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##
#W pargap/misc.gi  LPRES    René Hartung
##

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#F LPRESPar_CollectorToFunction( <coll> )
##
InstallGlobalFunction( LPRESPar_CollectorToFunction,
  function( coll )
  local file, # temporary file to store the collector <coll>
orders, # relative orders of <coll>
n, # number of generators of <coll>
i,j; # loop variables

  file := Filename( DirectoryTemporary(), "coll.g" );

  PrintTo( file, "local ftl;\n" );

  AppendTo( file, "ftl := FromTheLeftCollector( ",
                          NumberOfGenerators( coll ), " );\n");

  orders := RelativeOrders( coll );
  n := coll![ PC_NUMBER_OF_GENERATORS ];
  for i in Filtered( [ 1 .. n ], x -> orders[x] <> 0 ) do
    AppendTo( file, "SetRelativeOrder( ftl, ", i, ", ", orders[i] ," );\n" );
    AppendTo( file, "SetPower( ftl, ", i, ", ", GetPower( coll , i )," );\n");
    if IsBound( coll![ PC_POWERS ][i] ) then
      AppendTo( file, "ftl![ PC_INVERSEPOWERS ][", i, "] := ",
                      coll![ PC_INVERSEPOWERS ][i], ";\n");
    fi;
  od;

  for i in [ 1 .. n-1 ] do
    for j in [ i+1 .. n ] do
      AppendTo( file, "SetConjugate( ftl, ",j,", ",i,", ",
                       GetConjugate( coll, j, i )," );\n");
      if orders[i] = 0 then
        AppendTo( file, "SetConjugate( ftl, ",j,", ",-i,", ",
                         GetConjugate( coll, j, -i )," );\n");
        if orders[j] = 0 then
          AppendTo( file, "SetConjugate( ftl, ",-j,", ",-i,", ",
                           GetConjugate( coll, -j, -i )," );\n");
        fi;
      elif orders[j] = 0 then
        AppendTo( file, "SetConjugate( ftl, ",-j,", ",i,", ",
                         GetConjugate( coll, -j, i )," );\n");
      fi;
    od;
  od;
  AppendTo( file, "FromTheLeftCollector_SetCommute( ftl );\n");
  AppendTo( file, "SetFilterObj( ftl, IsUpToDatePolycyclicCollector );\n");
  AppendTo( file, "FromTheLeftCollector_CompleteConjugate( ftl );\n");
# redundant due to the < coll![ PC_INVERSEPOWERS ] > above
# AppendTo( file, "FromTheLeftCollector_CompletePowers( ftl );\n");
  AppendTo( file, "SetFilterObj( ftl, IsUpToDatePolycyclicCollector );\n");
  AppendTo( file, "return( ftl );\n" );

  return( ReadAsFunction( file ) );

  end);

############################################################################
##
#F  LPRESPar_MapRelations
##
ParInstallTOPCGlobalFunction( "LPRESPar_MapRelations",
  function( Imgs, frels, irels )
  local F, # the free group
fam, # elements family of the free group <F>
FRels, # the fixed relators as elements of <F>
IRels, # the iterated relators as elements of <F>
H, # the covering group
Epi, # the epimorphism onto the covering group
rels, # the relations FRels and IRels
imgs, # the images of <Rels>
i,  # loop variable
SubmitTaskInput, DoTask, CheckTaskResult; # MasterSlave

  # initialize the free group
  F := FreeGroup( Length( Imgs ) );
  fam := ElementsFamily( FamilyObj( F ) );
  FRels := List( frels, x -> ObjByExtRep( fam, x ) );
  IRels := List( irels, x -> ObjByExtRep( fam, x ) );

  # initialize the covering group
  H := PcpGroupByCollectorNC( ReadEvalFromString( "ftl" ) );

  # initialize the epimorphism
  imgs := [];
  for i in [ 1 .. Length( Imgs ) ] do
    if IsInt( Imgs[i] ) then
      imgs[i] := PcpElementByGenExpList( ReadEvalFromString( "ftl" ),
                                        [ Imgs[i], 1 ] );
    else
      imgs[i] := PcpElementByGenExpList( ReadEvalFromString( "ftl" ), Imgs[i] );
    fi;
  od;
  Epi := GroupHomomorphismByImagesNC( F, H, GeneratorsOfGroup( F ), imgs );
  Unbind( imgs );

  rels := Concatenation( FRels, IRels );
  imgs := [];

  SubmitTaskInput := TaskInputIterator( [ 1 .. Length( rels ) ] );

  DoTask := function( x )
    return( Exponents( Image( Epi, rels[x] ) ) );
    end;

  CheckTaskResult := function( input, output )
    if not IsList( output ) then Error("in computing the images"); fi;
    imgs[ input ] := output;
    return NO_ACTION;
    end;

  MasterSlave( SubmitTaskInput, DoTask, CheckTaskResult, Error );

  return( imgs );
  end);

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