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 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