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kOrderAnnFa -- k-th order D-annihilator of a power of a polynomial

Usage:

kOrderAnnFa(k,f,a)

kOrderAnnFs(k,f)
Inputs:
- k, an integer, positive
- f, a ring element, a polynomial in $K[x_1,...,x_n]$
- a, an integer, (usually negative) exponent
Outputs:
- I, an ideal, an ideal in the Weyl algebra $K<x_1,...,x_n,\partial_1,...,\partial_n>$ (or $K[s]<x_1,...,x_n,\partial_1,...,\partial_n>$)

Description

kOrderAnnFa (kOrderAnnFs) return an ideal generated by elements of order at most $k$ of the annihilator of $f^a$ ($f^s$). See [Castro-Jimenez, Leykin "Computing localizations iteratively" (2012)] for details.

i1 : R = QQ[x_1,x_2]; f = x_1^2-x_2^3;

i3 : A1 = kOrderAnnFa(1,f,-1)

                                   2               3       2        2
o3 = ideal (3x dx  + 2x dx  + 6, 3x dx  + 2x dx , x dx  - x dx  + 3x )
              1  1     2  2        2  1     1  2   2  2    1  2     2

o3 : Ideal of QQ[x ..x , dx ..dx ]
                  1   2    1    2

i4 : As = kOrderAnnFs(1,f)

              2
o4 = ideal (3x dx  + 2x dx , 6s - 3x dx  - 2x dx )
              2  1     1  2         1  1     2  2

o4 : Ideal of QQ[x ..x , dx ..dx , s]
                  1   2    1    2

See also

kappaAnnF1PlanarCurve -- D-annihilator of 1/f for a planar curve
AnnFs -- differential annihilator of a polynomial in a Weyl algebra

Ways to use kOrderAnnFa:

kOrderAnnFa(ZZ,RingElement,ZZ)

For the programmer

The object kOrderAnnFa is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BernsteinSato/DOC/paco-anton-paper.m2:88:0.