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Dmodules :: RatExt

RatExt -- Ext(holonomic D-module, polynomial ring localized at the sigular locus)

Synopsis

Description

The Ext groups between M and N are the derived functors of Hom, and are finite-dimensional vector spaces over the ground field when M and N are holonomic.

The algorithm used appears in the paper 'Polynomial and rational solutions of holonomic systems' by Oaku-Takayama-Tsai (2000). The method is to combine isomorphisms of Bjork and Kashiwara with the restriction algorithm.

i1 : W = QQ[x, D, WeylAlgebra=>{x=>D}]

o1 = W

o1 : PolynomialRing, 1 differential variables
i2 : M = W^1/ideal(x*D+5)

o2 = cokernel | xD+5 |

                            1
o2 : W-module, quotient of W
i3 : RatExt M

                      1
o3 = HashTable{0 => QQ }
                      1
               1 => QQ

o3 : HashTable

Caveat

Input modules M or D/I should be holonomic.

See also

Ways to use RatExt :

For the programmer

The object RatExt is a method function with options.