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D.12.7.13 symmfunc

Procedure from library rootsmr.lib (see rootsmr_lib).

Usage:
symmfunc(s); s list

Return:
list: the symmetric functions of the roots of a polynomial, given the power sums of those roots.

Example:
 
LIB "rootsmr.lib";
ring r = 0,x,dp;
poly p = (x-1)*(x-2)*(x-3);
list psums = list(1+2+3,1+4+9,1+8+27);
list l = symmfunc(psums);
l;
==> [1]:
==>    1
==> [2]:
==> -6
==> [3]:
==> 11
==> [4]:
==> -6
p; // Compare p with the elements of l
==> x3-6x2+11x-6
See also: powersums.