intersect matrix1 ... matrix n result computation

Compute the intersection

of the submodules corresponding to the given matrices. A standard basis and a minimal set of generators of this submodule are also computed.

For example,

%  type j1
; b2-ac c2-bd -bc+ad 

%  type j2
; a2 b2 c2 d2 

%  intersect j1 j2 w
; 0.1.2.3..4..5..
; computation complete after degree 5

%  type w
; c2d-bd2 bc2-b2d c3-ad2 ab2-a2c b3-a2d b2c-ac2 b2d2-acd2 a2c2-a2bd 

%  type w.0  ;; this is the auxiliary matrix.
; 1 b2-ac c2-bd -bc+ad 0  0  0  0  
; 1 0     0     0      a2 b2 c2 d2

The intersect command

The intersection is computed by creating an auxiliary matrix (w.0 in the above example) and then using the syz command to find the first component(s) of each syzygy on the columns of this matrix.

Each matrix matrix i must be graded, and have the same number of rows. If the resulting auxiliary matrix is not graded, then an error message is given, and result computation itself is set to this matrix.