# ApCoCoA-1:Weyl.WRedGB

## Weyl.WRedGB

Computes reduced Groebner basis of a D-ideal in Weyl algebra A_n.

### Syntax

```Weyl.WRedGB(GB:LIST):LIST
```

### Description

This function converts Groebner basis GB computed by ApCoCoAServer into the reduced Groebner Basis. If GB is not a Groebner basis then the output will not be the reduced Groebner basis. In fact, this function reduces a list GB of Weyl polynomials using Weyl.WNR into a new list L such that Ideal(L) = Ideal(GB).

Note: This function is faster than Weyl.WRGB for a list GB of large size.

• @param GB Groebner Basis of an ideal in the Weyl algebra.

• @result The reduced Groebner Basis of the given ideal.

#### Example

```A1::=QQ[x,d];	--Define appropriate ring
Use A1;
L:=[x,d,1];
Weyl.WRedGB(L);
[1]
-------------------------------
-- Done.
-------------------------------
```

#### Example

```A2::=ZZ/(7)[x[1..2],y[1..2]]; -- define appropriate ring
Use A2;
I:=Ideal(2x[1]^14y[1]^7,x[1]^2y[1]^3+x[1]^2-1,y[2]^7-1,x[2]^3y[2]^2-x[2]y[2]-3x[2]-1);
GbI:=Weyl.WGB(I,0);Len(GbI);

-------------------------------
-- CoCoAServer: computing Cpu Time = 0.485
-------------------------------
42   -- size of complete GB of the ideal I
-------------------------------
Time GbI:=Weyl.WRedGB(GbI);

Cpu time = 10.89, User time = 11
-------------------------------
11  -- GbI is now reduced Groebner Basis of the ideal I.
-------------------------------
-- Done.
-------------------------------
```