> #I used that to calculate the relations defining the homogenous ideal of the Grassmannian Grass(2, 4). For convenience, use a "Maple notaion" in the options/Output display. I then copied the generators (equal to the entries of the Adjoint matrix (only in this case!) to another file called "Example1.txt". That file is "program" for Macaulay2. I calculate there the radical. It is given by a SINGLE generator. This in not surprising. Since Grass(2, 4) is of dimension 4 in P^5, it is a hypersurface and hence given, as any hypersurface is, by a single relation.

> with(linalg):

> A:=matrix([[a23, -a13, a12, 0], [a24, -a14, 0, a12], [a34, 0, -a14, a13], [0, a34, -a24, a23]]);

A := matrix([[a23, -a13, a12, 0], [a24, -a14, 0, a12], [a34, 0, -a14, a13], [0, a34, -a24, a23]])

> B:=adj(A);

B := matrix([[a14^2*a23-a14*a13*a24+a34*a12*a14, -a13*a14*a23+a13^2*a24-a34*a12*a13, -a13*a12*a24+a14*a12*a23+a34*a12^2, 0], [a24*a14*a23-a13*a24^2+a34*a12*a24, -a14*a23^2+a23*a13*a24-a34*a12*a23, 0, -a13*a12*a24+a14*a12*a23+a34*a12^2], [-a24*a13*a34+a34*a14*a23+a12*a34^2, 0, -a14*a23^2+a23*a13*a24-a34*a12*a23, a13*a14*a23-a13^2*a24+a34*a12*a13], [0, -a24*a13*a34+a34*a14*a23+a12*a34^2, -a24*a14*a23+a13*a24^2-a34*a12*a24, a14^2*a23-a14*a13*a24+a34*a12*a14]])

> for i from 1 to 4 do for j from 1 to 4 do print(B[i, j]) od od;

a14^2*a23-a14*a13*a24+a34*a12*a14

-a13*a14*a23+a13^2*a24-a34*a12*a13

-a13*a12*a24+a14*a12*a23+a34*a12^2

0

a24*a14*a23-a13*a24^2+a34*a12*a24

-a14*a23^2+a23*a13*a24-a34*a12*a23

0

-a13*a12*a24+a14*a12*a23+a34*a12^2

-a24*a13*a34+a34*a14*a23+a12*a34^2

0

-a14*a23^2+a23*a13*a24-a34*a12*a23

a13*a14*a23-a13^2*a24+a34*a12*a13

0

-a24*a13*a34+a34*a14*a23+a12*a34^2

-a24*a14*a23+a13*a24^2-a34*a12*a24

a14^2*a23-a14*a13*a24+a34*a12*a14

>