| #### D.8.7.15 num_elim Procedure from library `recover.lib` (see recover_lib). 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. Example:
    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;

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