DlocalizeMap -- localization map from a D-module to its localization

Synopsis

• Usage:

  DlocalizeMap(M,f), DlocalizeMap(I,f)

• Inputs:
  • M, a module, over the Weyl algebra D
  • I, an ideal, which represents the module M = D/I
  • f, a ring element, a polynomial
• Optional inputs:
  • Strategy => ..., default value OTW, strategy for computing a localization of a D-module
• Outputs:
  • a matrix, which represents the natural map from M to M_f = M[f^{-1}]

Description

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 : DlocalizeMap(M, f)

o4 = | y6-2x2y3+x4 |

o4 : Matrix

See also

• Dlocalize -- localization of a D-module
• AnnFs -- the annihilating ideal of f^s
• Dintegration -- integration modules of a D-module