bFunction(Ideal,List) -- b-function of an ideal

Function: bFunction
Usage:

b = bFunction(I,w)
Inputs:
- I, an ideal, a holonomic ideal in the Weyl algebra A_n(K).
- w, a list, a list of integer weights corresponding to the differential variables in the Weyl algebra.
Optional inputs:
- Strategy => ..., default value IntRing, specify strategy for computing b-function
Outputs:
- b, a ring element, a polynomial b(s) which is the b-function of I with respect to w

Description

Use setHomSwitch(true) to force all the subroutines to use homogenized WeylAlgebra

Definition. The b-function b(s) is defined as the monic generator of the intersection of in_(-w,w)(I) and K[s], where s = [w₁t₁ + ... + w_nt_n] (here t_i = x_iD_i).

i1 : R = QQ[x_1,x_2,D_1,D_2,WeylAlgebra=>{x_1=>D_1,x_2=>D_2}]

o1 = R

o1 : PolynomialRing, 2 differential variable(s)

i2 : I = ideal(x_1, D_2-1)

o2 = ideal (x , D  - 1)
             1   2

o2 : Ideal of R

i3 : bFunction(I,{1, 0})

o3 = s + 1

o3 : QQ[s]

Caveat

The ring of I should not have any parameters: it should be a pure Weyl algebra. Similarly, this ring should not be a homogeneous WeylAlgebra

Ways to use this method:

bFunction(Ideal,List) -- b-function of an ideal

The source of this document is in BernsteinSato/DOC/bFunctions.m2:80:0.

bFunction(Ideal,List) -- b-function of an ideal

Description

Caveat

See also

Ways to use this method: