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Dmodules :: bFunction(Ideal,List)

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

Synopsis

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 + ... + wntn] (here ti = xiDi).

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 variables
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

See also