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D.15.3.1 symm
Procedure from library chern.lib (see chern_lib).
- Usage:
- symm(l [,n]); l a list of polynomials, n integer
- Return:
- list of polynomials
- Purpose:
- computes the list of elementary symmetric functions in the entries of l
- Note:
- makes sense only for a list of polynomials
Example:
| | LIB "chern.lib";
// elementary symmetric functions in x, y, z:
ring r = 0, (x, y, z), dp;
list l=(x, y, z);
print(symm(l));
==> [1]:
==> x+y+z
==> [2]:
==> xy+xz+yz
==> [3]:
==> xyz
//now let us compute only the first two symmetric polynomials in a(1), ... , a(10)
ring q= 0,(a(1..10)), dp;
list l=a(1..10);
print(symm(l, 2));
==> [1]:
==> a(1)+a(2)+a(3)+a(4)+a(5)+a(6)+a(7)+a(8)+a(9)+a(10)
==> [2]:
==> a(1)*a(2)+a(1)*a(3)+a(2)*a(3)+a(1)*a(4)+a(2)*a(4)+a(3)*a(4)+a(1)*a(5)+\
a(2)*a(5)+a(3)*a(5)+a(4)*a(5)+a(1)*a(6)+a(2)*a(6)+a(3)*a(6)+a(4)*a(6)+a(5\
)*a(6)+a(1)*a(7)+a(2)*a(7)+a(3)*a(7)+a(4)*a(7)+a(5)*a(7)+a(6)*a(7)+a(1)*a\
(8)+a(2)*a(8)+a(3)*a(8)+a(4)*a(8)+a(5)*a(8)+a(6)*a(8)+a(7)*a(8)+a(1)*a(9)\
+a(2)*a(9)+a(3)*a(9)+a(4)*a(9)+a(5)*a(9)+a(6)*a(9)+a(7)*a(9)+a(8)*a(9)+a(\
1)*a(10)+a(2)*a(10)+a(3)*a(10)+a(4)*a(10)+a(5)*a(10)+a(6)*a(10)+a(7)*a(10\
)+a(8)*a(10)+a(9)*a(10)
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