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



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

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]


Must be over a ring of characteristic $0$.

Ways to use AnnFs :

For the programmer

The object AnnFs is a method function.