  
  
                          [1XBasic Package Documentation[0m
  
  
                                  Version 1.0
  
  
                                    May 2008
  
  
                                  Tom Hoffman
  
                                   Klaus Lux
  
  
  
  Tom Hoffman
      Email:    [7Xmailto:thoffman@coastal.edu[0m
  Klaus Lux
      Email:    [7Xmailto:klux@math.arizona.edu[0m
  
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  [1XAbstract[0m
  This  package  calculates  the basic algebra which is Morita equivalent to a
  block  of  a  group algebra of a finite group in characteristic dividing the
  order  of  the  group. [5XGAP[0m must be able to access the table of marks and the
  modular  character  table for the group. It is beneficial, but not required,
  for  [5XGAP[0m to have access to the Atlas of Finite Group Representations via the
  [5XAtlasRep[0m package.
  
  
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  [1XCopyright[0m
  © 2006 by Tom Hoffman and Klaus Lux
  
  
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  [1XAcknowledgements[0m
  This  documentation was prepared with the [5XGAPDoc[0m package of Frank Lübeck and
  Max Neunhöffer.
  
  
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  [1XContents (Basic)[0X
  
  1 Introduction
    1.1 Installation Instructions
    1.2 The Algorithm
    1.3 [5XGAP[0m data structure for basic algebras
  2 User Functions
    2.1 User Variables
      2.1-1 BasicWorkingSpace
      2.1-2 BasicMemAvailable
    2.2 Fully automated calculation
      2.2-1 AutoCalcBasic
      2.2-2 InfoKond
  3 Constructing Basic Algebras
    3.1 Condensation
      3.1-1 FindFaithBurn
      3.1-2 FindCondSubgroup
      3.1-3 GetPerms
      3.1-4 FindAlgGens
      3.1-5 Condense
    3.2 Constructing Projective Indecomposable Modules
      3.2-1 CondenseModuleTom
      3.2-2 SpinUpPIMs
    3.3 Constructing the Basic Algebra
      3.3-1 FindBasicHoms
  4 Other Functions in the [5XBasic[0m Package
    4.1 Functions for Groups
      4.1-1 FindOverGroupsTom
      4.1-2 FindMaximalOverGroupsTom
    4.2 Permutation Calculations
      4.2-1 FindPerms
      4.2-2 ImprimPerm
      4.2-3 MakePermOnCond
      4.2-4 Kond
      4.2-5 MakeGensKondSubgroup
    4.3 Algebra Calculations
      4.3-1 GetConstList
      4.3-2 NewSpinUp
      4.3-3 BigSpin
      4.3-4 QuiverToBasic
      4.3-5 Spinning
      4.3-6 MultiplyVecMat
      4.3-7 MakeAction
      4.3-8 ReadWords
      4.3-9 ParseWord
      4.3-10 WordPol
    4.4 Miscellaneous Functions
      4.4-1 CompressMat
      4.4-2 UncompressMat
  A Variables
    A.1 Miscellaneous Variables
      A.1-1 CFInfo
      A.1-2 MeatAxe
      A.1-3 MesserHalter
  B A note on algebra generators
  
  
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