database.g

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##
#W  database.g                GAP4 Package `RCWA'                 Stefan Kohl
##
##  Data library of the groups generated by 3 class transpositions which
##  interchange residue classes with moduli <= 9.
##
##  This data library is a record with the following components:
##
##    - 'cts' is a list of all class transpositions which interchange
##      residue classes with moduli <= 9.
##    - 'mods' is the list of moduli, i.e. we have
##      mods[i][j][k] = Mod(Group(cts{[i,j,k]})).
##    - 'partlengths' is the list of lengths of shortest respected
##      partitions, i.e. we have partlengths[i][j][k] =
##      Length(RespectedPartition(Group(cts{[i,j,k]}))).
##    - 'sizes' is the list of group orders, i.e. we have
##      sizes[i][j][k] = Size(Group(cts{[i,j,k]})).
##      This list is recovered from the two lists 'sizesset' and 'sizespos',
##      where sizes[i][j][k] = sizesset[sizespos[i][j][k]].
##    - 'All3CTs9Indices' is a selector function which takes as argument
##      a function <func> of three arguments i, j and k.
##      It returns a list of all triples of indices [i,j,k] for which
##      <func> returns `true'.
##      'All3CTs9Groups' is a selector function which takes as argument
##      a function <func> of three arguments i, j and k.
##      It returns a list of all groups Group(cts{[i,j,k]}) from the
##      database for which <func>(i,j,k) returns `true'.
##
return rec(

  cts := List(List(ClassPairs(9),ClassTransposition),SparseRep),

  mods :=
    ReadAsFunction(Concatenation(PackageInfo("rcwa")[1].InstallationPath,
                                 "/data/3ctsgroups9/mods.g"))(),

  partlengths :=
    ReadAsFunction(Concatenation(PackageInfo("rcwa")[1].InstallationPath,
                                 "/data/3ctsgroups9/partitionlengths.g"))(),

  sizesset :=
    ReadAsFunction(Concatenation(PackageInfo("rcwa")[1].InstallationPath,
                                 "/data/3ctsgroups9/sizesset.g"))(),

  sizespos :=
    ReadAsFunction(Concatenation(PackageInfo("rcwa")[1].InstallationPath,
                                 "/data/3ctsgroups9/sizespos.g"))(),

  All3CTs9Indices := function ( func )

    local  indices, i, j, k;

    indices := [];
    for i in [3..264] do
      for j in [2..i-1] do
        for k in [1..j-1] do
          if   CallFuncList(func,[i,j,k]) = true
          then Add(indices,[i,j,k]); fi;
        od;
      od;
    od;
    return indices;
  end,

  All3CTs9Groups := function ( func )

    local  indices, groups, cts, i, j, k;

    cts := List(ClassPairs(9),ClassTransposition);
    indices := [];
    for i in [3..264] do
      for j in [2..i-1] do
        for k in [1..j-1] do
          if   CallFuncList(func,[i,j,k]) = true
          then Add(indices,[i,j,k]); fi;
        od;
      od;
    od;
    groups  := List(indices,inds->Group(cts{inds}));
    return groups;
  end

);

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##
#E  database.g . . . . . . . . . . . . . . . . . . . . . . . . . .  ends here