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 = [w_{1}t_{1} + ... + w_{n}t_{n}] (here t_{i} = x_{i}D_{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 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] |