D.8.7.15 num_elim

Usage:

num_elim(I,f,D); ideal I, poly f, int D
f the product of the ring variables you want to eliminate D a bound to the degree of the elements of the components

Return:

ideal: the ideal obtained from I by eliminating the variables specified in f

Remarks:

This procedure uses Bertini to compute a set of witness points for I, projects them onto the components corresponding to the variables specified in f and then proceeds as num_radical_via_randlincom.

Note:

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

LIB "recover.lib";
ring r=0,(x,y,z),dp;
poly f1=x-y;
poly f2=z*(x+3y);
poly f3=z*(x2+y2);
ideal I=f1,f2,f3;
//First, we attempt to compute the elimination ideal with the hybrid algorithm.
ideal E1=num_elim(I,z,3,200);
//Now, we compute the elimination ideal symbolically.
ideal E2=elim(I,z);
//Lastly, we compare the results.
E1;
E2;