AnnIFs(Ideal,RingElement) -- the annihilating ideal of f^s for an arbitrary D-module
Synopsis
-
Function: AnnIFs
-
- Usage:
AnnIFs(I,f)
-
Inputs:
-
I, that represents a holonomic D-module An/I (the ideal is expected to be f-saturated; one may use WeylClosure if it is not)
-
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 variable(s)
|
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.
See also
-
AnnFs -- differential annihilator of a polynomial in a Weyl algebra
-
WeylAlgebra -- specify differential operators in the ring
-
WeylClosure -- Weyl closure of an ideal