syz

a syz [b c]
array a; array b; array c
b is a set of generators of the syzygies of f.
c = [gb, backward transformation, syzygy without dehomogenization].
See groebner.
a : [f ];    array f;  f is a set of generators of an ideal in a ring.
a : [f v];   array f; string v;  v is the variables.
a : [f v w]; array f; string v; array of array w; w is the weight matirx.
 v may be a ring object. 
Example 1: [(x,y) ring_of_polynomials 0] define_ring 
           [ [(x^2+y^2-4). (x y -1).] ] syz :: 
Example 2: [ [(x^2+y^2) (x y)]   (x,y)  [ [(x) -1 (y) -1] ] ] syz :: 
Example 3: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) 
             [ [ (Dx) 1 ] ] ] syz pmat ; 
Example 4:  [ [(2 x Dx + 3 y Dy+6) (2 y Dx + 3 x^2 Dy)] (x,y) 
             [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] syz pmat ;
Example 5:  [ [ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] 
              (x,y) ] syz pmat ;
Example 6:  [ [ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] 
              (x,y) [[(x) -1 (y) -2]] ] syz pmat ;
Example 7:  [ [ [(0) (0)] [(0) (0)] [(x) (y)]] 
              [(x) (y)]] syz pmat ;