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HolonomicSystems -- Examples of Holonomic D-modules

Description

Some examples of D-modules

  • gkz -- create the A-hypergeometric system of Gelfand, Kapranov and Zelevinsky (GKZ)
  • eulerOperators -- Euler Operators
  • toricIdealPartials -- create the toric ideal of an integer matrix
  • AppellF1 -- Appell F1 system of PDE's

Canonical Series Tutorial -- Computing series solutions to regular holonomic systems

  • distraction -- the image in the thetaRing of a torus-fixed element or ideal in a Weyl algebra
  • cssExpts -- the exponents of the canonical series solutions of I in the direction of a weight vector
  • cssExptsMult -- the exponents and multiplicities of the canonical series solutions
  • isTorusFixed -- checks if an ideal in a Weyl algebra is torus-fixed
  • solveFrobeniusIdeal -- solving Frobenius ideals

Differential Operators

  • diffOps -- differential operators of up to the given order for a quotient polynomial ring

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Authors

Version

This documentation describes version 1.0 of HolonomicSystems.

Citation

If you have used this package in your research, please cite it as follows:

@misc{HolonomicSystemsSource,
  title = {{HolonomicSystems: A \emph{Macaulay2} package. Version~1.0}},
  author = {Mahrud Sayrafi and Christine Berkesch and Anton Leykin and Harrison Tsai},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

  • Functions and commands
    • AppellF1 -- Appell F1 system of PDE's
    • createThetaRing (missing documentation)
    • cssExpts -- the exponents of the canonical series solutions of I in the direction of a weight vector
    • cssExptsMult -- the exponents and multiplicities of the canonical series solutions
    • cssLeadTerm -- lead term of the canonical series solutions of I
    • diffOps -- differential operators of up to the given order for a quotient polynomial ring
    • distraction -- the image in the thetaRing of a torus-fixed element or ideal in a Weyl algebra
    • eulerOperators -- Euler Operators
    • gkz -- create the A-hypergeometric system of Gelfand, Kapranov and Zelevinsky (GKZ)
    • indicialIdeal -- the image in the thetaRing of an indicial ideal in a Weyl algebra
    • isTorusFixed -- checks if an ideal in a Weyl algebra is torus-fixed
    • nilssonSupport (missing documentation)
    • putWeylAlgebra -- transforms output of diffOps into elements of Weyl algebra
    • solveFrobeniusIdeal -- solving Frobenius ideals
    • toricIdealPartials -- create the toric ideal of an integer matrix
    • truncatedCanonicalSeries (missing documentation)
  • Methods
    • AppellF1(List) -- see AppellF1 -- Appell F1 system of PDE's
    • createThetaRing(PolynomialRing) (missing documentation)
    • cssExpts(Ideal,List) -- see cssExpts -- the exponents of the canonical series solutions of I in the direction of a weight vector
    • cssExptsMult(Ideal,List) -- see cssExptsMult -- the exponents and multiplicities of the canonical series solutions
    • cssLeadTerm(Ideal,List) -- see cssLeadTerm -- lead term of the canonical series solutions of I
    • diffOps(Ideal,ZZ) -- see diffOps -- differential operators of up to the given order for a quotient polynomial ring
    • diffOps(RingElement,ZZ) -- see diffOps -- differential operators of up to the given order for a quotient polynomial ring
    • distraction(Ideal,Ring) -- see distraction -- the image in the thetaRing of a torus-fixed element or ideal in a Weyl algebra
    • distraction(RingElement,Ring) -- see distraction -- the image in the thetaRing of a torus-fixed element or ideal in a Weyl algebra
    • eulerOperators(Matrix,List,PolynomialRing) -- see eulerOperators -- Euler Operators
    • eulerOperators(Matrix,PolynomialRing) -- see eulerOperators -- Euler Operators
    • gkz(Matrix,List) -- see gkz -- create the A-hypergeometric system of Gelfand, Kapranov and Zelevinsky (GKZ)
    • gkz(Matrix,List,PolynomialRing) -- see gkz -- create the A-hypergeometric system of Gelfand, Kapranov and Zelevinsky (GKZ)
    • indicialIdeal(Ideal,List) -- see indicialIdeal -- the image in the thetaRing of an indicial ideal in a Weyl algebra
    • isTorusFixed(Ideal) -- see isTorusFixed -- checks if an ideal in a Weyl algebra is torus-fixed
    • nilssonSupport(Ideal,List) (missing documentation)
    • nilssonSupport(Ideal,List,ZZ) (missing documentation)
    • putWeylAlgebra(HashTable) -- see putWeylAlgebra -- transforms output of diffOps into elements of Weyl algebra
    • solveFrobeniusIdeal(Ideal) -- see solveFrobeniusIdeal -- solving Frobenius ideals
    • solveFrobeniusIdeal(Ideal,Ring) -- see solveFrobeniusIdeal -- solving Frobenius ideals
    • toricIdealPartials(Matrix,PolynomialRing) -- see toricIdealPartials -- create the toric ideal of an integer matrix
    • truncatedCanonicalSeries(Ideal,List,ZZ) (missing documentation)
  • Symbols
    • Vars -- see AppellF1 -- Appell F1 system of PDE's
    • BasisElts -- see diffOps -- differential operators of up to the given order for a quotient polynomial ring
    • PolyGens -- see diffOps -- differential operators of up to the given order for a quotient polynomial ring
    • ThetaRing (missing documentation)
    • WtoT (missing documentation)

For the programmer

The object HolonomicSystems is a package, defined in HolonomicSystems.m2, with auxiliary files in HolonomicSystems/.

The source of this document is in HolonomicSystems/DOC/main.m2:30:0.