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Dmodules :: DlocalizeAll

DlocalizeAll -- localization of a D-module (extended version)

Synopsis

Description

An extension of Dlocalize that in addition computes the localization map, the b-function, and the power s of the generator f^s.
i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]

o1 = W

o1 : PolynomialRing, 2 differential variables
i2 : M = W^1/(ideal(x*Dx+1, Dy))

o2 = cokernel | xDx+1 Dy |

                            1
o2 : W-module, quotient of W
i3 : f = x^2-y^3

        3    2
o3 = - y  + x

o3 : W
i4 : DlocalizeAll(M, f)

o4 = HashTable{GeneratorPower => -2                                        }
                                                    4      5      5      7
               IntegrateBfunction => (s)(s + 1)(s + -)(s + -)(s + -)(s + -)
                                                    3      3      6      6
               LocMap => | y6-2x2y3+x4 |
               LocModule => cokernel | 3xDx+2yDy+15 y3Dy-x2Dy+6y2 |

o4 : HashTable

See also

Ways to use DlocalizeAll :

For the programmer

The object DlocalizeAll is a method function with options.