GL(n)pack Home Page


Introduction:

Dorian Goldfeld had the idea of writing a book on "GL(n)" which was very explicit and used the real field rather than the adels and padics. I had attended his graduate class at Columbia while there on study leave on several occasions and he invited me to write software in Mathematica to accompany the book. The manual for the software is included as an appendix in the book Automorphic Forms and L functions for the group GL(n,R), by Dorian Goldfeld (CUP - Cambridge Studies in Advanced Mathematics - 2006). The software is in the form of a Mathematica package and is available for use under the GPL (Gnu Public License) by download from this web site, following a simple registration procedure. Registration is so that users can be informed of bug fixes and updates.

To use the software having Mathematica version 4.0 or later is recommended. Since the software is in the form of a standard mathematica package, it should run under any operating system (Windows, MacOS, Unix/Linux). For users who need tutorial help for Mathematica or an operating system some links are provided below.

Parts of GL(n)pack provided significant challenges to write. These included Casimir operators, Whittaker functions and Kloosterman sums for GL(n,R). Preprints of articles on each of these topics are also available under the "Links" section below. Requests for assistance and advice are welcome, as are bug reports and suggestions for new software. If you find GL(n)pack useful please let me know, and give references for any published work which references the software.

The Functions of GL(n)pack:

ApplyCasimirOperator, BruhatCVector, BruhatForm, BlockMatrix, CartanForm, ConstantMatrix, CreQ, DiagonalToMatrix, EisensteinFourierCoefficient, EisensteinSeriesTerm,ElementaryMatrix, FunctionalEquation, GetCasimirOperator, GetMatrixElement, GlnVersion, HeckeEigenvalues, HeckeMultiplicativeSplit, HeckeCoefficientSum, HeckeOperator, HeckePowerSum, HermiteFormLower, HermiteFormUpper, IFun, InsertMatrixElement, IwasawaForm, IwasawaXMatrix, IwasawaXVariables, IwasawaYMatrix, IwasawaYVariables, IwasawaQ, KloostermanBruhatCell,KloostermanCompatibility, KloostermanSum, LanglandsForm, LanglandsIFun, LeadingMatrixBlock, LongElement, LowerTriangleToMatrix, MakeBlockMatrix, MakeMatrix, MakeXMatrix, MakeXVariables, MakeYMatrix, MakeYVariables,MakeZMatrix, MakeZVariables, MatrixColumn, MatrixDiagonal, MatrixJoinHorizontal, MatrixJoinVertical, MatrixUpperTriangle, MatrixLowerTriangle, MatrixRow, ModularGenerators, MPEisensteinLambdas, MPEisensteinSeries, MPEisensteinGamma, MPExteriorPowerGamma, MPExteriorPowerLFun, MPSymmetricPowerLFun, MPSymmetricPowerGamma, NRows, NColumns, ParabolicQ, PluckerCoordinates, PluckerInverse, PluckerRelations, RamanujanSum, RemoveMatrixRow, RemoveMatrixColumn, SchurPolynomial, SmithForm, SmithElementaryDivisors, SmithInvariantFactors, SpecialWeylGroup, SubscriptedForm, SwapMatrixRows, SwapMatrixColumns, TailingMatrixBlock, UpperTriangleToMatrix, VolumeFormDiagonal, VolumeFormGln, VolumeFormHn, VolumeFormUnimodular, VolumeBall, VolumeHn, VolumeSphere, Wedge, WeylGenerator, WeylGroup, Whittaker, WhittakerGamma, WMatrix, ZeroMatrix.

Downloads:

Links:


  • Kevin A. Broughan
  • Email:kab@waikato.ac.nz

    Last modified: 5th November 2008.