# Difference between revisions of "ApCoCoA-1:Weyl.WDim"

## Weyl.WDim

Computes the dimension of an ideal I in Weyl algebra A_n.

### Syntax

```Weyl.WDim(I:IDEAL):INT
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This function computes the dimension of an Ideal I = (f_1,f_2, ..., f_r) which represents the module A_n/I where every generator f_i should be a Weyl polynomial in Normal form. This dimension of I is equal to the dimension of the associated graded module with respect to the Bernstein filtration.

• @param I An ideal in the Weyl algebra.

• @return The dimension of the given ideal.

#### Example

```W3::=ZZ/(7)[x[1..3],d[1..3]];
Use W3;
-- Cpu time = 0.00, User time = 0
-------------------------------
F1:=-d^3d^5d^5+x^5;
F2:=-3xd^5d^5+xd^3;
F3:=-2d^4d^5-xd^7+x^3d^5;
I:=Ideal(F1,F2,F3);
Weyl.WDim(I);
-- CoCoAServer: computing Cpu Time = 2.36
-------------------------------
2
-------------------------------
```

#### Example

```A3::=QQ[x[1..2],d[1..2]];
Use A3;
-------------------------------
I:=Ideal(xd + 2xd - 5, d^2 - d);
-------------------------------
Weyl.WDim(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
2
-------------------------------
-- If the dimension is ZERO, -1 will be returned
Weyl.WDim(Ideal(x,d));
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
-1
-------------------------------
```