  
  [1m[4m[31m5. The Modular Isomorphism Problem[0m
  
  
  [1m[4m[31m5.1 Known results on MIP[0m
  
  ???????????????????????????????????
  
  
  [1m[4m[31m5.2 Invariants determined by group algebras[0m
  
  [1m[4m[31m5.2-1 SandlingFactorGroup[0m
  
  [1m[34m> SandlingFactorGroup( [0m[22m[34mG[0m[1m[34m ) ________________________________________[0mattribute
  [1mReturns:[0m  factorgroup
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.2-2 JenningsFactors[0m
  
  [1m[34m> JenningsFactors( [0m[22m[34mG[0m[1m[34m ) ____________________________________________[0mattribute
  [1mReturns:[0m  list of lists of IdGroup
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.2-3 NumberOfConjugacyClassesPPowers[0m
  
  [1m[34m> NumberOfConjugacyClassesPPowers( [0m[22m[34mG[0m[1m[34m ) ____________________________[0mattribute
  [1mReturns:[0m  list of integers
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.2-4 ClassSumNumbers[0m
  
  [1m[34m> ClassSumNumbers( [0m[22m[34mG[0m[1m[34m ) ____________________________________________[0mattribute
  [1mReturns:[0m  list of integers
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.2-5 QuillenSeries[0m
  
  [1m[34m> QuillenSeries( [0m[22m[34mG[0m[1m[34m ) ______________________________________________[0mattribute
  [1mReturns:[0m  list of integers
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.2-6 RoggenkampParameter[0m
  
  [1m[34m> RoggenkampParameter( [0m[22m[34mG[0m[1m[34m ) ________________________________________[0mattribute
  [1mReturns:[0m  integer
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.2-7 RoggenkampParameterForNormalSubset[0m
  
  [1m[34m> RoggenkampParameterForNormalSubset( [0m[22m[34mG, S[0m[1m[34m ) _______________________[0mfunction
  [1mReturns:[0m  integer
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.2-8 KernelSize[0m
  
  [1m[34m> KernelSize( [0m[22m[34mFG[, n, m, k][0m[1m[34m ) _____________________________________[0mattribute
  [1mReturns:[0m  integer or fail
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  
  [1m[4m[31m5.3 MIP testing tools[0m
  
  [1m[4m[31m5.3-1 PrintMIPInvariants[0m
  
  [1m[34m> PrintMIPInvariants( [0m[22m[34mG[0m[1m[34m ) __________________________________________[0mfunction
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-2 PrintMIPInvariantsTable[0m
  
  [1m[34m> PrintMIPInvariantsTable( [0m[22m[34mlist, filename[0m[1m[34m ) ________________________[0mfunction
  [1mReturns:[0m  text file generated in the current directory
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-3 MIPInvariantsRecord[0m
  
  [1m[34m> MIPInvariantsRecord( [0m[22m[34mG[0m[1m[34m ) _________________________________________[0mfunction
  [1mReturns:[0m  record
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-4 MIPInvariantsLibrary[0m
  
  [1m[34m> MIPInvariantsLibrary( [0m[22m[34mn[0m[1m[34m ) ________________________________________[0mfunction
  [1mReturns:[0m  text file generated in the current directory
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-5 MIPInvariantsLibraryClassification[0m
  
  [1m[34m> MIPInvariantsLibraryClassification( [0m[22m[34minvlib, mode[0m[1m[34m ) _______________[0mfunction
  [1mReturns:[0m  list  of  lists  and  (optionally)  a  text  file generated in the
            current directory
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-6 KernelSizeTest[0m
  
  [1m[34m> KernelSizeTest( [0m[22m[34mFG, FH[0m[1m[34m ) _________________________________________[0mfunction
  [1mReturns:[0m  a list of parameters and kernel sizes or fail
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-7 JenningsLieAlgebraTest[0m
  
  [1m[34m> JenningsLieAlgebraTest( [0m[22m[34mFG, FH[0m[1m[34m ) _________________________________[0mfunction
  [1mReturns:[0m  true or false
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-8 MIPSplittingByKernelSize[0m
  
  [1m[34m> MIPSplittingByKernelSize( [0m[22m[34mlist, no, mode[0m[1m[34m ) _______________________[0mfunction
  [1mReturns:[0m  text file generated in the current directory
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-9 MIPSplittingByJenningsLieAlgebra[0m
  
  [1m[34m> MIPSplittingByJenningsLieAlgebra( [0m[22m[34mlist, no, mode[0m[1m[34m ) _______________[0mfunction
  [1mReturns:[0m  text file generated in the current directory
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
  [1m[4m[31m5.3-10 MIPSplittingReport[0m
  
  [1m[34m> MIPSplittingReport( [0m[22m[34mlist[0m[1m[34m ) _______________________________________[0mfunction
  
  ???????????????????????????????????
  
  [22m[35m---------------------------  Example  ----------------------------[0m
    [22m[35m[0m
    [22m[35m[0m
  [22m[35m------------------------------------------------------------------[0m
  
