-- Exterior algebra and Grassmannians:
-- construction of the incidence variety
k=1;
n=3;
G = Grassmannian(k,n) -- projective lines in P^3
R = QQ[x_0..x_n,gens ring G] -- the ring for (P^3)x(G(1,3)) 
V = R^(n+1) -- this "vector space" is, in fact, a free R-module
E = exteriorPower(2,V) -- second exterior power
WP = wedgeProduct(1,2,V) 
xs = submatrix(vars R, 0..3) 
v = transpose xs
w = transpose sub(vars ring G, R)
Sigma = WP*(v**w) -- this wedge product determines the equations of the incidence variety
J = ideal Sigma + sub(G,R)