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BernsteinSato :: AnnFs

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

Synopsis

Description

This routine computes the ideal of the differential annihilator of a polynomial or list of polynomials in a Weyl algebra $D$. This ideal is a left ideal of the ring $D[s]$ or $D[t_0,..,t_k,dt_0,..,dt_k]$. More details can be found in [SST, Chapter 5]. The computation in the case of the element $f$ is via Algorithm 5.3.6, and the computation in the case of the list $L$ is via the Algorithm 5.3.15.

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]
i4 : makeWA(QQ[x,y,z])

o4 = QQ[x..z, dx, dy, dz]

o4 : PolynomialRing, 3 differential variable(s)
i5 : L = {x^3,y+5*z}

       3
o5 = {x , y + 5z}

o5 : List

Caveat

Must be over a ring of characteristic $0$.

Ways to use AnnFs :

For the programmer

The object AnnFs is a method function.