-- The Veronese surface in P^5
-- consider the perameterized surface of P^5 obtained mapping P^2 into P^5 using all degree 2 monomials in 3 variables; this is the Veronese surface of P^5
Use Domain::=Q[x,y,z];
-- a trick to produce all degree d monomials
I:=Ideal(x,y,z)^2;
F:=Gens(I);
-- Es 1c determine the equations of the Veronese surface in P^5
-- Es 2c determine the equation for the variety of secant lines of the veronese surface; is what we get the expected result?