D.8.7.11 num_radical_via_decom

Usage:

num_radical_via_decom(I,D); ideal I, int D
D a bound to the degree of the elements of the components.

Return:

ideal: the radical of I

Remarks:

Uses Bertini.
This procedure merely calls num_prime_decom with the same input and then intersects the returned components.

Note:

Should only be called from a ring over the rational numbers.

LIB "recover.lib";
//First, we attempt to compute the radical via the hybrid algorithm.
ring R=0,(x,y,z),dp;
ideal I=(x+y)^2*(y+2z)^3, (x+y)^3*(x-3z)^2;
int D=2;
int Prec=300;
ideal numRad=num_radical_via_decom(I,D,Prec);
numRad;
//Then we compute the radical symbolically and compare the results.
ideal Rad=radical(I);
Rad;
reduce(Rad,std(numRad));
reduce(numRad,std(Rad));