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 ;