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

Synopsis

• 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

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