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D.12.7.12 powersums
Procedure from libraryrootsmr.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
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
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