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

## Weyl.IsHolonomic

Checks whether an ideal in Weyl algebra A_n is holonomic or not.

### Syntax

```Weyl.IsHolonomic(I:IDEAL):BOOL
```

### 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.

An ideal I is holonomic if it has dimension n, the number of variables in the Weyl algebra A_n = C[x_1,...,x_n,y_1,...,y_n].

This function determines whether an ideal I is holonomic by checking its dimension.

• @param I An ideal in the Weyl algebra A_n.

• @return TRUE if the given ideal is holonomic.

#### 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.IsHolonomic(I);
-- CoCoAServer: computing Cpu Time = 2.36
-------------------------------
FALSE
-------------------------------
```

#### Example

```A2::=QQ[x[1..2],d[1..2]];
Use A2;
-------------------------------
I:=Ideal(xd + 2xd - 5, d^2 - d);
-------------------------------
Weyl.IsHolonomic(I);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
TRUE
-------------------------------
```