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D.12.6.12 powersums

Procedure from library rootsmr.lib (see rootsmr_lib).

Usage:
powersums(f,b,i); f poly; b,i ideal

Return:
list: the powersums of the results of evaluating f at the zeros of I

Assume:
i is a Groebner basis and b is an ordered monomial basis of r/i, r = basering

Example:
 
LIB "rootsmr.lib";
ring r = 0,(x,y,z),dp;
ideal i = (x-1)*(x-2),(y-1),(z+5); // V(I) = {(1,1,-5),(2,1,-5)}
i = std(i);
ideal b = qbase(i);
poly f = x+y+z;
list psums = list(-2-3,4+9); // f evaluated at V(I) gives {-3,-2}
list l = powersums(f,b,i);
psums;
==> [1]:
==>    -5
==> [2]:
==>    13
l;
==> [1]:
==> -5
==> [2]:
==> 13
See also: symmfunc.


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