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#W storing.gi LPRES René Hartung
##
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#M ExtendQuotientSystem( <QuotSys> )
##
## Extends the quotient system for G/gamma_i(G) to a consistent quotient
## system for G/gamma_{i+1}(G).
##
InstallMethod( ExtendQuotientSystem,
"using a multiple-core machine with ParGap; storing results", true,
[ IsObject ], 2,
function( Q )
local c, # nilpotency class
weights, # weights of the generators
Defs, # definitions of each generator of the covering group
Imgs, # images of the generators in the covering group
ftl, # collector of the covering group
b, # position of the first tail
n, # number of generators of the covering group
HNF, # Hermite normal form of the consistency rels/relators
endo,Endo, # the induced endomorphisms
mat,Mats, # matrix representations of the induced endomorphisms
stack, # stack for the spinning algorithm
ev,evn, # exponent vectors for the spinning algorithm
QS, # the extended quotient system
i, # loop variable
Rels, # the mapped relations
IRels,FRels, # the mapped iterated and fixed relations
tmpParTrace, # the old value of <ParTrace>
dir,file, # for storing the results
time;
if not LPRESPar_StoreResults or not IsMaster() then
TryNextMethod();
fi;
# storing the result
dir := DirectoryTemporary();
file := Filename( dir, "LPRESPar.g" );
Info( InfoLPRES, 1, "Storing results in \"", file, "\"" );
# enable/disable tracing in ParGap w.r.t. InfoLPRES
tmpParTrace := ParTrace;
if InfoLevel( InfoLPRES ) >= 2 then
ParTrace := true;
else
ParTrace := false;
fi;
# just to be sure...
FlushAllMsgs();
# initialization
c := Maximum( Q.Weights );
weights := ShallowCopy( Q.Weights );
Defs := ShallowCopy( Q.Definitions );
Imgs := ShallowCopy( Q.Imgs );
# quotient system of the covering group
ftl := LPRES_QSystemOfCoveringGroupByQSystem(Q.Pccol,weights,Defs,Imgs);
# use tails-routine to complete the nilpotent presentation
Info( InfoLPRES, 1, "Computing a polycyclic presentation ",
"for the covering group..." );
UpdateNilpotentCollector( ftl, weights, Defs );
# store the completed collector (incl. weights etc.)
AppendTo( file, "func := ", LPRESPar_CollectorToFunction( ftl ), ";\n");
AppendTo( file, "weights := ", weights, ";\n" );
AppendTo( file, "Defs := ", Defs, ";\n" );
AppendTo( file, "Imgs := ", Imgs, ";\n" );
# further initializations
b := Position( weights, Maximum( weights ) );
n := ftl![ PC_NUMBER_OF_GENERATORS ];
# Check the consisistency relations
Info( InfoLPRES, 1, "Checking the consistency relations..." );
HNF := LPRESPar_CheckConsistencyRelations( ftl, weights );
# store the HNF of the consistency-checks...
AppendTo( file, "HNF := rec( Heads := ", HNF.Heads, ", mat := ",
HNF.mat, " );\n");
Info( InfoLPRES, 1, "Broadcasting the slaves...");
for i in [1..MPI_Comm_size()-1] do
Info( InfoLPRES, 2, "HOST", i,": ",SendRecvMsg("UNIX_Hostname();",i));
od;
# induce the endomorphisms to the cover
Info( InfoLPRES, 1, "Inducing the endomorphisms..." );
Mats := [];
AppendTo( file, "Mats := [];;\n");
for endo in EndomorphismsOfLpGroup( Q.Lpres ) do
Endo := LPRESPar_InduceEndomorphism(
List( FreeGeneratorsOfLpGroup( Q.Lpres ),
x -> ExtRepOfObj( Image( endo, x ) ) ),
Defs, Imgs, weights );
mat := List( [b..n], x -> Exponents( Image( Endo,
GeneratorsOfGroup( Source( Endo ) )[ x ] ) ) );
for i in [ 1 .. Length( mat ) ] do
if not IsZero( mat[i]{[ 1 .. b-1 ]} ) then
Info( InfoLPRES, 3, "not inducing an endomorphism of the multiplier");
return( fail );
else
mat[i] := mat[i]{[b..n]};
fi;
od;
Add( Mats, mat );
AppendTo( file, "Add( Mats, ", mat , " );;\n" );
od;
Info( InfoLPRES, 1, "Broadcasting the slaves...");
for i in [1..MPI_Comm_size()-1] do
Info( InfoLPRES, 2, "HOST", i,": ",SendRecvMsg("UNIX_Hostname();",i));
od;
ParTrace:=true;
Info( InfoLPRES, 1, "Mapping the relations..." );
AppendTo( file, "Rels := [];;\n" );
Rels := LPRESPar_MapRelationsStoring( Imgs,
Concatenation( List( FixedRelatorsOfLpGroup( Q.Lpres ), ExtRepOfObj ),
List( IteratedRelatorsOfLpGroup( Q.Lpres ), ExtRepOfObj ) ), file );
FRels := Rels{[ 1 .. Length( FixedRelatorsOfLpGroup( Q.Lpres ) ) ]};
IRels := Rels{[ Length( FixedRelatorsOfLpGroup( Q.Lpres ) ) + 1 .. Length( Rels ) ]};
if InfoLevel( InfoLPRES ) >= 2 then
ParTrace := true;
else
ParTrace := false;
fi;
Info( InfoLPRES, 1, "Start spinning..." );
# start the spinning algorithm
for i in [ 1 .. Length( FRels ) ] do
LPRES_AddRow( HNF, FRels[i]{[b..n]} );
od;
stack := List( IRels, x -> x{[b..n]} );
for i in [ 1 .. Length( stack ) ] do
LPRES_AddRow( HNF, stack[i] );
od;
while IsBound( stack[1] ) do
ev := stack[1];
Remove( stack, 1 );
if not IsZero(ev) then
for mat in Mats do
evn := ev * mat;
if LPRES_AddRow( HNF, evn ) then
Add( stack, evn );
fi;
od;
fi;
od;
Info( InfoLPRES, 1, "Extend the quotient system..." );
if Length(HNF.mat)=0 then
# the presentation ftl satisfy the relations and is consistent
QS := rec( Lpres := Q.Lpres,
Weights := weights,
Definitions := Defs,
Pccol := ftl,
Imgs := ShallowCopy( Imgs ) );
Imgs:=[];
for i in [ 1 .. Length( QS.Imgs ) ] do
if IsInt( QS.Imgs[i] ) then
Add( Imgs, PcpElementByGenExpList( QS.Pccol, [ QS.Imgs[i], 1 ] ) );
else
Add( Imgs, PcpElementByGenExpList( QS.Pccol, QS.Imgs[i] ) );
fi;
od;
QS.Epimorphism := GroupHomomorphismByImagesNC( Q.Lpres,
PcpGroupByCollectorNC( QS.Pccol ),
GeneratorsOfGroup( Q.Lpres ), Imgs );
ParTrace := tmpParTrace;
ParEval( "Unbind( ftl );" );
return(QS);
fi;
# recover the current setting
ParTrace := tmpParTrace;
ParEval( "Unbind(ftl);" );
return( LPRES_BuildNewCollector( Q, ftl, HNF, weights, Defs, Imgs ) );
end);
############################################################################
##
#M ExtendQuotientSystem( <QuotSys>, <func>, <HNF>, <mats>, <rels> )
##
## Extends the quotient system for G/gamma_i(G) to a consistent quotient
## system for G/gamma_{i+1}(G).
##
InstallOtherMethod( ExtendQuotientSystem,
"using a multiple-core machine with ParGap; recovering results", true,
[ IsObject, IsRecord, IsList, IsList ], 1,
function( Q, HNF, Mats, Rels )
local c, # nilpotency class
weights, # weights of the generators
Defs, # definitions of each generator of the covering group
Imgs, # images of the generators in the covering group
ftl, # collector of the covering group
b, # position of the first tail
n, # number of generators of the covering group
endo,Endo, # the induced endomorphisms
mat, # matrix representations of the induced endomorphisms
stack, # stack for the spinning algorithm
ev,evn, # exponent vectors for the spinning algorithm
QS, # the extended quotient system
i, # loop variable
IRels, FRels, # the mapped iterated and fixed relations
rels, # the union of <IRels> and <FRels>
nIRels,nFRels, # number of mapped fixed relations
tmpParTrace, # the old value of <ParTrace>
Defects,defects,# defects in <Rels>
dir,file, # for storing the results
time;
if not IsMaster() then
TryNextMethod();
fi;
Info( InfoLPRES, 1, "Continue calculations..." );
# storing the results
dir := DirectoryTemporary();
file := Filename( dir, "LPRESPar.g" );
Info( InfoLPRES, 1, "Storing results in \"", file, "\"" );
# enable/disable tracing in ParGap w.r.t. InfoLPRES
tmpParTrace := ParTrace;
if InfoLevel( InfoLPRES ) >= 2 then
ParTrace := true;
else
ParTrace := false;
fi;
# just to be sure...
FlushAllMsgs();
# initialization
c := Maximum( Q.Weights );
weights := ShallowCopy( Q.Weights );
Defs := ShallowCopy( Q.Definitions );
Imgs := ShallowCopy( Q.Imgs );
# quotient system of the covering group
# if IsFunction( func ) then
# ftl := func();;
# fi;
# if not IsFunction( func ) or not IsBound( ftl ) or
# not IsFromTheLeftCollectorRep( ftl ) then
ftl := LPRES_QSystemOfCoveringGroupByQSystem(Q.Pccol,weights,Defs,Imgs);
# use tails-routine to complete the nilpotent presentation
Info( InfoLPRES, 1, "Computing a polycyclic presentation ",
"for the covering group..." );
UpdateNilpotentCollector( ftl, weights, Defs );
# fi;
# store the completed collector
# AppendTo( file, "func := ", LPRESPar_CollectorToFunction( ftl ), ";\n");
# further initializations
b := Position( weights, Maximum( weights ) );
n := ftl![ PC_NUMBER_OF_GENERATORS ];
# Check the consisistency relations
if Length( HNF.Heads ) = 0 then
Info( InfoLPRES, 1, "Checking the consistency relations..." );
HNF := LPRESPar_CheckConsistencyRelations( ftl, weights );
else
# broadcast the collector...
ParEval( PrintToString( "fnc:=", LPRESPar_CollectorToFunction( ftl ) ) );
ParEval( "ftl := fnc();");
ParEval( "Unbind( fnc );" );
fi;
# store the HNF of the consistency-checks...
AppendTo( file, "HNF := rec( Heads := ", HNF.Heads, ", mat := ",
HNF.mat, " );\n");
Info( InfoLPRES, 1, "Broadcasting the slaves...");
for i in [1..MPI_Comm_size()-1] do
Info( InfoLPRES, 2, "HOST", i,": ",SendRecvMsg("UNIX_Hostname();",i));
od;
# store the induced matrices...
AppendTo( file, "Mats := [];;\n");
for mat in Mats do
AppendTo( file, "Add( Mats, ", mat , " );;\n" );
od;
# induce the endomorphisms to the cover
if Length( Mats ) <> Length( EndomorphismsOfLpGroup( Q.Lpres ) ) then
Info( InfoLPRES, 1, "Inducing the endomorphisms..." );
for endo in EndomorphismsOfLpGroup( Q.Lpres ){[ Length( Mats ) + 1 .. Length( EndomorphismsOf
LpGroup( Q.Lpres ) )]} do
Endo := LPRESPar_InduceEndomorphism(
List( FreeGeneratorsOfLpGroup( Q.Lpres ),
x -> ExtRepOfObj( Image( endo, x ) ) ),
Defs, Imgs, weights );
# computing matrix representation...
mat := List( [b..n], x -> Exponents( Image( Endo,
GeneratorsOfGroup( Source( Endo ) )[ x ] ) ) );
for i in [ 1 .. Length( mat ) ] do
if not IsZero( mat[i]{[ 1 .. b-1 ]} ) then
Info( InfoLPRES, 3, "not inducing an endomorphism of the multiplier");
return( fail );
else
mat[i] := mat[i]{[b..n]};
fi;
od;
Add( Mats, mat );
AppendTo( file, "Add( Mats, ", mat , " );;\n" );
od;
fi;
Info( InfoLPRES, 1, "Broadcasting the slaves...");
for i in [1..MPI_Comm_size()-1] do
Info( InfoLPRES, 2, "HOST", i,": ",SendRecvMsg("UNIX_Hostname();",i));
od;
# store the mapped relations...
AppendTo( file, "Rels := [ ];;\n" );
nFRels := Length( FixedRelatorsOfLpGroup( Q.Lpres ) );
nIRels := Length( IteratedRelatorsOfLpGroup( Q.Lpres ) );
rels := Concatenation( FixedRelatorsOfLpGroup( Q.Lpres ),
IteratedRelatorsOfLpGroup( Q.Lpres ) );
Defects := [];
for i in [ 1 .. nFRels + nIRels ] do
if not IsBound( Rels[i] ) then
Defects[i] := ExtRepOfObj( rels[i] );
else
AppendTo( file, "Rels[ ", i, " ] := ", Rels[i], ";;\n" );
fi;
od;
ParTrace:=true;
Info( InfoLPRES, 1, "Mapping the relations..." );
# fill up the mapped relations <Rels>
defects := LPRESPar_MapRelationsStoring( Imgs, Defects, file );
for i in [ 1 .. Length( Defects ) ] do
if IsBound( Defects[i] ) then
Rels[i] := defects[i];
fi;
od;
FRels := Rels{[ 1 .. nFRels ]};
IRels := Rels{[ nFRels + 1 .. Length( Rels ) ]};
if InfoLevel( InfoLPRES ) >= 2 then
ParTrace := true;
else
ParTrace := false;
fi;
Info( InfoLPRES, 1, "Start spinning..." );
# start the spinning algorithm
for i in [ 1 .. Length( FRels ) ] do
LPRES_AddRow( HNF, FRels[i]{[b..n]} );
od;
stack := List( IRels, x -> x{[b..n]} );
for i in [ 1 .. Length( stack ) ] do
LPRES_AddRow( HNF, stack[i] );
od;
while IsBound( stack[1] ) do
ev := stack[1];
Remove( stack, 1 );
if not IsZero(ev) then
for mat in Mats do
evn := ev * mat;
if LPRES_AddRow( HNF, evn ) then
Add( stack, evn );
fi;
od;
fi;
od;
Info( InfoLPRES, 1, "Extend the quotient system..." );
if Length(HNF.mat)=0 then
# the presentation ftl satisfy the relations and is consistent
QS := rec( Lpres := Q.Lpres,
Weights := weights,
Definitions := Defs,
Pccol := ftl,
Imgs := ShallowCopy( Imgs ) );
Imgs:=[];
for i in [ 1 .. Length( QS.Imgs ) ] do
if IsInt( QS.Imgs[i] ) then
Add( Imgs, PcpElementByGenExpList( QS.Pccol, [ QS.Imgs[i], 1 ] ) );
else
Add( Imgs, PcpElementByGenExpList( QS.Pccol, QS.Imgs[i] ) );
fi;
od;
QS.Epimorphism := GroupHomomorphismByImagesNC( Q.Lpres,
PcpGroupByCollectorNC( QS.Pccol ),
GeneratorsOfGroup( Q.Lpres ), Imgs );
ParTrace := tmpParTrace;
ParEval( "Unbind( ftl );" );
return(QS);
fi;
# recover the current setting
ParTrace := tmpParTrace;
ParEval( "Unbind(ftl);" );
return( LPRES_BuildNewCollector( Q, ftl, HNF, weights, Defs, Imgs ) );
end);
############################################################################
##
#F LPRESPar_MapRelationsStoring
##
ParInstallTOPCGlobalFunction( "LPRESPar_MapRelationsStoring",
function( Imgs, Rels, file )
local F, # the free group
fam, # elements family of the free group <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 ) );
rels := [];
for i in [ 1 .. Length( Rels ) ] do
if IsBound( Rels[i] ) then
rels[i] := ObjByExtRep( fam, Rels[i] );
fi;
od;
# 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 );
# initialize the images
imgs := [];
SubmitTaskInput := TaskInputIterator( Filtered( [ 1 .. Length( rels ) ],
i -> IsBound( rels[i] ) ) );
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;
AppendTo( file, "Rels[",input,"] := ", output, ";;\n" );
imgs[ input ] := output;
return NO_ACTION;
end;
MasterSlave( SubmitTaskInput, DoTask, CheckTaskResult, Error );
return( imgs );
end);
