--8/16/05
--author: Greg Smith
--This code, written by Greg Smith, computes the ideal of the secant variety
--of the variety defined by I.  

--7/05/09
--author: Jessica Sidman
--Greg Smith wrote secantIdeal in an old version of M2 which gives error messages now. 
--This is a slight revision of his code.

--input ideal I, output secant ideal of I
secantIdeal = I -> (
     R := ring I;
     n := numgens R;
     S := (coefficientRing R)[y_0..y_(n-1),x_0..x_(n-1), MonomialOrder => Eliminate n];
     iota := map(S,R, apply(n, i->  S_i));
     delta := map(S,R, apply(n, i -> S_i - S_(i+n)));
     L:={};
     for i from 0 to n-1 do(
	  L = append(L, 0_R);
	  );
     f := map(R,S, join(L,flatten entries vars R));
     f(ideal selectInSubring(1, gens gb (iota(I) + delta(I))))
         )