D.8.7.16 num_elim1

Usage:

num_elim1(P,D,C,v); list P, int D, bigint C, intvec v
P a list of lists representing a witness point set representing an ideal J 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 v an intvec specifying the numbers/positions of the variables to be eliminated

Return:

ideal: the ideal obtained from J by eliminating the variables specified in v

Remarks:

This procedure just canonically projects the witness points onto the components specified in the intvec v and then applies num_radical1 to the resulting points.

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 elimination ideal
//symbolically.
ring r=0,(x,y,z),dp;
poly f1=x-y;
poly f2=z*(x+3y);
poly f3=z*(x2+y2);
ideal J=f1,f2,f3;
ideal E2=elim(J,z);
writeBertiniInput(J,100);
//Then we attempt to compute the elimination ideal via the hybrid algorithm.
ring R=(complex,100,i),(x,y,z),dp;
system("sh","bertini input");
list P=getWitnessSet();
intvec v=3;
bigint C=bigint(10)**25;
ideal E1=num_elim1(P,2,C,v);
//Lastly, we compare the results.
E1;
setring r;
E2;