# ApCoCoA-1:Weyl.AnnFs

## Weyl.AnnFs

Computes annihilating ideal of a polynomial F^s in Weyl algebra `A_n`.

### Syntax

Weyl.AnnFs(F:POLY):IDEAL

### 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 annihilating ideal of a polynomial F^s using the Algorithm of Oaku and Takayama, where F is a polynomial in Weyl algebra D. F should not involve any of the indeterminates in {y1, ..., yn}. This ideal belongs to the Weyl algebra A_s =D[s]= QQ[x1, ..., xn, y1, ..., yn, s,w] where s commutes with all x_i and y_i's and w is redundant indeterminate used just to create internal structure of the weyl algebra.

@param

*F*A polynomial F in the indeterminates x1, ..., xn of a Weyl Algebra D.@return An ideal in A_s=QQ[x1, ..., xn,y1, ...,yn, s,w].

#### Example

A2::=QQ[x[1..2],d[1..2]]; --Define appropriate ring Use A2; F:=x[1]^3-x[2]^2; ------------------------------- AnnI:=Weyl.AnnFs(F); -- CoCoAServer: computing Cpu Time = 0.078 ------------------------------- Ideal of Ring A_s = QQ[x[1..2],y[1..2],s,w] Where current indeterminates are mapped into ring A_s as follows: x[1] --> x[1] and d[1] --> y[1] x[2] --> x[2] and d[2] --> y[2] ------------------------------- AnnI; A_s :: Ideal( 3x[1]^2y[2] + 2x[2]y[1], 2x[1]y[1] + 3x[2]y[2] - 6s) --AnnI belongs to the new ring A_s -------------------------------

#### Example

### See also