Dmodules -- algorithms for D-modules

To begin, read the D-modules tutorial.

How to make Weyl algebras

• monoid(...,WeylAlgebra=>...) -- specify differential operators in the ring
• makeWeylAlgebra -- Weyl algebra corresponding to a polynomial ring

Basic commands

• gbw -- compute a Gröbner basis with respect to a weight vector
• inw -- get the initial term or ideal with respect to a weight vector
• Fourier -- Fourier transform for Weyl algebra
• Dtransposition -- standard transposition for Weyl algebra
• stafford -- computes 2 generators for a given ideal in the Weyl algebra
• makeCyclic -- finds a cyclic generator of a D-module
• Dprune -- prunes a D-module

Basic invariants of D-modules

• Ddim -- dimension of a D-module
• isHolonomic -- determines whether a D-module (or ideal in Weyl algebra) is holonomic
• holonomicRank -- holonomic rank of a D-module
• characteristicIdeal -- characteristic ideal of a D-module
• DsingularLocus -- singular locus of a D-module

Programming aids

• createDpairs -- pairs coordinate and derivation variables in a Weyl algebra
• extractDiffsAlgebra -- underlying polynomial ring in the differentials of a Weyl algebra
• extractVarsAlgebra -- underlying polynomial ring in the ordinary variables of a Weyl algebra
• Dtrace -- set or get the depth of comments made by D-module routines

Authors

• Anton Leykin <[email protected]>
• Harrison Tsai

Version

This documentation describes version 1.4.1.1 of Dmodules.

Source code

The source code from which this documentation is derived is in the file Dmodules.m2. The auxiliary files accompanying it are in the directory Dmodules/.

Exports