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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:

7.7.4.0. annPoly  annihilator of a polynomial f in the corr. Weyl algebra
7.7.4.0. annRat  annihilator of a rational function f/g in the corr. Weyl algebra
7.7.4.0. DLoc  presentation of the localization of D/I w.r.t. f^s
7.7.4.0. SDLoc  a generic presentation of the localization of D/I w.r.t. f^s
7.7.4.0. DLoc0  presentation of the localization of D/I w.r.t. f^s, based on SDLoc
7.7.4.0. initialMalgrange  Groebner basis of the initial Malgrange ideal for f
7.7.4.0. initialIdealW  initial ideal of a given ideal w.r.t. given weights
7.7.4.0. inForm  initial form of a poly/ideal w.r.t. a given weight
7.7.4.0. isFsat  check whether the ideal I is F-saturated
Auxiliary procedures:
7.7.4.0. bFactor  computes the roots of irreducible factors of an univariate poly
7.7.4.0. appelF1  create an ideal annihilating Appel F1 function
7.7.4.0. appelF2  create an ideal annihilating Appel F2 function
7.7.4.0. appelF4  create an ideal annihilating Appel F4 function
7.7.4.0. engine  computes a Groebner basis with the algorithm given by i
7.7.4.0. poly2list  decompose a polynomial into a list of terms and exponents
7.7.4.0. fl2poly  reconstruct a monic univariate polynomial from its factorization
7.7.4.0. insertGenerator  insert an element into an ideal/module
7.7.4.0. deleteGenerator  delete the k-th element from an ideal/module
See also: bfun_lib; dmod_lib; gmssing_lib.


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