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7.7.4 dmodapp_lib
- Library:
- dmodapp.lib
- Purpose:
- Applications of algebraic D-modules
- Authors:
- Viktor Levandovskyy, levandov@math.rwth-aachen.de
Daniel Andres, daniel.andres@math.rwth-aachen.de
- Guide:
- Let K be a field of characteristic 0, R = K[x1,..xN] and
D be the Weyl algebra in variables x1,..xN,d1,..dN.
In this library there are the following procedures for algebraic D-modules:
- localization of a holonomic module D/I with respect to a mult. closed set
of all powers of a given polynomial F from R. Our aim is to compute an
ideal L in D, such that D/L is a presentation of a localized module. Such L
always exists, since such localizations are known to be holonomic and thus
cyclic modules. The procedures for the localization are DLoc,SDLoc and DLoc0.
- annihilator in D of a given polynomial F from R as well as
of a given rational function G/F from Quot(R). These can be computed via
procedures annPoly resp. annRat.
- initial form and initial ideals in Weyl algebras with respect to a given
weight vector can be computed with inForm, initialMalgrange, initialIdealW.
- appelF1, appelF2 and appelF4 return ideals in parametric Weyl algebras,
which annihilate corresponding Appel hypergeometric functions.
- References:
(SST) Saito, Sturmfels, Takayama 'Groebner Deformations of Hypergeometric
Differential Equations', Springer, 2000
(ONW) Oaku, Takayama, Walther 'A Localization Algorithm for D-modules', 2000
Main procedures:
Auxiliary procedures:
See also:
bfun_lib;
dmod_lib;
gmssing_lib.
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