [up to degree N] of
the Chern character, where the entries of l are considered as the Chern classes
- Note:
- makes sense only for a list of polynomials
Example:
| | LIB "chern.lib";
// Chern character (terms of degree 1, 2, 3)
// corresponding to the Chern classes c(1), c(2), c(3):
ring r = 0, (c(1..3)), dp;
list l=(c(1..3));
print(chAll(l));
==> [1]:
==> c(1)
==> [2]:
==> 1/2*c(1)^2-c(2)
==> [3]:
==> 1/6*c(1)^3-1/2*c(1)*c(2)+1/2*c(3)
// terms up to degree 5 in the same situation
print(chAll(l, 5));
==> [1]:
==> c(1)
==> [2]:
==> 1/2*c(1)^2-c(2)
==> [3]:
==> 1/6*c(1)^3-1/2*c(1)*c(2)+1/2*c(3)
==> [4]:
==> 1/24*c(1)^4-1/6*c(1)^2*c(2)+1/12*c(2)^2+1/6*c(1)*c(3)
==> [5]:
==> 1/120*c(1)^5-1/24*c(1)^3*c(2)+1/24*c(1)*c(2)^2+1/24*c(1)^2*c(3)-1/24*c\
(2)*c(3)
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