D.8.7.12 num_radical_via_randlincom

Usage:

num_radical_via_randlincom(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.
Instead of using the images of the Veronese embeddings of each individual witness point, this procedure first computes a random linear combination of those images and searches for homogeneous polynomial relations for this linear combination.

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_randlincom(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));