next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Dmodules :: PolyExt

PolyExt -- Ext groups between a holonomic module and a polynomial ring

Synopsis

Description

The Ext groups between a D-module M and the polynomial ring are the derived functors of Hom, and are finite-dimensional vector spaces over the ground field when M is 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^2*D^2)

o2 = cokernel | x2D2 |

                            1
o2 : W-module, quotient of W
i3 : PolyExt(M)

                      2
o3 = HashTable{0 => QQ }
                      2
               1 => QQ

o3 : HashTable

Caveat

Does not yet compute explicit representations of Ext groups such as Yoneda representation.

See also

Ways to use PolyExt :

For the programmer

The object PolyExt is a method function with options.