AnnFs -- differential annihilator of a polynomial in a Weyl algebra

Synopsis

Usage:

AnnFs(f)
Inputs:
- f, a ring element, polynomial in a Weyl algebra $D$
Outputs:
- an ideal, the differential annihilator of $f$ in $D[s]$, for a new variable $s$.

Description

This routine computes the ideal of the differential annihilator of a polynomial. This ideal is a left ideal of the ring $D[s]$. More details can be found in [SST, Chapter 5]. The computation in the case of the element $f$ is via Algorithm 5.3.6.

i1 : makeWA(QQ[x,y])

o1 = QQ[x..y, dx, dy]

o1 : PolynomialRing, 2 differential variable(s)

i2 : f = x^2+y

      2
o2 = x  + y

o2 : QQ[x..y, dx, dy]

i3 : AnnFs f

o3 = ideal (2x*dy - dx, x*dx + 2y*dy - 2s)

o3 : Ideal of QQ[x..y, dx, dy, s]

Caveat

Must be over a ring of characteristic $0$.

Ways to use AnnFs:

AnnFs(RingElement)

For the programmer

The object AnnFs is a method function.