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#W pargap/misc.gi LPRES René Hartung
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#F LPRESPar_CollectorToFunction( <coll> )
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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);
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#F LPRESPar_MapRelations
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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);
[ 0.90Quellennavigators
]
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2026-03-28
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