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Dmodules :: bFunction(Module,List,List)

bFunction(Module,List,List) -- b-function of a holonomic D-module

Synopsis

Description

The algorithm represents M as F/N where F is free and N is a submodule of F. Then it computes b-functions bi(s) for N \cap Fi (i-th component of F) and outputs lcm{ bi(s-mi) }
i1 : R = QQ[x, dx, WeylAlgebra => {x=>dx}]

o1 = R

o1 : PolynomialRing, 1 differential variables
i2 : M = cokernel matrix {{x^2, 0, 0}, {0, dx^3, 0}, {0, 0, x^3}}

o2 = cokernel | x2 0    0  |
              | 0  dx^3 0  |
              | 0  0    x3 |

                            3
o2 : R-module, quotient of R
i3 : factorBFunction bFunction(M, {1}, {0,0,0})

o3 = (s)(s - 2)(s - 1)(s + 1)(s + 2)(s + 3)

o3 : Expression of class Product
i4 : factorBFunction bFunction(M, {1}, {1,2,3})

o4 = (s)(s - 4)(s - 3)(s - 2)(s - 1)(s + 1)

o4 : Expression of class Product

Caveat

The Weyl algebra should not have any parameters. Similarly, it should not be a homogeneous Weyl algebra

See also