# AnnIFs(Ideal,RingElement) -- the annihilating ideal of f^s for an arbitrary D-module

## Synopsis

• Function: AnnIFs
• Usage:
AnnIFs(I,f)
• Inputs:
• I, an ideal, that represents a holonomic D-moduleAn/I
• f, , a polynomial in a Weyl algebra An (should contain no differential variables)
• Outputs:
• an ideal, the annihilating ideal of A_n[f^{-1},s] f^s tensored with A_n/I over the ring of polynomials

## Description

 i1 : W = QQ[x,dx, WeylAlgebra=>{x=>dx}] o1 = W o1 : PolynomialRing, 1 differential variables i2 : AnnIFs (ideal dx, x^2) o2 = ideal(x*dx - 2s) o2 : Ideal of QQ[x, dx, s]

## Caveat

Caveats and known problems: The ring of f should not have any parameters: it should be a pure Weyl algebra. Similarly, this ring should not be a homogeneous Weyl algebra.