D.8.7.14 num_radical2

Usage:

num_radical2(P,D,C); list P, int D, bigint C
P a list of lists representing a witness point set representing an ideal I D should be a bound to the degree of the elements of the components C the number with which the images of the Veronese embeddings are multiplied

Return:

list of ideals: each of the ideals a prime component of the radical of I

Remarks:

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 complex numbers.

LIB "recover.lib";
//First, we write the input file for bertini and compute the radical symbolically.
ring r=0,(x,y,z),dp;
ideal I=4xy2-4z3,-2x2y+5xz2;
ideal Rad=radical(I);
writeBertiniInput(I,100);
//Then we attempt to compute the radical via the hybrid algorithm.
ring R=(complex,100,i),(x,y,z),dp;
system("sh","bertini input");
list P=getWitnessSet();
int D=2;
bigint C=bigint(10)**30;
ideal Rad2=num_radical2(P,D,C);
//Lastly, we compare the results.
Rad2;
ideal Rad=fetch(r,Rad);
Rad;
reduce(Rad,std(Rad2));
reduce(Rad2,std(Rad));