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

Weyl.WDim

Computes the dimension of an ideal I in Weyl algebra ${\displaystyle A_{n}}$.

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[1]^3d[2]^5d[3]^5+x[2]^5;
F2:=-3x[2]d[2]^5d[3]^5+x[2]d[1]^3;
F3:=-2d[1]^4d[2]^5-x[1]d[2]^7+x[3]^3d[3]^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(x[1]d[1] + 2x[2]d[2] - 5, d[1]^2 - d[2]);
-------------------------------
Weyl.WDim(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
2
-------------------------------
-- If the dimension is ZERO, -1 will be returned
Weyl.WDim(Ideal(x[1],d[1]));
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
-1
-------------------------------
```