: genericAnn : Macros in libraries : fctr

## gb

```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 ;

cf. gb, groebner, groebner_sugar, syz.
```

Nobuki Takayama 平成17年2月10日