a gb b array a; array b; b : [g ii]; array g; array in; g is a Grobner basis of f in the ring of differential operators. ii is the initial ideal in case of w is given or <<a>> belongs to a ring. In the other cases, it returns the initial monominal. 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. a : [f v w ds]; array f; string v; array of array w; w is the weight matirx. array ds; ds is the degree shift gb.authoHomogenize 1 [default] gb.oxRingStructure Example 1: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) [ [ (Dx) 1 ] ] ] gb pmat ; Example 2: To put h=1, type in, e.g., [ [(2 x Dx + 3 y Dy+6) (2 y Dx + 3 x^2 Dy)] (x,y) [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] gb /gg set gg dehomogenize pmat ; Example 3: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) [ [ (Dx) 1 (Dy) 1] ] ] gb pmat ; Example 4: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) [ [ (x) -1 (y) -1] ] ] gb pmat ; Example 5: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) [ [ (x) -1 (y) -1] ] [[0 1] [-3 1] ] ] gb pmat ; Example 6: [ [( (x Dx)^2 + (y Dy)^2 - x y Dx Dy + 1) ( x y Dx Dy -1)] (x,y) [ [ (Dx) 1 ] ] ] [(reduceOnly) 1] setAttributeList gb pmat ; Example 7: [ [( (x Dx)^2 + (y Dy)^2 + 1) ( x y Dx Dy -1)] (x,y) [ [ (Dx) 1 ] ] ] [(gbCheck) 1] setAttributeList gb getAttributeList :: cf. gb, groebner, groebner_sugar, syz.