ApCoCoA-1:Weyl.IsHolonomic

Weyl.IsHolonomic

Checks whether an ideal in Weyl algebra An 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 ${\displaystyle A_{n}=C[x_{1},...,x_{n},y_{1},...,y_{n}]}$

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

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

Example

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