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D.15.2.9 powSumSym
Procedure from library chern.lib (see chern_lib).
- Usage:
- powSumSym(l [,N]); l a list of polynomials, N integer
- Return:
- list of polynomials
- Purpose:
- computes the expressions for the sums of powers [up to degree N]
in terms of the elementary symmetric polynomials (entries of l),
- Note:
- returns the terms of the Chern character
multiplied by the correspoding factorials
Example:
| | LIB "chern.lib";
// the expressions of the first 3 sums of powers of 3 variables a(1), a(2), a(3)
// in terms of the elementary symmetric polynomials c(1), c(2), c(3):
ring r = 0, (c(1..3)), dp;
list l=(c(1..3));
print(powSumSym(l));
==> [1]:
==> c(1)
==> [2]:
==> c(1)^2-2*c(2)
==> [3]:
==> c(1)^3-3*c(1)*c(2)+3*c(3)
// The first 5 sums in the same situation
print(powSumSym(l, 5));
==> [1]:
==> c(1)
==> [2]:
==> c(1)^2-2*c(2)
==> [3]:
==> c(1)^3-3*c(1)*c(2)+3*c(3)
==> [4]:
==> c(1)^4-4*c(1)^2*c(2)+2*c(2)^2+4*c(1)*c(3)
==> [5]:
==> c(1)^5-5*c(1)^3*c(2)+5*c(1)*c(2)^2+5*c(1)^2*c(3)-5*c(2)*c(3)
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