WeylAlgebras : Table of Contents

• WeylAlgebras -- algorithms for D-modules

  • makeWeylAlgebra -- Weyl algebra corresponding to a polynomial ring

    • 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
  • gbw -- compute a Gröbner basis with respect to a weight vector

    • setHomSwitch -- toggle the use of homogeneous Weyl algebra
  • 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
  • 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
  • Dtrace -- set or get the depth of comments made by D-module routines