/usr/share/gap/pkg/AtlasRep/gap/test.g is in gap-atlasrep 1.5.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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##
#W test.g GAP 4 package AtlasRep Thomas Breuer
##
#Y Copyright (C) 2001, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
##
## This file contains functions to test the data available in the
## ATLAS of Group Representations.
##
#############################################################################
##
## <#GAPDoc Label="tests">
## The fact that the &ATLAS; of Group Representations is designed as an
## open database
## (see Section <Ref Subsect="subsect:Local or remote access"/>)
## makes it especially desirable to have consistency checks available
## which can be run automatically
## whenever new data are added by the developers of the &ATLAS;.
## The tests described in Section
## <Ref Subsect="subsect:AGR sanity checks by toc"/> can be used
## also for data from private extensions of the package
## (see Chapter <Ref Chap="chap:Private Extensions"/>),
## Section <Ref Subsect="subsect:AGR other sanity checks"/> lists tests
## which do not have this property.
## <P/>
## All these tests apply only to the <E>local</E> table of contents
## (see Section <Ref Sect="sect:The Tables of Contents of the AGR"/>)
## or to private extensions.
## So only those data files are checked that are actually available
## in the local &GAP; installation.
## No files are fetched from servers during these tests.
## The required space and time for running these tests
## depend on the amount of locally available data.
## <P/>
## The file <F>tst/testall.g</F> of the package
## contains <Ref Func="Test" BookName="ref"/> statements
## for executing a collection of such sanity checks;
## one can run them by calling
## <C>ReadPackage( "AtlasRep", "tst/testall.g" )</C>.
## If no problem occurs then &GAP; prints only lines starting with one of
## the following.
## <P/>
## <Log><![CDATA[
## + Input file:
## + GAP4stones:
## ]]></Log>
## <P/>
## Some of the checks compute and verify additional data,
## such as information about point stabilizers of permutation
## representations.
## In these cases, output lines starting with <C>#E</C> are error messages
## that point to inconsistencies,
## whereas output lines starting with <C>#I</C> inform about data that have
## been computed and were not yet stored, or about stored data that were not
## verified.
## <P/>
## The examples in the package manual form a part of the tests,
## they are collected in the file <F>tst/docxpl.tst</F> of the package.
##
## <Subsection Label="subsect:AGR sanity checks by toc">
## <Heading>Sanity Checks for a Table of Contents</Heading>
##
## The following tests can be used to check the data that belong to a given
## table of contents.
## Each of these tests is given by a function with optional argument
## <A>tocid</A>, the identifying string that had been entered as the second
## argument of
## <Ref Func="AtlasOfGroupRepresentationsNotifyPrivateDirectory"/>.
## The contents of the local <F>dataword</F> directory can be checked by
## entering <C>"local"</C>, which is also the default for <A>tocid</A>.
## The function returns <K>false</K> if an error occurs,
## otherwise <K>true</K>.
## Currently the following tests of this kind are available.
## <P/>
## <List>
## <#Include Label="test:AGR.Test.Words">
## <#Include Label="test:AGR.Test.FileHeaders">
## <#Include Label="test:AGR.Test.Files">
## <#Include Label="test:AGR.Test.BinaryFormat">
## <#Include Label="test:AGR.Test.Primitivity">
## <#Include Label="test:AGR.Test.Characters">
## </List>
##
## </Subsection>
##
## <Subsection Label="subsect:AGR other sanity checks">
## <Heading>Other Sanity Checks</Heading>
##
## The tests described in this section are not intended for checking data
## from private extensions of the <Package>AtlasRep</Package> package.
## Each of the tests is given by a function without arguments that
## returns <K>false</K> if a contradiction was found during the test,
## and <K>true</K> otherwise.
## Additionally, certain messages are printed
## when contradictions between stored and computed data are found,
## when stored data cannot be verified computationally,
## or when the computations yield improvements of the stored data.
## Currently the following tests of this kind are available.
## <P/>
## <List>
## <#Include Label="test:AGR.Test.GroupOrders">
## <#Include Label="test:AGR.Test.MaxesOrders">
## <#Include Label="test:AGR.Test.MaxesStructure">
## <#Include Label="test:AGR.Test.StdCompatibility">
## <#Include Label="test:AGR.Test.CompatibleMaxes">
## <#Include Label="test:AGR.Test.ClassScripts">
## <#Include Label="test:AGR.Test.CycToCcls">
## <#Include Label="test:AGR.Test.Standardization">
## <#Include Label="test:AGR.Test.StdTomLib">
## <#Include Label="test:AGR.Test.KernelGenerators">
## <#Include Label="test:AGR.Test.MinimalDegrees">
## </List>
##
## </Subsection>
## <#/GAPDoc>
##
if not IsPackageMarkedForLoading( "TomLib", "" ) then
HasStandardGeneratorsInfo:= "dummy";
IsStandardGeneratorsOfGroup:= "dummy";
LIBTOMKNOWN:= "dummy";
StandardGeneratorsInfo:= "dummy";
fi;
if not IsPackageMarkedForLoading( "CTblLib", "" ) then
ConstructionInfoCharacterTable:= "dummy";
HasConstructionInfoCharacterTable:= "dummy";
LibInfoCharacterTable:= "dummy";
fi;
if IsBound( StructureDescriptionCharacterTableName ) then
AGR.StructureDescriptionCharacterTableName:=
StructureDescriptionCharacterTableName;
else
AGR.StructureDescriptionCharacterTableName:= name -> name;
fi;
#############################################################################
##
#V AGR.Test
##
AGR.Test:= rec();
#############################################################################
##
#V AGR.Test.HardCases
#V AGR.Test.HardCases.MaxNumberMaxes
#V AGR.Test.HardCases.MaxNumberStd
#V AGR.Test.MaxTestDegree
##
## This is a record whose components belong to the various tests,
## and list data which shall be omitted from the tests
## because they would be too space or time consuming.
##
## In the test loops, we assume upper bounds on the numbers of available
## maximal subgroups and standardizations,
## and we perform some tests only if a sufficiently small permutation
## representation is available.
##
AGR.Test.HardCases:= rec();
AGR.Test.HardCases.MaxNumberMaxes:= 50;
AGR.Test.HardCases.MaxNumberStd:= 2;
AGR.Test.MaxTestDegree:= 10^5;
#############################################################################
##
#F AGR.Test.Words( [<tocid>[, <groupname>]][,][<verbose>] )
##
## <#GAPDoc Label="test:AGR.Test.Words">
## <Mark><C>AGR.Test.Words( [<A>tocid</A>] )</C></Mark>
## <Item>
## processes all straight line programs that are stored in the directory
## with identifier <A>tocid</A>,
## using the function stored in the <C>TestWords</C> component of the
## data type in question.
## </Item>
## <#/GAPDoc>
##
AGR.Test.HardCases.TestWords:= [
[ "find", [ "B", "HN", "S417", "F24d2" ] ],
[ "check", [ "B" ] ],
[ "maxes", [ "Co1" ] ],
];
AGR.Test.Words:= function( arg )
local result, maxdeg, tocid, verbose, types, toc, name, r, type, omit,
entry, prg, gens, grp, size;
# Initialize the result.
result:= true;
maxdeg:= AGR.Test.MaxTestDegree;
if Length( arg ) = 0 then
return AGR.Test.Words( "local", false );
elif Length( arg ) = 1 and IsBool( arg[1] ) then
return AGR.Test.Words( "local", arg[1] );
elif Length( arg ) = 1 and IsString( arg[1] ) then
return AGR.Test.Words( arg[1], false );
elif Length( arg ) = 2 and IsString( arg[1] ) and IsString( arg[2] ) then
return AGR.Test.Words( arg[1], arg[2], false );
elif Length( arg ) = 2 and IsString( arg[1] ) and IsBool( arg[2] ) then
for name in AtlasOfGroupRepresentationsInfo.groupnames do
result:= AGR.Test.Words( arg[1],
name[3], arg[2] ) and result;
od;
return result;
elif not ( Length( arg ) = 3 and IsString( arg[1] )
and IsString( arg[2] )
and IsBool( arg[3] ) ) then
Error( "usage: AGR.Test.Words( [<tocid>[, ",
"<groupname>]][,][<verbose>] )" );
fi;
tocid:= arg[1];
verbose:= arg[3];
# Check only straight line programs.
types:= AGR.DataTypes( "prg" );
toc:= AtlasTableOfContents( tocid );
if toc = fail then
# No test is reasonable.
return true;
fi;
name:= First( AtlasOfGroupRepresentationsInfo.GAPnames,
x -> x[2] = arg[2] );
if IsBound( toc.TableOfContents.( name[2] ) ) then
r:= toc.TableOfContents.( name[2] );
# Note that the ordering in the `and' statement must not be
# changed, in order to execute all tests!
for type in types do
omit:= First( AGR.Test.HardCases.TestWords,
pair -> pair[1] = type[1] );
if IsBound( r.( type[1] ) ) then
if IsList( omit ) and name[2] in omit[2] then
if verbose then
Print( "#I omit TestWords for ", type[1], " and ", name[2],
"\n" );
fi;
else
for entry in r.( type[1] ) do
result:= type[2].TestWords( tocid, name[2],
entry[ Length( entry ) ], type, verbose )
and result;
od;
fi;
fi;
od;
# Check also the `maxext' scripts (which do not form a data type
# and which are stored in the remote table of contents only).
r:= AtlasTableOfContents( "remote" ).TableOfContents.( name[2] );
if IsBound( r.maxext ) then
for entry in r.maxext do
prg:= AtlasProgram( name[1], entry[1], "maxes", entry[2] );
if prg = fail then
if verbose then
Print( "#I omit TestWords for maxext no. ", entry[2], " and ",
name[2], "\n" );
fi;
elif not IsInternallyConsistent( prg.program ) then
Print( "#E program `", entry[3],
"' not internally consistent\n" );
result:= false;
else
# Get a representation if available, and map the generators.
gens:= OneAtlasGeneratingSetInfo( prg.groupname,
prg.standardization, NrMovedPoints, [ 2 .. maxdeg ] );
if gens = fail then
if verbose then
Print( "#I no perm. repres. for `", prg.groupname,
"', no check for `", entry[3], "'\n" );
fi;
else
gens:= AtlasGenerators( gens );
grp:= Group( gens.generators );
if IsBound( gens.size ) then
SetSize( grp, gens.size );
fi;
gens:= ResultOfStraightLineProgram( prg.program,
gens.generators );
size:= Size( SubgroupNC( grp, gens ) );
if IsBound( prg.size ) and size <> prg.size then
Print( "#E program `", entry[3], "' for group of order ",
size, " not ", prg.size, "\n" );
result:= false;
fi;
fi;
fi;
od;
fi;
fi;
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.FileHeaders( [<tocid>[,<groupname>]] )
##
## <#GAPDoc Label="test:AGR.Test.FileHeaders">
## <Mark><C>AGR.Test.FileHeaders( [<A>tocid</A>] )</C></Mark>
## <Item>
## checks whether all &MeatAxe; text format data files in the directory
## with identifier <A>tocid</A> have a header line that is consistent with
## the filename, and whether the contents of all &GAP; format data files
## in this directory is consistent with the contents of the file.
## </Item>
## <#/GAPDoc>
##
AGR.Test.FileHeaders:= function( arg )
local result, toc, record, type, entry, test, triple;
# Initialize the result.
result:= true;
if Length( arg ) = 2 then
toc:= AtlasTableOfContents( arg[1] );
if toc = fail then
# No test is reasonable.
return true;
fi;
toc:= toc.TableOfContents;
if IsBound( toc.( arg[2] ) ) then
record:= toc.( arg[2] );
for type in AGR.DataTypes( "rep" ) do
if IsBound( record.( type[1] ) ) then
for entry in record.( type[1] ) do
test:= type[2].TestFileHeaders( arg[1], arg[2], entry, type );
if not IsBool( test ) then
Print( "#E ", test, " for ", entry[ Length( entry ) ],
"\n" );
test:= false;
fi;
result:= test and result;
od;
fi;
od;
fi;
elif Length( arg ) = 1 then
for triple in AtlasOfGroupRepresentationsInfo.groupnames do
result:= AGR.Test.FileHeaders( arg[1], triple[3] ) and result;
od;
elif Length( arg ) = 0 then
result:= AGR.Test.FileHeaders( "local" );
fi;
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.BinaryFormat( [<tocid>] )
##
## <#GAPDoc Label="test:AGR.Test.BinaryFormat">
## <Mark><C>AGR.Test.BinaryFormat( [<A>tocid</A>] )</C></Mark>
## <Item>
## checks whether all &MeatAxe; text format data files in the directory
## with identifier <A>tocid</A> satisfy that applying first
## <Ref Func="CMtxBinaryFFMatOrPerm"/> and then
## <Ref Func="FFMatOrPermCMtxBinary"/> yields the same object.
## </Item>
## <#/GAPDoc>
##
AGR.Test.BinaryFormat:= function( arg )
local tmpfile, tocid, result, r, gens, gen, test, cnv;
# Create one temporary file.
tmpfile:= Filename( DirectoryTemporary(), "testfile" );
# Get the data directory.
if IsEmpty( arg ) then
tocid:= "local";
else
tocid:= arg[1];
fi;
result:= true;
for r in Concatenation( AllAtlasGeneratingSetInfos( "contents", tocid,
IsPermGroup, true ),
AllAtlasGeneratingSetInfos( "contents", tocid,
Characteristic, IsPosInt ) ) do
gens:= AtlasGenerators( r );
if gens <> fail then
gens:= gens.generators;
for gen in gens do
test:= false;
if IsPerm( gen ) then
CMtxBinaryFFMatOrPerm( gen, LargestMovedPoint( gen ), tmpfile );
test:= true;
elif IsMatrix( gen ) then
cnv:= ConvertToMatrixRep( gen );
if IsInt( cnv ) then
CMtxBinaryFFMatOrPerm( gen, cnv, tmpfile );
test:= true;
fi;
else
Print( "#E not permutation or matrix for ", r, "\n" );
test:= false;
result:= false;
fi;
if test and gen <> FFMatOrPermCMtxBinary( tmpfile ) then
Print( "#E AGR.Test.BinaryFormat: differences for `", r,
"'\n" );
result:= false;
fi;
od;
fi;
od;
# Remove the temporary file.
RemoveFile( tmpfile );
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.Standardization( [<gapname>] )
##
## <#GAPDoc Label="test:AGR.Test.Standardization">
## <Mark><C>AGR.Test.Standardization()</C></Mark>
## <Item>
## checks whether all generating sets corresponding to the same set of
## standard generators have the same element orders; for the case that
## straight line programs for computing certain class representatives are
## available, also the orders of these representatives are checked
## w. r. t. all generating sets.
## </Item>
## <#/GAPDoc>
##
AGR.Test.Standardization:= function( arg )
local result, name, gapname, gensorders, cclorders, cycorders, tbl, info,
gens, std, ords, pair, prg, names, choice;
# Initialize the result.
result:= true;
if Length( arg ) = 0 then
for name in AtlasOfGroupRepresentationsInfo.GAPnames do
result:= AGR.Test.Standardization( name[1] ) and result;
od;
elif Length( arg ) = 1 and IsString( arg[1] ) then
gapname:= arg[1];
if AGR.InfoForName( gapname ) = fail then
Print( "#E AGR.Test.Standardization: no group with GAP name `",
gapname, "'\n" );
return false;
fi;
gensorders:= [];
cclorders:= [];
cycorders:= [];
tbl:= CharacterTable( gapname );
# Loop over the relevant representations.
for info in AllAtlasGeneratingSetInfos( gapname ) do
gens:= AtlasGenerators( info.identifier );
std:= gens.standardization;
# Check that the generators are invertible,
# and that the orders are equal in all representations.
if ForAll( gens.generators, x -> Inverse( x ) <> fail ) then
ords:= List( gens.generators, Order );
else
ords:= [ fail ];
fi;
if not ForAll( ords, IsInt ) then
Print( "#E representation `", gens.identifier[2],
"': non-finite order\n" );
result:= false;
elif IsBound( gensorders[ std+1 ] ) then
if gensorders[ std+1 ] <> ords then
Print( "#E '", gapname, "': representation '",
gens.identifier[2],
"':\n#E incompatible generator orders ",
ords, " and ", gensorders[ std+1 ], "\n" );
result:= false;
fi;
else
gensorders[ std+1 ]:= ords;
fi;
# If scripts for computing representatives of cyclic subgroups
# or representatives of conjugacy classes are available
# then check that their orders are equal in all representations.
for pair in [ [ cclorders, "classes" ], [ cycorders, "cyclic" ] ] do
if not IsBound( pair[1][ std+1 ] ) then
prg:= AtlasProgram( gapname, std, pair[2] );
if prg = fail then
pair[1][ std+1 ]:= fail;
else
pair[1][ std+1 ]:= [ prg.program,
List( ResultOfStraightLineProgram(
prg.program, gens.generators ), Order ) ];
if tbl <> fail then
names:= AtlasClassNames( tbl );
if IsBound( prg.outputs ) then
choice:= List( prg.outputs, x -> Position( names, x ) );
if ( not fail in choice ) and pair[1][ std+1 ][2]
<> OrdersClassRepresentatives( tbl ){ choice } then
Print( "#E '", gapname, "': representation '",
gens.identifier[2], "':\n#E ", pair[2],
" orders differ from character table\n" );
result:= false;
fi;
else
Print( "#E no component `outputs' in `", pair[2],
"' for `", gapname, "'\n" );
fi;
fi;
fi;
elif pair[1][ std+1 ] <> fail then
if pair[1][ std+1 ][2] <> List( ResultOfStraightLineProgram(
pair[1][ std+1 ][1], gens.generators ), Order ) then
Print( "#E '", gapname, "': representation '",
gens.identifier[2],
"':\n#E incompatible ", pair[2], " orders\n" );
result:= false;
fi;
fi;
od;
od;
fi;
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.StdTomLib( [<gapname>] )
##
## <#GAPDoc Label="test:AGR.Test.StdTomLib">
## <Mark><C>AGR.Test.StdTomLib()</C></Mark>
## <Item>
## checks whether the standard generators are compatible with those that
## occur in the <Package>TomLib</Package> package.
## </Item>
## <#/GAPDoc>
##
AGR.Test.StdTomLib:= function( arg )
local result, name, tomnames, tbl, tom, gapname, info, allgens, stdavail,
verified, falsified, G, i, type, prg, res, gens, G2,
fitstotom, fitstohom;
if TestPackageAvailability( "TomLib", "1.0" ) <> true then
Print( "#E TomLib not loaded, cannot verify ATLAS standardizations\n" );
return false;
fi;
# Initialize the result.
result:= true;
if Length( arg ) = 0 then
for name in AtlasOfGroupRepresentationsInfo.GAPnames do
result:= AGR.Test.StdTomLib( name[1] ) and result;
od;
# Check also that all tables of marks which provide a standardization
# info with an `ATLAS' component belong to ATLAS groups.
#T ... with a `standardization' component ...
tomnames:= Set( List( Filtered( LIBTOMKNOWN.STDGEN, x -> x[2] <> "N" ),
x -> x[1] ) );
for name in AtlasOfGroupRepresentationsInfo.GAPnames do
tbl:= CharacterTable( name[1] );
if tbl <> fail then
tom:= TableOfMarks( tbl );
if tom <> fail then
RemoveSet( tomnames, Identifier( tom ) );
fi;
fi;
od;
if not IsEmpty( tomnames ) then
Print( "#E cannot verify ATLAS standardizations for tables of ",
"marks in ", tomnames, "\n" );
result:= false;
fi;
elif Length( arg ) = 1 and IsString( arg[1] ) then
gapname:= arg[1];
if AGR.InfoForName( gapname ) = fail then
Print( "#E AGR.Test.Standardization: no group with GAP name `",
gapname, "'\n" );
return false;
fi;
tbl:= CharacterTable( gapname );
# Check the ATLAS standardization against the TomLib standardization.
# (We consider only ATLAS permutation representations.)
if tbl = fail then
tom:= fail;
else
tom:= TableOfMarks( tbl );
fi;
if tom <> fail then
if HasStandardGeneratorsInfo( tom ) then
info:= StandardGeneratorsInfo( tom )[1];
#T can be a longer list???
else
info:= fail;
fi;
allgens:= AllAtlasGeneratingSetInfos( gapname, IsPermGroup, true );
stdavail:= Set( List( allgens, x -> x.standardization ) );
allgens:= List( stdavail,
i -> First( allgens, x -> x.standardization = i ) );
verified:= [];
falsified:= [];
G:= UnderlyingGroup( tom );
# Apply `pres' and `check' scripts to the TomLib generators.
for i in stdavail do
for type in [ "pres", "check" ] do
prg:= AtlasProgram( gapname, i, type );
if prg <> fail then
res:= ResultOfStraightLineDecision( prg.program,
GeneratorsOfGroup( G ) );
if res = true then
AddSet( verified, i );
if info = fail then
Print( "#I ", gapname,
": extend TomLib standardization info, ",
"standardization = ", i, "\n" );
elif IsBound( info.standardization ) and
info.standardization <> i then
Print( "#E ", gapname,
": set TomLib standardization info to ",
i, " not ", info.standardization, "\n" );
result:= false;
fi;
else
AddSet( falsified, i );
if info <> fail and IsBound( info.standardization )
and info.standardization = i then
Print( "#E ", gapname,
": TomLib standardization info is not ",
info.standardization, "\n" );
result:= false;
fi;
fi;
fi;
od;
od;
if info <> fail then
# Compare the ATLAS generators with the TomLib standardization.
for gens in allgens do
gens:= AtlasGenerators( gens.identifier );
if info.script = fail then
Print( "#E ", gapname, ": fail script in TomLib standardization\n" );
else
G2:= Group( gens.generators );
fitstotom:= IsStandardGeneratorsOfGroup( info, G2, gens.generators );
fitstohom:= GroupHomomorphismByImages( G, G2, GeneratorsOfGroup( G ), gens.generators ) <> fail;
if fitstotom <> fitstohom then
Print( "#E ", gapname, ": IsStandardGeneratorsOfGroup and homom. construction for standardization ", gens.standardization, " inconsistent\n" );
fi;
if fitstotom then
AddSet( verified, gens.standardization );
if IsBound( info.standardization ) then
if info.standardization <> gens.standardization then
Print( "#I ", gapname,
": TomLib standardization is ",
gens.standardization, " not ", info.standardization,
"\n" );
result:= false;
fi;
else
Print( "#I ", gapname,
": TomLib standardization is ",
gens.standardization, "\n" );
fi;
else
AddSet( falsified, gens.standardization );
if IsBound( info.standardization ) and info.standardization = gens.standardization then
Print( "#E ", gapname,
": TomLib standardization is not ",
info.standardization, "\n" );
fi;
fi;
fi;
od;
elif not IsEmpty( stdavail ) then
Print( "#I ", gapname, ": extend STDGEN info\n" );
fi;
if verified = [] and falsified = stdavail then
if info = fail then
Print( "#I ", gapname,
": extend TomLib standardization info, ",
"ATLAS = \"N\"\n" );
elif info.ATLAS = true then
Print( "#E ", gapname,
": TomLib standardization info must be ATLAS = \"N\"\n" );
fi;
elif info <> fail and info.ATLAS = false then
Print( "#E ", gapname,
": cannot verify TomLib info ATLAS = \"N\"\n" );
fi;
fi;
fi;
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.Files( [<tocid>[, <groupname>]] )
##
## <#GAPDoc Label="test:AGR.Test.Files">
## <Mark><C>AGR.Test.Files( [<A>tocid</A>] )</C></Mark>
## <Item>
## checks whether the &MeatAxe; text files that are stored in the
## directory with identifier <A>tocid</A> can be read with
## <Ref Func="ScanMeatAxeFile"/> such that the result is not <K>fail</K>.
## The function does not check whether the first line of a &MeatAxe; text
## file is consistent with the filename, since this can be tested with
## <C>AGR.Test.FileHeaders</C>.
## </Item>
## <#/GAPDoc>
##
AGR.Test.Files:= function( arg )
local result, toc, record, type, entry, triple;
# Initialize the result.
result:= true;
if IsEmpty( arg ) then
result:= AGR.Test.Files( "local" );
elif Length( arg ) = 1 then
for triple in AtlasOfGroupRepresentationsInfo.groupnames do
result:= AGR.Test.Files( arg[1], triple[3] ) and result;
od;
elif Length( arg ) = 2 then
toc:= AtlasTableOfContents( arg[1] );
if toc = fail then
return false;
fi;
toc:= toc.TableOfContents;
if IsBound( toc.( arg[2] ) ) then
record:= toc.( arg[2] );
for type in AGR.DataTypes( "rep" ) do
if IsBound( record.( type[1] ) ) then
for entry in record.( type[1] ) do
result:= type[2].TestFiles( arg[1], arg[2], entry, type )
and result;
od;
fi;
od;
fi;
fi;
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.ClassScripts( [<groupname>] )
##
## <#GAPDoc Label="test:AGR.Test.ClassScripts">
## <Mark><C>AGR.Test.ClassScripts()</C></Mark>
## <Item>
## checks whether the straight line programs that compute representatives
## of certain conjugacy classes are consistent with information stored on
## the &GAP; character table of the group in question, in the sense that
## the given class names really occur in the character table and that
## the element orders and centralizer orders for the classes are correct.
## </Item>
## <#/GAPDoc>
##
AGR.Test.ClassScripts:= function( arg )
local result, maxdeg, groupname, gapname, toc, record, std, name, prg,
tbl, outputs, ident, classnames, map, gens, roots, grp, reps,
orders1, orders2, cents1, cents2, triple, pos, pos2, cycscript;
# Initialize the result.
result:= true;
maxdeg:= AGR.Test.MaxTestDegree;
if Length( arg ) = 1 and IsString( arg[1] ) then
groupname:= arg[1];
gapname:= First( AtlasOfGroupRepresentationsInfo.GAPnames,
pair -> pair[2] = groupname );
if gapname = fail then
Print( "#E no group with name `", groupname, "'\n" );
return false;
fi;
gapname:= gapname[1];
toc:= AtlasTableOfContents( "local" );
if toc = fail then
return false;
fi;
toc:= toc.TableOfContents;
#T admit also private tables of contents!
if IsBound( toc.( groupname ) ) then
record:= toc.( groupname );
for name in [ "cyclic", "classes", "cyc2ccl" ] do
if IsBound( record.( name ) ) then
for std in Set( List( record.( name ), x -> x[1] ) ) do
prg:= AtlasProgram( gapname, std, name );
if prg = fail then
Print( "#E inconsistent program `", name, "' for `",
gapname, "'\n" );
result:= false;
else
# Fetch the character table of the group.
# (No further tests are possible if it is not available.)
tbl:= CharacterTable( gapname );
if tbl <> fail then
ident:= prg.identifier[2];
classnames:= AtlasClassNames( tbl );
if IsBound( prg.outputs ) then
outputs:= prg.outputs;
map:= List( outputs, x -> Position( classnames, x ) );
else
Print( "#E no component `outputs' in `", name,
"' for `", gapname, "'\n" );
result:= false;
outputs:= [ "-" ];
map:= [ fail ];
fi;
prg:= prg.program;
# (If `-' signs occur then we cannot test the names,
# but the number of outputs can be checked.)
roots:= ClassRoots( tbl );
roots:= Filtered( [ 1 .. Length( roots ) ],
i -> IsEmpty( roots[i] ) );
roots:= Set( List( roots, x -> ClassOrbit( tbl, x ) ) );
if ForAll( outputs, x -> not '-' in x ) then
# Check the class names.
if fail in map then
Print( "#E strange class names ",
Difference( outputs, classnames ),
" for `dataword/", ident, "'\n" );
result:= false;
fi;
if name in [ "classes", "cyc2ccl" ]
and Set( classnames ) <> Set( outputs ) then
Print( "#E class names ",
Difference( classnames, outputs ),
" not hit for `dataword/", ident, "'\n" );
result:= false;
fi;
if name = "cyclic" then
# Check whether all maximally cyclic subgroups
# are covered.
roots:= Filtered( roots,
list -> IsEmpty( Intersection( outputs,
classnames{ list } ) ) );
if not IsEmpty( roots ) then
Print( "#E maximally cyclic subgroups ",
List( roots, x -> classnames{ x } ),
" not hit for `dataword/", ident, "'\n" );
result:= false;
fi;
fi;
elif name = "cyclic" and
Length( outputs ) <> Length( roots ) then
Print( "#E no. of outputs and cyclic subgroups differ",
" for `dataword/", ident, "'\n" );
fi;
if not fail in map then
# Compute the representatives in a representation.
# (No further tests are possible if none is available.)
gens:= OneAtlasGeneratingSetInfo( gapname, std,
NrMovedPoints, [ 2 .. maxdeg ] );
if gens <> fail then
gens:= AtlasGenerators( gens.identifier );
if gens <> fail then
gens:= gens.generators;
fi;
if fail in gens then
gens:= fail;
fi;
if not name in [ "cyclic", "classes" ] then
# The input consists of the images of the standard
# generators under the `cyc' script.
pos:= Position( ident, '-' ) - 1;
pos2:= pos;
while ident[ pos2 ] <> 'W' do
pos2:= pos2 - 1;
od;
cycscript:= Concatenation( groupname, "G",
String( std ), "-cycW",
ident{ [ pos2+1 .. pos ] } );
cycscript:= AtlasProgram(
[ gapname, cycscript, std ] );
if cycscript = fail then
gens:= fail;
Print( "#E no script `", cycscript,
"' available\n" );
result:= false;
else
gens:= ResultOfStraightLineProgram(
cycscript.program, gens );
fi;
fi;
fi;
if gens <> fail then
grp:= Group( gens );
reps:= ResultOfStraightLineProgram( prg, gens );
if Length( reps ) <> Length( outputs ) then
Print( "#E inconsistent output numbers for ",
"`dataword/", ident, "'\n" );
result:= false;
else
# Check element orders and centralizer orders.
orders1:= OrdersClassRepresentatives( tbl ){ map };
orders2:= List( reps, Order );
if orders1 <> orders2 then
Print( "#E element orders of ",
outputs{ Filtered( [ 1 .. Length( outputs ) ],
i -> orders1[i] <> orders2[i] ) },
" differ for `dataword/", ident, "'\n" );
result:= false;
fi;
cents1:= SizesCentralizers( tbl ){ map };
cents2:= List( reps, x -> Size( Centralizer(grp,x) ) );
if cents1 <> cents2 then
Print( "#E centralizer orders of ",
outputs{ Filtered( [ 1 .. Length( outputs ) ],
i -> cents1[i] <> cents2[i] ) },
" differ for `dataword/", ident, "'\n" );
result:= false;
fi;
fi;
fi;
fi;
fi;
fi;
od;
fi;
od;
fi;
elif IsEmpty( arg ) then
for triple in AtlasOfGroupRepresentationsInfo.groupnames do
result:= AGR.Test.ClassScripts( triple[3] ) and result;
od;
fi;
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.CycToCcls( [<groupname>] )
##
## <#GAPDoc Label="test:AGR.Test.CycToCcls">
## <Mark><C>AGR.Test.CycToCcls()</C></Mark>
## <Item>
## checks whether some straight line program that computes representatives
## of conjugacy classes of a group can be computed from the ordinary
## &GAP; character table of that group and a straight line program that
## computes representatives of cyclic subgroups.
## In this case the missing scripts are printed if the level of
## <Ref InfoClass="InfoAtlasRep"/> is at least <M>1</M>.
## </Item>
## <#/GAPDoc>
##
AGR.Test.CycToCcls:= function( arg )
local result, groupname, gapname, toc, tbl, record, pref, datadirs,
entry, tomatch, cyc2ccl, str, prg, triple;
# Initialize the result.
result:= true;
if Length( arg ) = 1 and IsString( arg[1] ) then
groupname:= arg[1];
gapname:= First( AtlasOfGroupRepresentationsInfo.GAPnames,
pair -> pair[2] = groupname );
if gapname = fail then
Print( "#E no group with name `", groupname, "'\n" );
return false;
fi;
gapname:= gapname[1];
toc:= AtlasTableOfContents( "local" );
if toc = fail then
return false;
fi;
toc:= toc.TableOfContents;
# Fetch the character table of the group.
# (No test is possible if it is not available.)
tbl:= CharacterTable( gapname );
if tbl = fail then
Print( "#I no character table of `", gapname, "' is available\n" );
return true;
elif not IsBound( toc.( groupname ) ) then
return true;
fi;
record:= toc.( groupname );
if IsBound( record.cyclic ) then
if IsBound( record.cyc2ccl ) then
cyc2ccl:= List( record.cyc2ccl, x -> SplitString( x[2], "-" ) );
else
cyc2ccl:= [];
fi;
pref:= UserPreference( "AtlasRep", "AtlasRepDataDirectory" );
datadirs:= [ Directory( Concatenation( pref, "dataword" ) ) ];
for entry in record.cyclic do
# Check the `cyc2ccl' scripts available.
tomatch:= Filtered( entry[2], x -> x <> '-' );
cyc2ccl:= Filtered( cyc2ccl, x -> x[1] = tomatch );
if IsEmpty( cyc2ccl ) then
# There is no `cyc2ccl' script but perhaps we can create it.
str:= StringOfAtlasProgramCycToCcls(
StringFile( Filename( datadirs, entry[2] ) ),
tbl, "names" );
if str <> fail then
prg:= ScanStraightLineProgram( str, "string" );
if prg = fail then
Print( "#E automatically created script for `", tomatch,
"-cclsW1' would be incorrect" );
fi;
prg:= prg.program;
#T check the composition?
Print( "#I add the following script, in the new file `",
tomatch, "-cclsW1':\n",
str, "\n" );
result:= false;
fi;
fi;
od;
fi;
elif IsEmpty( arg ) then
for triple in AtlasOfGroupRepresentationsInfo.groupnames do
result:= AGR.Test.CycToCcls( triple[3] ) and result;
od;
fi;
# Return the result.
return result;
end;
#############################################################################
##
#F AGR.Test.GroupOrders( [true] )
##
## <#GAPDoc Label="test:AGR.Test.GroupOrders">
## <Mark><C>AGR.Test.GroupOrders()</C></Mark>
## <Item>
## checks whether the group orders stored in the <C>GAPnames</C> component
## of <Ref Var="AtlasOfGroupRepresentationsInfo"/> coincide with the
## group orders computed from an &ATLAS; permutation representation of
## degree up to <C>AGR.Test.MaxTestDegree</C>,
## from the character table or the table of marks with the given name,
## or from the structure of the name.
## Supported is a splitting of the name at the first dot (<C>.</C>),
## where the two parts of the name are examined with the same criteria in
## order to derive the group order.
## </Item>
## <#/GAPDoc>
##
AGR.Test.GroupOrders:= function( arg )
local verbose, formats, maxdeg, SizesFromName, result, entry, size;
verbose:= ( Length( arg ) <> 0 and arg[1] = true );
formats:= [
[ [ "L", IsDigitChar, "(", IsDigitChar, ")" ],
l -> Size( PSL( l[2], l[4] ) ) ],
[ [ "2.L", IsDigitChar, "(", IsDigitChar, ")" ],
l -> 2 * Size( PSL( l[2], l[4] ) ) ],
[ [ "S", IsDigitChar, "(", IsDigitChar, ")" ],
l -> Size( PSp( l[2], l[4] ) ) ],
[ [ "2.S", IsDigitChar, "(", IsDigitChar, ")" ],
l -> 2 * Size( PSp( l[2], l[4] ) ) ],
[ [ "U", IsDigitChar, "(", IsDigitChar, ")" ],
l -> Size( PSU( l[2], l[4] ) ) ],
];
maxdeg:= AGR.Test.MaxTestDegree;
SizesFromName:= function( name )
local result, pair, parse, tbl, tom, flag, data, pos, size1, size2;
result:= [];
# Deal with the case of integers.
if ForAll( name, x -> IsDigitChar( x ) or x = '^' ) then
#T improve: admit also brackets and '+' (problem of *matching* brackets)
# No other criterion matches with this format, so we return.
return [ EvalString( name ) ];
fi;
for pair in formats do
parse:= ParseBackwards( name, pair[1] );
if parse <> fail then
AddSet( result, pair[2]( parse ) );
fi;
od;
# Try to use the character table information.
tbl:= CharacterTable( name );
if tbl <> fail then
AddSet( result, Size( tbl ) );
fi;
# Try to use the table of marks information.
tom:= TableOfMarks( name );
if tom <> fail then
AddSet( result, Size( UnderlyingGroup( tom ) ) );
fi;
# Try to use the (locally available) database.
flag:= AtlasOfGroupRepresentationsInfo.remote;
AtlasOfGroupRepresentationsInfo.remote:= false;
data:= OneAtlasGeneratingSetInfo( name,
NrMovedPoints, [ 1 .. maxdeg ] );
# if data = fail then
# data:= OneAtlasGeneratingSetInfo( name,
# Dimension, [ 1 .. 10 ] );
# fi;
if data <> fail then
data:= AtlasGenerators( data );
if data <> fail then
AddSet( result, Size( Group( data.generators ) ) );
fi;
fi;
AtlasOfGroupRepresentationsInfo.remote:= flag;
# Try to evaluate the name structure.
pos:= Position( name, '.' );
#T improve: split also at ':'
if pos <> fail then
size1:= SizesFromName( name{ [ 1 .. pos-1 ] } );
size2:= SizesFromName( name{ [ pos+1 .. Length( name ) ] } );
if Length( size1 ) = 1 and Length( size2 ) = 1 then
AddSet( result, size1[1] * size2[1] );
elif Length( size1 ) > 1 or Length( size2 ) > 1 then
Print( "#E group orders: problem with `", name, "'\n" );
fi;
fi;
return result;
end;
result:= true;
for entry in AtlasOfGroupRepresentationsInfo.GAPnames do
size:= SizesFromName( entry[1] );
if 1 < Length( size ) then
Print( "#E AGR.Test.GroupOrders: several group orders for `",
entry[1], "':\n#E ", size, "\n" );
result:= false;
elif not IsBound( entry[3].size ) then
if Length( size ) = 0 then
if verbose then
Print( "#I AGR.Test.GroupOrders: group order for `", entry[1],
"' unknown\n" );
fi;
else
entry[3].size:= size[1];
Print( "#I AGR.Test.GroupOrders: set group order for `", entry[1],
"'\n",
"AGR.GRS(\"", entry[1], "\",", size[1], ");\n" );
fi;
elif Length( size ) = 0 then
if verbose then
Print( "#I AGR.Test.GroupOrders: cannot verify group order for `",
entry[1], "'\n" );
fi;
elif size[1] <> entry[3].size then
Print( "#E AGR.Test.GroupOrders: wrong group order for `",
entry[1], "'\n" );
result:= false;
fi;
od;
return result;
end;
#############################################################################
##
#F AGR.IsKernelInFrattiniSubgroup( <tbl>, <factfus> )
##
## We try to deduce the orders of maximal subgroups from those of factor
## groups.
## Namely, if <M>K</M> is a normal subgroup in <M>G</M> such that <M>K</M>
## is contained in the Frattini subgroup <M>\Phi(G)</M> of <M>G</M>
## (i. e., contained in any maximal subgroup of <M>G</M>)
## then the maximal subgroups of <M>G</M> are exactly the preimages of the
## maximal subgroups of <M>G/K</M> under the natural epimorphism.
## <P/>
## Since <M>G' \cap Z(G) \leq \Phi(G)</M>, this situation occurs in the case
## of central extensions of perfect groups,
## for example the orders of the maximal subgroups of <M>3.A_6</M> are
## the orders of the maximal subgroups of <M>A_6</M>, multiplied by the
## factor three.
## <P/>
## Since <M>\Phi(N) \leq \Phi(G)</M> holds for any normal subgroup <M>N</M>
## of <M>G</M>
## (see <Cite Key="Hup67" SubKey="Kap. III, §3, Hilfssatz 3.3 b)"/>),
## this situation occurs in the case of upward extensions of central
## extensions of perfect groups,
## for example the orders of the maximal subgroups of <M>3.A_6.2_1</M> are
## the orders of the maximal subgroups of <M>A_6.2_1</M>, multiplied by the
## factor three.
##
AGR.IsKernelInFrattiniSubgroup:= function( tbl, factfus )
local ker, nam, subtbl, subfus, subker;
# Compute the kernel <M>K</M> of the epimorphism.
ker:= ClassPositionsOfKernel( factfus.map );
if Length( ker ) = 1 or not
IsSubset( ClassPositionsOfDerivedSubgroup( tbl ), ker ) then
return false;
elif IsSubset( ClassPositionsOfCentre( tbl ), ker ) then
# We have <M>K \leq G' \cap Z(G)</M>,
# so the maximal subgroups are exactly the preimages of the
# maximal subgroups in the factor group.
return true;
fi;
# Look for a suitable normal subgroup <M>N</M> of <M>G</M>.
for nam in NamesOfFusionSources( tbl ) do
subtbl:= CharacterTable( nam );
subfus:= GetFusionMap( subtbl, tbl );
if Size( subtbl ) = Sum( SizesConjugacyClasses( tbl ){
Set( subfus ) } ) and
IsSubset( subfus, ker ) then
# <M>N</M> is normal in <M>G</M>, with <M>K \leq N</M>
subker:= Filtered( [ 1 .. Length( subfus ) ],
i -> subfus[i] in ker );
if IsSubset( ClassPositionsOfDerivedSubgroup( subtbl ),
subker ) and
IsSubset( ClassPositionsOfCentre( subtbl ), subker ) then
# We have <M>K \leq N' \cap Z(N)</M>.
return true;
fi;
fi;
od;
return false;
end;
#############################################################################
##
#F AGR.Test.MaxesOrders( [true] )
##
## <#GAPDoc Label="test:AGR.Test.MaxesOrders">
## <Mark><C>AGR.Test.MaxesOrders()</C></Mark>
## <Item>
## checks whether the orders of maximal subgroups stored in the component
## <C>GAPnames</C> of <Ref Var="AtlasOfGroupRepresentationsInfo"/>
## coincide with the orders computed from the restriction of an &ATLAS;
## permutation representation of degree up to
## <C>AGR.Test.MaxTestDegree</C>,
## from the character table, or the table of marks with the given name,
## or from the information about maximal subgroups of a factor group
## modulo a normal subgroup that is contained in the Frattini subgroup.
## </Item>
## <#/GAPDoc>
##
AGR.Test.MaxesOrders:= function( arg )
local verbose, maxdeg, maxmax, MaxesInfoForName, result, toc, entry,
info, size, struct;
verbose:= ( Length( arg ) <> 0 and arg[1] = true );
maxdeg:= AGR.Test.MaxTestDegree;
maxmax:= AGR.Test.HardCases.MaxNumberMaxes;
MaxesInfoForName:= function( name )
local result, nrmaxes, tbl, oneresult, i,
subtbl, tom, std, data, prg, gens, factfus, recurs, good;
result:= [];
nrmaxes:= [];
# Try to use the character table information.
tbl:= CharacterTable( name );
if tbl <> fail then
if HasMaxes( tbl ) then
AddSet( nrmaxes, Length( Maxes( tbl ) ) );
AddSet( result, List( Maxes( tbl ),
nam -> Size( CharacterTable( nam ) ) ) );
else
# Try whether individual maxes are supported.
oneresult:= [];
if tbl <> fail then
for i in [ 1 .. maxmax ] do
subtbl:= CharacterTable( Concatenation( Identifier( tbl ), "M",
String( i ) ) );
if subtbl <> fail then
oneresult[i]:= Size( subtbl );
fi;
od;
fi;
if not IsEmpty( oneresult ) then
AddSet( result, oneresult );
fi;
fi;
fi;
# Try to use the table of marks information.
# more tests: how to identify FusionsToLibTom( tom )?
tom:= TableOfMarks( name );
if tom <> fail then
AddSet( nrmaxes, Length( MaximalSubgroupsTom( tom )[1] ) );
AddSet( result, Reversed( SortedList( OrdersTom( tom ){
MaximalSubgroupsTom( tom )[1] } ) ) );
fi;
# Try to use the database.
for std in [ 1 .. AGR.Test.HardCases.MaxNumberStd ] do
data:= OneAtlasGeneratingSetInfo( name, std,
NrMovedPoints, [ 1 .. maxdeg ] );
# if data = fail then
# data:= OneAtlasGeneratingSetInfo( name, std,
# Dimension, [ 1 .. 10 ] );
# fi;
if data <> fail then
data:= AtlasGenerators( data );
if data <> fail then
oneresult:= [];
for i in [ 1 .. maxmax ] do
prg:= AtlasProgram( name, std, "maxes", i );
if prg <> fail then
gens:= ResultOfStraightLineProgram( prg.program,
data.generators );
oneresult[i]:= Size( Group( gens ) );
fi;
od;
if not IsEmpty( oneresult ) then
AddSet( result, oneresult );
fi;
fi;
fi;
od;
# Try to deduce the orders of maximal subgroups from those of factors.
if tbl <> fail then
for factfus in ComputedClassFusions( tbl ) do
if AGR.IsKernelInFrattiniSubgroup( tbl, factfus ) then
recurs:= MaxesInfoForName( factfus.name );
UniteSet( nrmaxes, recurs.nrmaxes );
UniteSet( result,
recurs.maxesorders * Sum( SizesConjugacyClasses( tbl ){
ClassPositionsOfKernel( factfus.map ) } ) );
fi;
od;
fi;
# Compact the partial results.
good:= true;
for oneresult in result{ [ 2 .. Length( result ) ] } do
for i in [ 1 .. Length( oneresult ) ] do
if IsBound( result[1][i] ) then
if IsBound( oneresult[i] ) then
if result[1][i] <> oneresult[i] then
good:= false;
fi;
fi;
elif IsBound( oneresult[i] ) then
result[1][i]:= oneresult[i];
fi;
od;
od;
if good and not IsEmpty( result ) then
result:= [ result[1] ];
fi;
return rec( maxesorders:= result,
nrmaxes:= Set( nrmaxes ) );
end;
result:= true;
toc:= AtlasOfGroupRepresentationsInfo.TableOfContents.remote;
for entry in AtlasOfGroupRepresentationsInfo.GAPnames do
info:= MaxesInfoForName( entry[1] );
if not IsBound( entry[3].nrMaxes ) then
if Length( info.nrmaxes ) = 1 then
Print( "#I AGR.MXN: set maxes number for `", entry[1], "':\n",
"AGR.MXN(\"", entry[1], "\",", info.nrmaxes[1], ");\n" );
fi;
elif Length( info.nrmaxes ) <> 1 then
if verbose then
Print( "#I AGR.MXN: cannot verify stored maxes number ",
"for `", entry[1], "'\n" );
fi;
fi;
size:= info.maxesorders;
if 1 < Length( size ) then
Print( "#E AGR.Test.MaxesOrders: several maxes orders for `",
entry[1], "':\n#E ", size, "\n" );
result:= false;
elif not IsBound( entry[3].sizesMaxes )
or IsEmpty( entry[3].sizesMaxes ) then
# No maxes orders are stored yet.
if Length( size ) = 0 then
if verbose or ( IsBound( toc.( entry[2] ) ) and
IsBound( toc.( entry[2] ).maxes ) and
not IsEmpty( toc.( entry[2] ).maxes ) ) then
Print( "#I AGR.Test.MaxesOrders: maxes orders for `", entry[1],
"' unknown\n" );
fi;
else
if IsBound( entry[3].size ) then
if entry[3].size in size[1] then
Print( "#E AGR.Test.MaxesOrders: group order in maxes ",
"orders list for `", entry[1], "'\n" );
result:= false;
fi;
if ForAny( size[1], x -> entry[3].size mod x <> 0 ) then
Print( "#E AGR.Test.MaxesOrders: strange subgp. order for `",
entry[1], "'\n" );
result:= false;
fi;
fi;
if IsSortedList( - Compacted( size[1] ) ) then
entry[3].sizesMaxes:= size[1];
Print( "#I AGR.Test.MaxesOrders: set maxes orders for `",
entry[1], "':\n" );
Print( "AGR.MXO(\"", entry[1], "\",",
Filtered( String( size[1] ), x -> x <> ' ' ), ");\n" );
else
Print( "#E AGR.Test.MaxesOrders: computed maxes orders for `",
entry[1], "' are not sorted:\n", size[1], "\n" );
fi;
fi;
elif Length( size ) = 0 then
if verbose then
Print( "#I AGR.Test.MaxesOrders: cannot verify stored ",
"maxes orders for `", entry[1], "'\n" );
fi;
elif not IsSortedList( - Compacted( size[1] ) ) then
Print( "#E AGR.Test.MaxesOrders: computed maxes orders for `",
entry[1], "' are not sorted:\n", size[1], "\n" );
elif size[1] <> entry[3].sizesMaxes then
Print( "#E AGR.Test.MaxesOrders: computed and stored ",
"maxes orders for `", entry[1], "' differ:\n" );
Print( "#E ", size[1], " vs. ", entry[3].sizesMaxes, "\n" );
result:= false;
fi;
od;
return result;
end;
#############################################################################
##
#F AGR.Test.MaxesStructure( [true] )
##
## <#GAPDoc Label="test:AGR.Test.MaxesStructure">
## <Mark><C>AGR.Test.MaxesStructure()</C></Mark>
## <Item>
## checks whether the names of maximal subgroups stored in the component
## <C>GAPnames</C> of <Ref Var="AtlasOfGroupRepresentationsInfo"/>
## coincide with the names computed from the &GAP; character table with
## the given name.
## </Item>
## <#/GAPDoc>
##
AGR.Test.SubgroupData:= function( arg )
local verbose, maxdeg, maxmax, MaxesInfoForName, result, toc, entry,
info, size, struct;
verbose:= ( Length( arg ) <> 0 and arg[1] = true );
maxdeg:= AGR.Test.MaxTestDegree;
maxmax:= AGR.Test.HardCases.MaxNumberMaxes;
MaxesInfoForName:= function( name )
local result, tbl, oneresult, i,
subtbl, tom, std, data, prg, gens, factfus, recurs, good;
result:= [];
# Try to use the character table information.
tbl:= CharacterTable( name );
if tbl <> fail then
if HasMaxes( tbl ) then
AddSet( result,
List( Maxes( tbl ),
AGR.StructureDescriptionCharacterTableName ) );
else
# Try whether individual maxes are supported.
oneresult:= [];
if tbl <> fail then
for i in [ 1 .. maxmax ] do
subtbl:= CharacterTable( Concatenation( Identifier( tbl ), "M",
String( i ) ) );
if subtbl <> fail then
oneresult[i]:= AGR.StructureDescriptionCharacterTableName(
Identifier( subtbl ) );
fi;
od;
fi;
if not IsEmpty( oneresult ) then
AddSet( result, oneresult );
fi;
fi;
fi;
# Compact the partial results.
good:= true;
for oneresult in result{ [ 2 .. Length( result ) ] } do
for i in [ 1 .. Length( oneresult ) ] do
if IsBound( result[1][i] ) then
if IsBound( oneresult[i] ) then
if result[1][i] <> oneresult[i] then
good:= false;
fi;
fi;
elif IsBound( oneresult[i] ) then
result[1][i]:= oneresult[i];
fi;
od;
od;
if good and not IsEmpty( result ) then
result:= [ result[1] ];
fi;
return rec( maxesstructure:= result );
end;
result:= true;
toc:= AtlasOfGroupRepresentationsInfo.TableOfContents.remote;
for entry in AtlasOfGroupRepresentationsInfo.GAPnames do
info:= MaxesInfoForName( entry[1] );
struct:= info.maxesstructure;
if 1 < Length( struct ) then
Print( "#E AGR.Test.MaxesStructure: several maxes structures for `",
entry[1], "':\n#E ", struct, "\n" );
result:= false;
elif not IsBound( entry[3].structureMaxes ) then
# No maxes structures are stored yet.
if Length( struct ) = 0 then
if verbose or ( IsBound( toc.( entry[2] ) ) and
IsBound( toc.( entry[2] ).maxes ) and
not IsEmpty( toc.( entry[2] ).maxes ) ) then
Print( "#I AGR.Test.MaxesStructure: maxes structures for `",
entry[1], "' unknown\n" );
fi;
elif Length( struct ) = 1 then
Print( "#I AGR.Test.MaxesStructure: set maxes structures for `",
entry[1], "':\n",
"AGR.MXS(\"", entry[1], "\",",
Filtered( String( struct[1] ), x -> x <> ' ' ), ");\n" );
fi;
elif Length( struct ) = 0 then
if verbose then
Print( "#I AGR.Test.MaxesStructure: cannot verify stored ",
"maxes structures for `", entry[1], "'\n" );
fi;
elif struct[1] <> entry[3].structureMaxes then
Print( "#E AGR.Test.MaxesStructure: computed and stored ",
"maxes structures for `", entry[1], "' differ:\n" );
Print( "#E ", struct[1], " vs. ", entry[3].structureMaxes, "\n" );
result:= false;
fi;
od;
return result;
end;
#############################################################################
##
#F AGR.Test.StdCompatibility( [[<entry>, ]<verbose>] )
##
## <#GAPDoc Label="test:AGR.Test.StdCompatibility">
## <Mark><C>AGR.Test.StdCompatibility()</C></Mark>
## <Item>
## checks whether the information about the compatibility of
## standard generators of a group and its factor groups that is stored in
## the <C>GAPnames</C> component of
## <Ref Var="AtlasOfGroupRepresentationsInfo"/>
## coincides with computed values.
## <P/>
## The following criterion is used for computing the value for a group
## <M>G</M>.
## Use the &GAP; Character Table Library to determine factor groups
## <M>F</M> of <M>G</M> for which standard generators are defined and
## moreover a presentation in terms of these standard generators is known.
## Evaluate the relators of the presentation in the standard generators of
## <M>G</M>, and let <M>N</M> be the normal closure of these elements in
## <M>G</M>.
## Then mapping the standard generators of <M>F</M> to the <M>N</M>-cosets
## of the standard generators of <M>G</M> is an epimorphism.
## If <M>|G/N| = |F|</M> holds then <M>G/N</M> and <M>F</M> are
## isomorphic, and the standard generators of <M>G</M> and <M>F</M> are
## compatible in the sense that mapping the standard generators of
## <M>G</M> to their <M>N</M>-cosets yields standard generators of
## <M>F</M>.
## </Item>
## <#/GAPDoc>
##
AGR.Test.StdCompatibility:= function( arg )
local verbose, maxstd, CompInfoForEntry, result, entry, info, l;
verbose:= ( Length( arg ) <> 0 and arg[ Length( arg ) ] = true );
maxstd:= AGR.Test.HardCases.MaxNumberStd;
CompInfoForEntry:= function( entry )
local result, tbl, flag, fus, factstd, pres, std, gens, prg, res, ker,
j, G, F, hom,
facttbl;
result:= [];
tbl:= CharacterTable( entry[1] );
if tbl <> fail then
flag:= AtlasOfGroupRepresentationsInfo.remote;
AtlasOfGroupRepresentationsInfo.remote:= false;
for fus in ComputedClassFusions( tbl ) do
if 1 < Length( ClassPositionsOfKernel( fus.map ) ) then
if AGR.InfoForName( fus.name ) <> fail then
for factstd in [ 1 .. maxstd ] do
pres:= AtlasProgram( fus.name, factstd, "presentation" );
if pres <> fail then
# The two sets of generators are compatible iff the
# relators in terms of the generators of the big group
# generate the kernel of the epimorphism.
for std in [ 1 .. maxstd ] do
gens:= OneAtlasGeneratingSetInfo( entry[1], std );
if gens <> fail then
gens:= AtlasGenerators( gens.identifier );
fi;
if gens <> fail then
prg:= StraightLineProgramFromStraightLineDecision(
pres.program );
res:= ResultOfStraightLineProgram( prg,
gens.generators );
ker:= Group( res );
# `ker' is assumed to be a very small group.
if Size( tbl ) / Size( CharacterTable( fus.name ) )
= Size( ker ) then
Add( result, [ std, fus.name, factstd, true ] );
else
Add( result, [ std, fus.name, factstd, false ] );
fi;
fi;
od;
else
# Try to form the homomorphism object in GAP,
# by mapping generators of the big group to generators
# of the factor group.
# If this defines a homomorphism and if this is surjective
# then the generators are compatible.
for std in [ 1 .. maxstd ] do
facttbl:= CharacterTable( fus.name );
if ClassPositionsOfFittingSubgroup( facttbl ) = [1] then
# currently classes scripts are available only for these tables,
# so other cases are not really interesting at the moment ...
G:= AtlasGroup( entry[1], std, IsPermGroup, true );
F:= AtlasGroup( fus.name, factstd, IsPermGroup, true );
if G <> fail and F <> fail then
if NrMovedPoints( G ) <= AGR.Test.MaxTestDegree and NrMovedPoints( F ) <= AGR.Test.MaxTestDegree then
#Print( "#I trying hom. ", entry[1], " ->> ", fus.name, "\n" );
hom:= GroupHomomorphismByImages( G, F,
GeneratorsOfGroup( G ),
GeneratorsOfGroup( F ) );
if hom <> fail then
Add( result, [ std, fus.name, factstd, true ] );
else
Add( result, [ std, fus.name, factstd, false ] );
fi;
else
#Print( "#I omit hom. ", entry[1], " ->> ", fus.name, ", too many points ...\n" );
fi;
elif std = 1 and factstd = 1 then
#Print( "#I no hom. ", entry[1], " ->> ", fus.name, " to try?\n" );
fi;
fi;
od;
fi;
od;
fi;
fi;
od;
AtlasOfGroupRepresentationsInfo.remote:= flag;
fi;
return result;
end;
result:= true;
if Length( arg ) = 0 or ( Length( arg ) = 1 and IsBool( arg[1] ) ) then
for entry in AtlasOfGroupRepresentationsInfo.GAPnames do
result:= AGR.Test.StdCompatibility( entry, verbose ) and result;
od;
else
entry:= arg[1];
info:= CompInfoForEntry( entry );
if not IsBound( entry[3].factorCompatibility ) then
entry[3].factorCompatibility:= [];
fi;
if info <> entry[3].factorCompatibility then
if verbose then
Print( "#I AGR.Test.StdCompatibility: change compatibility info\n" );
for l in info do
#T can be empty!
Print( "AGR.STDCOMP(\"", entry[1], "\",",
Filtered( String( l ), x -> x <> ' ' ), ");\n" );
od;
fi;
fi;
if verbose then
for l in Difference( entry[3].factorCompatibility, info ) do
Print( "#I AGR.Test.StdCompatibility: cannot verify compatibility ",
"info `", l, "' for `", entry[1], "'\n" );
od;
fi;
if ForAny( entry[3].factorCompatibility, l1 -> ForAny( info,
l2 -> l1{[1..3]} = l2{[1..3]} and ( l1[4] <> l2[4] ) ) ) then
Print( "#E AGR.Test.StdCompatibility: contradiction of ",
"compatibility info for `", entry[1], "'\n" );
result:= false;
fi;
fi;
return result;
end;
#############################################################################
##
#F AGR.Test.CompatibleMaxes( [[<entry>, ]<verbose>] )
##
## <#GAPDoc Label="test:AGR.Test.CompatibleMaxes">
## <Mark><C>AGR.Test.CompatibleMaxes()</C></Mark>
## <Item>
## checks whether the information about deriving straight line programs
## for restricting to subgroups from straight line programs that belong
## to a factor group coincide with computed values.
## <P/>
## The following criterion is used for computing the value for a group
## <M>G</M>.
## If <M>F</M> is a factor group of <M>G</M> such that the standard
## generators of <M>G</M> and <M>F</M> are compatible
## (see the test function <C>AGR.Test.StdCompatibility</C>)
## and if there are a presentation for <M>F</M> and a permutation
## representation of <M>G</M> then it is checked whether the
## <C>"maxes"</C> type straight line programs for <M>F</M> can be used to
## compute generators for the maximal subgroups of <M>G</M>;
## if not then generators of the kernel of the natural epimorphism from
## <M>G</M> to <M>F</M>, must be added.
## </Item>
## <#/GAPDoc>
##
AGR.Test.CompatibleMaxes:= function( arg )
local verbose, maxdeg, maxmax, CompMaxForEntry, result, toc, entry, info,
stored, entry2, filt;
verbose:= Length( arg ) <> 0 and arg[ Length( arg ) ] = true;
maxdeg:= AGR.Test.MaxTestDegree;
maxmax:= AGR.Test.HardCases.MaxNumberMaxes;
CompMaxForEntry:= function( entry )
local result, tbl, l, factname, factstd, gens, i, prg, max;
result:= [];
tbl:= CharacterTable( entry[1] );
if tbl <> fail and IsBound( entry[3].sizesMaxes )
and IsBound( entry[3].factorCompatibility ) then
# Maxes orders info and compatibility info are known.
for l in Filtered( entry[3].factorCompatibility,
x -> x[4] = true ) do
# Check whether the maxes of the two groups are in bijection.
factname:= l[2];
factstd:= l[3];
if ForAny( ComputedClassFusions( tbl ),
fus -> fus.name = factname and
AGR.IsKernelInFrattiniSubgroup( tbl, fus ) ) then
gens:= OneAtlasGeneratingSetInfo( entry[1], l[1],
NrMovedPoints, [ 1 .. maxdeg ] );
if gens <> fail then
gens:= AtlasGenerators( gens.identifier );
fi;
if gens <> fail then
for i in [ 1 .. maxmax ] do
prg:= AtlasProgram( factname, factstd, "maxes", i );
if prg <> fail and IsBound( entry[3].sizesMaxes[i] ) then
# try the program for the ext. gp.
max:= ResultOfStraightLineProgram( prg.program,
gens.generators );
max:= Group( max );
if Size( max ) = entry[3].sizesMaxes[i] then
# The program for the factor group is sufficient.
Add( result,
[ entry[2], factstd, i, [ prg.identifier[2] ] ] );
elif not IsBound( entry[3].kernelPrograms )
or ForAll( entry[3].kernelPrograms,
x -> x[2] <> factname ) then
Print( "#I SLP for kernel generators of ",
entry[1], " ->> ", factname, " missing ",
"\n#I (needed for max. ", i, ")\n" );
fi;
fi;
od;
fi;
fi;
od;
fi;
return result;
end;
result:= true;
toc:= AtlasOfGroupRepresentationsInfo.TableOfContents.remote;
if Length( arg ) = 0 or ( Length( arg ) = 1 and IsBool( arg[1] ) ) then
for entry in AtlasOfGroupRepresentationsInfo.GAPnames do
result:= AGR.Test.CompatibleMaxes( entry, verbose ) and result;
od;
else
entry:= arg[1];
info:= CompMaxForEntry( entry );
stored:= [];
if IsBound( toc.( entry[2] ) ) and
IsBound( toc.( entry[2] ).maxext ) then
stored:= List( toc.( entry[2] ).maxext,
x -> Concatenation( [ entry[2] ], x ) );
fi;
for entry2 in info do
filt:= Filtered( stored,
x -> x{ [ 1 .. 3 ] } = entry2{ [ 1 .. 3 ] }
and x[4][1] = entry2[4][1] );
if IsEmpty( filt ) then
# The entry is new.
if Length( entry2[4] ) = 1 then
# The script for restricting the repres. of the factor group
# is good enough for the group.
Print( "#I AGR.TOCEXT: set entry\nAGR.TOCEXT(\"", entry2[1],
"\",", entry2[2], ",", entry2[3], ",[\"",
entry2[4][1], "\"]);\n" );
else
# For restricting a repres. of the group, one needs the script
# for the factor group plus some kernel elements.
Print( "#I AGR.TOCEXT: set entry\nAGR.TOCEXT(\"", entry2[1],
"\",", entry2[2], ",", entry2[3], ",[\"",
entry2[4][1], "\",\"", entry2[4][2], "\"]);\n" );
fi;
elif Length( entry2[4] ) <> Length( filt[1][4] ) then
if Length( entry2[4] ) = 3 and Length( filt[1][4] ) = 2 then
if entry2[4]{ [ 1, 2 ] } <> filt[1][4] then
# We have already such an entry but it is different.
Print( "#E AGR.TOCEXT: difference ", entry2, " vs. ", filt[1],
"\n" );
result:= false;
fi;
#T check also equality of the script with a stored one if applicable!
else
# We have already such an entry but it is different.
Print( "#E AGR.TOCEXT: difference ", entry2, " vs. ", filt[1],
"\n" );
result:= false;
fi;
fi;
od;
for entry2 in stored do
filt:= Filtered( info,
x -> x{ [ 1 .. 3 ] } = entry2{ [ 1 .. 3 ] }
and x[4][1] = entry2[4][1] );
if IsEmpty( filt ) then
Print( "#I AGR.TOCEXT: cannot verify stored value ", entry2, "\n" );
fi;
od;
fi;
return result;
end;
#############################################################################
##
#F AGR.IsEquivalentSLP( <lines1>, <lines2> )
##
## simpleminded function; eventually better evaluate standard generators
## of the group in question
##
AGR.IsEquivalentSLP:= function( lines1, lines2 )
local n, slp1, slp2, f, gens;
if lines1 = lines2 then
return true;
fi;
n:= 2;
slp1:= StraightLineProgram( lines1, n );
slp2:= StraightLineProgram( lines2, n );
f:= FreeGroup( n );
gens:= GeneratorsOfGroup( f );
if ResultOfStraightLineProgram( slp1, gens )
= ResultOfStraightLineProgram( slp2, gens ) then
return true;
else
return false;
fi;
end;
#############################################################################
##
#F AGR.Test.KernelGenerators( [[<entry>, ]<verbose>] )
##
## <#GAPDoc Label="test:AGR.Test.KernelGenerators">
## <Mark><C>AGR.Test.KernelGenerators()</C></Mark>
## <Item>
## checks whether the information stored in the <C>GAPnames</C> component
## of <Ref Var="AtlasOfGroupRepresentationsInfo"/> about
## straight line programs for computing generators of the kernels of
## natural epimorphisms between &ATLAS; groups
## coincides with computed values.
## <P/>
## The following criterion is used for computing the value for a group
## <M>G</M>.
## Use the &GAP; Character Table Library to determine factor groups
## <M>F</M> of <M>G</M> for which standard generators are defined
## such that mapping standard generators of <M>G</M> to those of
## <M>F</M> defines a homomorphism, and such that a presentation of
## <M>F</M> in terms of its standard generators is known.
## Evaluating the relators of the presentation in the standard generators
## of <M>G</M> yields normal subgroup generators for the kernel.
## <P/>
## A message is printed for each group name
## for which some straight line program for computing kernel generators
## was not stored but now was computed,
## or for which the stored info cannot be verified,
## </Item>
## <#/GAPDoc>
##
AGR.Test.KernelGenerators:= function( arg )
local verbose, maxstd, CompInfoForEntry, result, pos, entry, new, old, i,
l;
verbose:= ( Length( arg ) <> 0 and arg[ Length( arg ) ] = true );
maxstd:= AGR.Test.HardCases.MaxNumberStd;
CompInfoForEntry:= function( entry )
local result, info, std, factname, factstd, pres, gens, prg, res, ker,
perm, words, kergens, sub, j, lines, G, F, hom, free, freegens,
freestrs, iter, addprgs, w, ord, elm,
facttbl;
result:= [];
for info in Filtered( entry[3].factorCompatibility,
x -> x[4] = true ) do
#T compute kernel generators also in other cases?
#T where does this happen? and how do we get the homomorphism then?
std:= info[1];
factname:= info[2];
factstd:= info[3];
if AGR.InfoForName( factname ) <> fail then
pres:= AtlasProgram( factname, factstd, "presentation" );
if pres <> fail then
# The two sets of generators are compatible.
gens:= OneAtlasGeneratingSetInfo( entry[1], std );
if gens <> fail then
gens:= AtlasGenerators( gens.identifier );
fi;
if gens <> fail then
prg:= StraightLineProgramFromStraightLineDecision(
pres.program );
res:= ResultOfStraightLineProgram( prg, gens.generators );
ker:= Group( res );
# `ker' is assumed to be a very small group.
# Create a script for generators of the kernel.
perm:= Sortex( -List( res, Order ) );
res:= Permuted( res, perm );
words:= Permuted( [ 1 .. Length( res ) ], perm );
kergens:= [ words[1] ];
sub:= SubgroupNC( ker, [ res[1] ] );
j:= 1;
while j <= Length( words ) and Size( sub ) <> Size( ker ) do
j:= j+1;
Add( kergens, words[j] );
sub:= ClosureGroup( sub, res[j] );
od;
if Size( sub ) = Size( ker ) then
lines:= LinesOfStraightLineProgram(
RestrictOutputsOfSLP( prg, kergens ) );
Add( result, [ std, factname, lines ] );
else
Print( "#I ", entry[1],
": not enough generators for the kernel found\n" );
fi;
fi;
else
# Try to form the homomorphism object in GAP,
# by mapping generators of the big group to generators
# of the factor group.
# If this defines a homomorphism and if this is surjective
# then the generators are compatible.
# For example, both 2.J2.2 and Isoclinic(2.J2.2) map to J2.2;
# then also the maxes can be identified etc.
facttbl:= CharacterTable( factname );
if ClassPositionsOfFittingSubgroup( facttbl ) = [1] then
# currently classes scripts are available only for these tables,
# so other cases are not really interesting at the moment ...
G:= AtlasGroup( entry[1], std, IsPermGroup, true );
F:= AtlasGroup( factname, factstd, IsPermGroup, true );
if G <> fail and F <> fail then
if NrMovedPoints( G ) <= AGR.Test.MaxTestDegree and
NrMovedPoints( F ) <= AGR.Test.MaxTestDegree then
#Print( "#I trying hom. ", entry[1], " ->> ", factname, "\n" );
hom:= GroupHomomorphismByImagesNC( G, F,
GeneratorsOfGroup( G ), GeneratorsOfGroup( F ) );
if hom <> fail then
# Find a script for generators of the kernel.
free:= FreeSemigroup( Length( GeneratorsOfGroup( G ) ) );
freegens:= GeneratorsOfSemigroup( free );
freestrs:= List( freegens, String );
iter:= Iterator( free );
ker:= TrivialSubgroup( G );
addprgs:= [];
while Size( ker ) * Size( F ) <> Size( G ) do
w:= NextIterator( iter );
ord:= Order( MappedWord( w, freegens,
GeneratorsOfGroup( F ) ) );
elm:= MappedWord( w, freegens,
GeneratorsOfGroup( G ) )^ord;
if not elm in ker then
Add( addprgs, CompositionOfStraightLinePrograms(
StraightLineProgram( [ [ [ 1, ord ], 2 ] ] ),
StraightLineProgramNC( String( w ), freestrs ) ) );
ker:= ClosureGroup( ker, elm );
fi;
od;
lines:= LinesOfStraightLineProgram(
IntegratedStraightLineProgram( addprgs ) );
Add( result, [ std, factname, lines ] );
fi;
else
#Print( "#I omit hom. ", entry[1], " ->> ", factname, ", too many points ...\n" );
fi;
elif std = 1 and factstd = 1 then
#Print( "#I no hom. ", entry[1], " ->> ", factname, " to try?\n" );
# fi;
fi;
fi;
fi;
fi;
od;
return result;
end;
result:= true;
if Length( arg ) = 0 or ( Length( arg ) = 1 and IsBool( arg[1] ) ) then
for entry in AtlasOfGroupRepresentationsInfo.GAPnames do
result:= AGR.Test.KernelGenerators( entry, verbose ) and result;
od;
elif IsBound( arg[1][3].factorCompatibility ) then
entry:= arg[1];
new:= CompInfoForEntry( entry );
if IsBound( entry[3].kernelPrograms ) then
old:= ShallowCopy( entry[3].kernelPrograms );
else
old:= [];
fi;
for i in [ 1 .. Length( old ) ] do
pos:= Position( new, old[i] );
if pos <> fail then
Unbind( old[i] );
Unbind( new[ pos ] );
else
pos:= PositionProperty( new, l -> old[i]{[1..2]} = l{[1..2]} );
if pos <> fail then
if AGR.IsEquivalentSLP( old[i][3], new[ pos ][3] ) then
Unbind( old[i] );
Unbind( new[ pos ] );
else
Print( "#E AGR.Test.KernelGenerators: contradiction of ",
"kernel info for `", entry[1], "' at\n",
"#E ", old[i], "\n" );
result:= false;
fi;
fi;
fi;
od;
for l in new do
Print( "#I AGR.Test.KernelGenerators: add kernel info\n",
"AGR.KERPRG(\"", entry[1], "\",",
Filtered( String( l ), x -> x <> ' ' ), ");\n" );
od;
for l in old do
Print( "#I AGR.Test.KernelGenerators: cannot verify kernel ",
"info `", l, "' for `", entry[1], "'\n" );
od;
fi;
return result;
end;
#############################################################################
##
#F AGR.CharacterNameFromMultiplicities( <tbl>, <mults> )
##
## - to be used for tables of perfect groups only;
## in other cases, relative names should be used
## - see also `MFER.PermCharInfo_ATLAS_FromCoefficients'
## (which works only for mult.-free characters)
##
AGR.CharacterNameFromMultiplicities:= function( tbl, mults )
local degrees, degreeset, positions, irrnames, i, alp, ATL, j, n, pair;
if UnderlyingCharacteristic( tbl ) = 0 then
if not IsPerfectCharacterTable( tbl ) then
return fail;
fi;
elif not IsPerfectCharacterTable( OrdinaryCharacterTable( tbl ) ) then
return fail;
fi;
degrees:= List( Irr( tbl ), x -> x[1] );
degreeset:= Set( degrees );
positions:= List( degreeset, x -> [] );
irrnames:= [];
for i in [ 1 .. Length( degrees ) ] do
Add( positions[ PositionSorted( degreeset, degrees[i] ) ], i );
od;
alp:= List( "abcdefghijklmnopqrstuvwxyz", x -> [ x ] );
while Length( alp ) < Maximum( List( positions, Length ) ) do
Append( alp, List( alp{ [ 1 .. 26 ] },
x -> Concatenation( "(", x, "')" ) ) );
od;
if IsInt( mults ) then
mults:= [ mults ];
fi;
ATL:= [];
for i in [ 1 .. Length( degreeset ) ] do
ATL[i]:= "";
for j in [ 1 .. Length( positions[i] ) ] do
n:= positions[i][j];
if n in mults then
# appears once
Append( ATL[i], alp[j] );
else
pair:= First( mults, x -> IsList( x ) and x[1] = n );
if pair <> fail then
# appears with larger mult.
Append( ATL[i], alp[j] );
Append( ATL[i], "^" );
Append( ATL[i], String( pair[2] ) );
fi;
fi;
od;
if ATL[i] <> "" then
ATL[i]:= Concatenation( String( degreeset[i] ), ATL[i] );
fi;
od;
return JoinStringsWithSeparator( Filtered( ATL, x -> x <> "" ), "+" );
end;
#############################################################################
##
#F AGR.Test.Characters( [<tocid>[, <name>[, <cond>]]] )
##
## <#GAPDoc Label="test:AGR.Test.Characters">
## <Mark><C>AGR.Test.Characters( [<A>tocid</A>] )</C></Mark>
## <Item>
## checks the stored character information for the matrix and permutation
## representations that are stored in the directory with identifier
## <A>tocid</A>.
## </Item>
## <#/GAPDoc>
##
AGR.Test.Characters:= function( arg )
local result, name, toc, cond, grpname, tbl, classnames, ccl, cyc, entry,
outputs1, std, prg1, poss, nam, ord, parts, outputs, prgs2,
info, p, id, modtbl, fus, phi, gens, galoisfams, choice, i, pos,
prgs, prg2, repprg, rep, val, dec, j, map, parsed, charpos, test;
# Initialize the result.
result:= true;
if IsEmpty( arg ) then
return AGR.Test.Characters( "local" );
elif Length( arg ) = 1 then
for name in AtlasOfGroupRepresentationsInfo.GAPnames do
result:= AGR.Test.Characters( arg[1], name[1] ) and result;
od;
return result;
elif Length( arg ) = 2 then
toc:= AtlasTableOfContents( arg[1] );
name:= arg[2];
cond:= [];
elif Length( arg ) = 3 then
toc:= AtlasTableOfContents( arg[1] );
name:= arg[2];
cond:= arg[3];
fi;
if toc = fail then
return true;
fi;
toc:= toc.TableOfContents;
grpname:= AGR.InfoForName( name );
if grpname = fail then
Print( "#E no AtlasRep info stored for ", name, "\n" );
return false;
elif not IsBound( toc.( grpname[2] ) ) then
# This table of contents has no info for `name'.
return true;
fi;
tbl:= CharacterTable( name );
if tbl = fail then
# There is nothing to identify.
return true;
fi;
classnames:= AtlasClassNames( tbl );
ccl:= AtlasProgram( name, "classes" );
cyc:= AtlasProgram( name, "cyclic" );
if ccl <> fail then
if not IsBound( ccl.outputs ) then
Print( "#E no component `outputs' in ccl script for ", name, "\n" );
return false;
fi;
outputs1:= ccl.outputs;
std:= ccl.standardization;
prg1:= ccl.program;
cyc:= fail;
elif cyc <> fail then
if not IsBound( cyc.outputs ) then
Print( "#E no component `outputs' in cyc script for ", name, "\n" );
return false;
fi;
outputs1:= cyc.outputs;
std:= cyc.standardization;
prg1:= cyc.program;
# Form all possibilities for proper class names.
poss:= [];
for nam in outputs1 do
if nam in classnames then
Add( poss, [ nam ] );
else
# Assume that only single letters appear.
# L216d4G1-cycW1:echo "Classes 15ABCD 17EFGH 10AB 8A 12A'"
# Sz32d5G1-cycW1:echo "Classes 25A-E 31A-O 41A-J 20A-B'''' 25F-F''''"
# TD42d3G1-cycW1:echo "Classes 6B 12A 13ABC 18ABC 21ABC 28ABC 6D 12C' 12E 18D' 21D 24A 24B"
ord:= nam{ [ 1 .. PositionProperty( nam, IsAlphaChar ) - 1 ] };
if '-' in nam then
parts:= SplitString( nam{ [ Length( ord ) + 1 .. Length( nam ) ] },
"-" );
Add( poss, List( Filtered( List( CHARS_UALPHA, x -> [ x ] ),
x -> parts[1] <= x and x <= parts[2] ),
y -> Concatenation( ord, y ) ) );
else
Add( poss, List( nam{ [ Length( ord ) + 1 .. Length( nam ) ] },
y -> Concatenation( ord, [ y ] ) ) );
fi;
fi;
od;
if ForAny( poss, IsEmpty ) then
Print( "#E not all classes identified in cyc script for ",
name, "\n" );
return false;
fi;
outputs:= List( Cartesian( poss ), names -> Concatenation( [
"oup ", String( Length( names ) ), " ",
JoinStringsWithSeparator( names, " " ), "\n",
"echo \"Classes ",
JoinStringsWithSeparator( names, " " ), "\"" ] ) );
outputs:= List( outputs, prgstring ->
StringOfAtlasProgramCycToCcls( prgstring, tbl, "names" ) );
outputs:= List( outputs, x -> ScanStraightLineProgram( x, "string" ) );
prgs2:= List( outputs,
x -> rec( program:= CompositionOfStraightLinePrograms(
x.program, prg1 ),
outputs:= x.outputs ) );
else
# We have no script for computing enough class representatives.
return true;
fi;
for info in CallFuncList( AllAtlasGeneratingSetInfos,
Concatenation( [ name, std ], cond ) ) do
if IsBound( info.p ) then
# a permutation representation
p:= 0;
id:= info.identifier[2][1];
modtbl:= tbl;
fus:= [ 1 .. Length( classnames ) ];
elif Characteristic( info.ring ) = 0 then
p:= 0;
id:= info.identifier[2];
modtbl:= tbl;
fus:= [ 1 .. Length( classnames ) ];
else
p:= Characteristic( info.ring );
id:= info.identifier[2][1];
modtbl:= tbl mod p;
if modtbl <> fail then
fus:= GetFusionMap( modtbl, tbl );
else
fus:= fail;
fi;
fi;
id:= id{ [ 1 .. Position( id, '.' )-1 ] };
phi:= fail;
if fus = fail then
Print( "#I no Brauer table available for identifying ", id, "\n" );
else
gens:= AtlasGenerators( info );
if gens <> fail then
# Determine representatives of Galois orbits.
galoisfams:= GaloisMat( TransposedMat( Irr( modtbl ) ) ).galoisfams;
choice:= Filtered( [ 1 .. Length( galoisfams ) ],
i -> galoisfams[i] <> 0 );
phi:= [];
# Print( "# need ", Length( choice ), " values\n#\c" );
for i in [ 1 .. Length( choice ) ] do
pos:= fus[ choice[i] ];
if classnames[ pos ] in outputs1 then
# The character value is uniquely determined.
prgs:= [ rec( program:= prg1, outputs:= outputs1 ) ];
else
# We have to check several possibilities.
prgs:= prgs2;
fi;
for prg2 in prgs do
repprg:= RestrictOutputsOfSLP( prg2.program,
Position( prg2.outputs, classnames[ pos ] ) );
rep:= ResultOfStraightLineProgram( repprg, gens.generators );
if IsBound( info.p ) then
val:= info.p - NrMovedPoints( rep );
elif Characteristic( info.ring ) = 0 then
val:= TraceMat( rep );
else
val:= BrauerCharacterValue( rep );
fi;
if not IsBound( phi[i] ) then
phi[i]:= val;
elif phi[i] <> val then
Print( "#I representation ", id,
" yields information about class ",
classnames[ pos ], "\n" );
phi:= fail;
break;
fi;
od;
if phi = fail then
break;
fi;
# Print( i, " \c");
od;
# Print("\n# have them!\n");
if phi = fail then
Print( "#I cannot write down character for ",
gens.identifier, "\n" );
else
dec:= Decomposition( List( Irr( modtbl ), x -> x{ choice } ),
[ phi ], "nonnegative" )[1];
if dec = fail then
Print( "#I not decomposable character for ", id, ":\n",
phi, "\n" );
phi:= fail;
else
pos:= [];
for i in [ 1 .. Length( dec ) ] do
if dec[i] = 1 then
Add( pos, i );
elif 1 < dec[i] then
Add( pos, [ i, dec[i] ] );
fi;
od;
if Length( pos ) = 1 and IsInt( pos[1] ) then
pos:= pos[1];
fi;
fi;
fi;
fi;
fi;
# Check the character data stored for this representation.
map:= AtlasOfGroupRepresentationsInfo.characterinfo;
if not IsBound( map.( name ) ) then
map.( name ):= [];
fi;
map:= map.( name );
if p = 0 then
charpos:= 1;
else
charpos:= p;
fi;
if not IsBound( map[ charpos ] ) then
map[ charpos ]:= [ [], [] ];
fi;
map:= map[ charpos ];
if phi = fail then
# Test that NO character info is stored.
if id in map[2] then
Print( "#E cannot verify stored character info for ", id,
"\n" );
fi;
elif id in map[2] then
# Test that NO OTHER character info is stored.
if map[1][ Position( map[2], id ) ] <> pos then
Print( "#E stored and computed character info for `", id,
"' differ\n" );
fi;
else
nam:= AGR.CharacterNameFromMultiplicities( modtbl, pos );
if nam <> fail then
# Test whether the character name is compatible with `id'.
if IsInt( pos ) then
parsed:= AGR.ParseFilenameFormat( id,
[ [ [ IsChar ],
[ "f", IsDigitChar, "r", IsDigitChar,
AGR.IsLowerAlphaOrDigitChar,
"B", IsDigitChar, ".m", IsDigitChar ] ],
[ ParseBackwards, ParseForwards ] ] );
if ( parsed[8] = "" and
nam <> Concatenation( String( parsed[7] ), "a" ) ) or
( parsed[8] <> "" and
nam <> Concatenation( String( parsed[7] ), parsed[8] ) ) then
Print( "#E character name `", nam, "' contradicts `", id,
"'\n" );
fi;
fi;
fi;
pos:= ReplacedString( String( pos ), " ", "" );
Print( "#I add new info\n",
"AGR.CHAR(\"", name, "\",\"", id, "\",", p, ",", pos );
if nam <> fail then
Print( ",\"", nam, "\"" );
fi;
Print( ");\n" );
fi;
od;
return result;
end;
#############################################################################
##
#F AGR.PrimitivityInfo( <inforec> )
##
## <inforec> is a record as returned by `OneAtlasGeneratingSetInfo',
## for a permutation representation.
##
## - If a perm. repres. is intransitive then just compute the orbit lengths.
## - For a transitive perm. repres. of degree n, say, check primitivity:
## - If the restriction to a maximal subgroup fixes a point then
## this maximal subgroup is identified as the point stabilizer.
## - If the the degree is not an index of a maximal subgroup then we know
## that the repres. is not primitive.
## - If the restriction from G to a maximal subgroup M of G has an orbit
## of length n / [G:M] then M contains the point stabilizer; so if the
## restriction to M does not fix a point then the repres. is not
## primitive, and we know a maximal overgroup of the point stabilizer.
##
AGR.PrimitivityInfo:= function( inforec )
local gens, gapname, orbs, G, tr, rk, atlasinfo, size, indices, cand,
result, i, prg, rest, filt, tbl, max, stab, maxmax, maxcand;
gens:= AtlasGenerators( inforec );
if gens <> fail then
gens:= gens.generators;
gapname:= inforec.groupname;
# Check whether the group is transitive.
orbs:= OrbitsPerms( gens, [ 1 .. inforec.p ] );
if 1 < Length( orbs ) then
return rec( isPrimitive:= false,
transitivity:= 0,
orbitLengths:= SortedList( List( orbs, Length ) ),
comment:= "explicit computation of orbits" );
fi;
atlasinfo:= First( AtlasOfGroupRepresentationsInfo.GAPnames,
x -> x[1] = gapname );
# Compute transitivity and primitivity.
G:= Group( gens );
if IsBound( atlasinfo[3].size ) then
SetSize( G, atlasinfo[3].size );
fi;
tr:= Transitivity( G );
rk:= RankAction( G );
if IsBound( atlasinfo[3].nrMaxes ) and
IsBound( atlasinfo[3].sizesMaxes ) and
Number( atlasinfo[3].sizesMaxes ) = atlasinfo[3].nrMaxes then
size:= Size( G );
indices:= List( atlasinfo[3].sizesMaxes, x -> size / x );
cand:= Filtered( [ 1 .. Length( indices ) ],
i -> inforec.p mod indices[i] = 0 );
if inforec.p in indices and Length( cand ) = 1 then
# The point stabilizer is contained in a unique class of maxes,
# and since the degree occurs as index of a maximal subgroup,
# this representation is necessarily primitive.
# Moreover, we know the class of maximal subgroups that are
# the point stabilizers.
result:= rec( isPrimitive:= true,
transitivity:= tr,
rankAction:= rk,
class:= cand[1],
comment:= "unique class of maxes for given degree" );
if IsBound( atlasinfo[3].structureMaxes ) and
IsBound( atlasinfo[3].structureMaxes[ cand[1] ] ) then
result.structure:= atlasinfo[3].structureMaxes[ cand[1] ];
fi;
return result;
fi;
else
cand:= [ 1 .. AGR.Test.HardCases.MaxNumberMaxes ];
fi;
# Check explicit restrictions to maximal subgroups M.
# (If we know their orders then we check only those that can contain
# the point stabilizer U.)
for i in cand do
prg:= AtlasProgram( gapname, "maxes", i );
if prg <> fail then
rest:= ResultOfStraightLineProgram( prg.program, gens );
if NrMovedPoints( rest ) < inforec.p then
# If the restriction to M fixes a point then M is equal to U.
result:= rec( isPrimitive:= true,
transitivity:= tr,
rankAction:= rk,
class:= i,
comment:= "restriction fixes a point" );
if IsBound( atlasinfo[3].structureMaxes ) and
IsBound( atlasinfo[3].structureMaxes[i] ) then
result.structure:= atlasinfo[3].structureMaxes[i];
fi;
return result;
elif IsBound( atlasinfo[3].sizesMaxes ) and
IsBound( atlasinfo[3].sizesMaxes[i] ) then
if inforec.p * atlasinfo[3].sizesMaxes[i] / Size( G ) in
OrbitLengths( Group( rest ) ) then
# The length of the M-orbit of a point is equal to the quotient
# |M|/|U|, thus U is a proper subgroup of M.
result:= rec( isPrimitive:= false,
transitivity:= tr,
rankAction:= rk,
class:= i,
comment:= "restriction contains point stab." );
if IsBound( atlasinfo[3].structureMaxes ) and
IsBound( atlasinfo[3].structureMaxes[i] ) then
# We know a maximal overgroup M of the stabilizer U.
# Try to identify also U itself:
# - If U is trivial then nothing is to do.
# - If [M:U] is the index of the largest maximal subgroup of M
# then take the description of it.
# - If [M:U] = 2 and [M:M']_2 = 2 then U is the unique index
# two subgroup of M.
result.overgroup:= atlasinfo[3].structureMaxes[i];
if inforec.p = Size( G ) then
result.subgroup:= "1";
else
tbl:= CharacterTable( inforec.groupname );
if tbl <> fail then
max:= CharacterTable( result.overgroup );
if max <> fail then
if inforec.p * atlasinfo[3].sizesMaxes[i] / Size( G )
= 2 and
Length( LinearCharacters( max ) ) mod 4 = 2 then
stab:= Filtered( NamesOfFusionSources( max ),
u -> Size( CharacterTable( u ) ) = Size( max ) / 2 );
if Length( stab ) = 1 then
result.subgroup:= stab[1];
elif HasConstructionInfoCharacterTable( max ) and
[ "Cyclic", 2 ] in ConstructionInfoCharacterTable( max )[2] then
Error("!");
stab:= Difference( ConstructionInfoCharacterTable( max )[2], [ [ "Cyclic", 2 ] ] );
if Length( stab ) = 1 and Length( stab[1] ) = 1 and
IsString( stab[1][1] ) then
result.subgroup:= stab[1][1];
Print( "identify ", result.subgroup, "\n\n" );
fi;
fi;
else
maxmax:= CharacterTable( Concatenation( Identifier( max ), "M1" ) );
if maxmax <> fail and inforec.p * atlasinfo[3].sizesMaxes[i] / Size( G )
= Size( max ) / Size( maxmax ) then
result.subgroup:= Identifier( maxmax );
fi;
fi;
fi;
fi;
fi;
fi;
return result;
fi;
fi;
fi;
od;
if IsBound( atlasinfo[3].nrMaxes ) and
IsBound( atlasinfo[3].sizesMaxes ) and
Number( atlasinfo[3].sizesMaxes ) = atlasinfo[3].nrMaxes and
not inforec.p in indices then
# This representation is not primitive
# but we do not know overgroups.
return rec( isPrimitive:= false,
transitivity:= tr,
rankAction:= rk,
comment:= "degree is not an index of a max. subgroup" );
fi;
# Check explictly whether the action is primitive.
if not IsPrimitive( G, MovedPoints( G ) ) then
return rec( isPrimitive:= false,
transitivity:= tr,
rankAction:= rk,
comment:= "explicit check of primitivity" );
fi;
# Now we know that the action is primitive.
if IsBound( atlasinfo[3].nrMaxes ) and
IsBound( atlasinfo[3].sizesMaxes ) and
Number( atlasinfo[3].sizesMaxes ) = atlasinfo[3].nrMaxes then
maxcand:= Filtered( [ 1 .. Length( indices ) ],
i -> inforec.p = indices[i] );
if Length( maxcand ) = 1 then
# We know the class.
result:= rec( isPrimitive:= true,
transitivity:= tr,
rankAction:= rk,
class:= maxcand[1],
comment:=
"unique class of maxes for the given degree and prim. action" );
if IsBound( atlasinfo[3].structureMaxes ) and
IsBound( atlasinfo[3].structureMaxes[ maxcand[1] ] ) then
result.structure:= atlasinfo[3].structureMaxes[ maxcand[1] ];
fi;
return result;
fi;
fi;
fi;
# We do not know how to deal with this case.
return rec( isPrimitive:= fail );
end;
#############################################################################
##
#F AGR.Test.Primitivity( [<tocid>[, <name>]] )
##
## <#GAPDoc Label="test:AGR.Test.Primitivity">
## <Mark><C>AGR.Test.Primitivity( [<A>tocid</A>] )</C></Mark>
## <Item>
## checks the stored primitivity information for the permutation
## representations that are stored in the directory with identifier
## <A>tocid</A>.
## </Item>
## <#/GAPDoc>
##
AGR.Test.Primitivity:= function( arg )
local result, name, tocid, tblid, arec, repname, info, maxid, tbl,
maxname, res, permrepinfo, stored, str, entry;
# Initialize the result.
result:= true;
if IsEmpty( arg ) then
return AGR.Test.Primitivity( "local" );
elif Length( arg ) = 1 then
for name in AtlasOfGroupRepresentationsInfo.GAPnames do
result:= AGR.Test.Primitivity( arg[1], name[1] ) and result;
od;
return result;
elif Length( arg ) = 2 then
tocid:= arg[1];
name:= arg[2];
fi;
tblid:= fail;
if TestPackageAvailability( "CTblLib", "1.0" ) = true then
tblid:= LibInfoCharacterTable( name );
if tblid <> fail then
tblid:= tblid.firstName;
fi;
fi;
for arec in AllAtlasGeneratingSetInfos( name, "contents", tocid,
IsPermGroup, true ) do
repname:= arec.identifier[2][1];
repname:= repname{ [ 1 .. Position( repname, '.' )-1 ] };
info:= AGR.PrimitivityInfo( arec );
if IsBound( info.transitivity ) and info.transitivity = 0 then
res:= [ repname, [ 0, info.orbitLengths ] ];
elif info.isPrimitive = true then
if IsBound( info.structure ) then
res:= [ repname, [ info.transitivity, info.rankAction, "prim",
info.structure, info.class ] ];
elif IsBound( info.class ) then
if tblid <> fail then
maxid:= Concatenation( tblid, "M", String( info.class ) );
tbl:= CharacterTable( maxid );
else
tbl:= fail;
fi;
if tbl <> fail then
maxname:= AGR.StructureDescriptionCharacterTableName(
Identifier( tbl ) );
else
maxname:= "???";
fi;
res:= [ repname, [ info.transitivity, info.rankAction, "prim",
maxname, info.class ] ];
else
res:= [ repname, [ info.transitivity, info.rankAction, "prim",
"???", info.possclass ] ];
fi;
elif info.isPrimitive = false then
if IsBound( info.overgroup ) then
if IsBound( info.subgroup ) then
res:= [ repname, [ info.transitivity, info.rankAction, "imprim",
Concatenation( info.subgroup, " < ",
info.overgroup ) ] ];
else
res:= [ repname, [ info.transitivity, info.rankAction, "imprim",
Concatenation( "??? < ", info.overgroup ) ] ];
fi;
else
res:= [ repname, [ info.transitivity, info.rankAction, "imprim",
"???" ] ];
fi;
else
res:= fail;
fi;
# Compare the computed info with the stored one.
permrepinfo:= AtlasOfGroupRepresentationsInfo.permrepinfo;
if IsBound( permrepinfo.( repname ) ) then
stored:= permrepinfo.( repname );
if stored.transitivity = 0 then
str:= [ stored.transitivity, stored.orbits ];
else
str:= [ stored.transitivity, stored.rankAction,, stored.stabilizer ];
if stored.isPrimitive then
str[3]:= "prim";
str[5]:= stored.maxnr;
if '<' in stored.stabilizer then
Print( "#E prim. repres. with '<' in stabilizer string ",
"for ", repname, "?\n" );
result:= false;
fi;
else
str[3]:= "imprim";
if stored.stabilizer <> "???" and not '<' in stored.stabilizer then
Print( "#E imprim. repres. without '<' in stabilizer string ",
"for ", repname, "?\n" );
result:= false;
fi;
fi;
fi;
else
stored:= fail;
fi;
if stored = fail then
if res <> fail then
Print( "#I new AGR.API value:\n" );
if "???" in res[2] then
Print( "# " );
fi;
str:= [];
for entry in res[2] do
if IsString( entry ) then
Add( str, Concatenation( "\"", entry, "\"" ) );
else
Add( str, String( entry ) );
fi;
od;
Print( "AGR.API(\"", res[1], "\",[",
JoinStringsWithSeparator( str, "," ), "]);\n" );
fi;
elif res = fail then
Print( "#I cannot verify stored value `", str, "' for ", repname,
"\n" );
elif res[2] <> str then
# We have a computed and a stored value.
# Report an error if the two values are not compatible,
# report a difference if some part was not identified.
if Length( str ) <> Length( res[2] ) or Length( str ) = 2 or
str{ [ 1 .. 3 ] } <> res[2]{ [ 1 .. 3 ] } then
Print( "#E difference stored <-> computed for ", repname,
":\n#E ", str, " <-> ", res[2], "\n" );
result:= false;
elif 4 <= Length( str ) and res[2][4] = "???" then
Print( "#I cannot identify stabilizer `", str[4], "' for ",
repname, "\n" );
elif 4 <= Length( str ) and 6 < Length( res[2][4] ) and
res[2][4]{ [ 1 .. 6 ] } = "??? < " then
if '<' in str[4] and
str[4]{ [ Position( str[4], '<' ) .. Length( str[4] ) ] }
= res[2][4]{ [ Position( res[2][4], '<' )
.. Length( res[2][4] ) ] } then
Print( "#I cannot identify subgroup in stabilizer `", str[4],
"' for ", repname, "\n" );
else
Print( "#E difference stored <-> computed for ", repname,
":\n#E ", str, " <-> ", res[2], "\n" );
result:= false;
fi;
else
Print( "#E difference stored <-> computed for ", repname,
":\n#E ", str, " <-> ", res[2], "\n" );
result:= false;
fi;
fi;
od;
return result;
end;
#############################################################################
##
#F AGR.Test.MinimalDegrees( [<verbose>] )
##
## <#GAPDoc Label="test:AGR.Test.MinimalDegrees">
## <Mark><C>AGR.Test.MinimalDegrees()</C></Mark>
## <Item>
## checks that the (permutation and matrix) representations available in
## the &ATLAS; of Group Representations do not have smaller degree than
## the claimed minimum.
## </Item>
## <#/GAPDoc>
##
AGR.Test.MinimalDegrees:= function( arg )
local result, verbose, info, grpname, known, knownzero, deg, mindeg,
knownfinite, chars_and_sizes, size, p, knowncharp, q, knownsizeq;
result:= true;
verbose:= ( Length( arg ) <> 0 );
for info in AtlasOfGroupRepresentationsInfo.GAPnames do
grpname:= info[1];
# Check permutation representations.
known:= AllAtlasGeneratingSetInfos( grpname, IsPermGroup, true );
if not IsEmpty( known ) then
deg:= Minimum( List( known, r -> r.p ) );
mindeg:= MinimalRepresentationInfo( grpname, NrMovedPoints,
"lookup" );
if mindeg = fail then
if verbose then
Print( "#I `", grpname, "': degree ", deg,
" perm. repr. known but no minimality info stored\n" );
fi;
elif deg < mindeg.value then
Print( "#E `", grpname, "': smaller perm. repr. (", deg,
") than minimal degree (", mindeg.value, ")\n" );
result:= false;
fi;
fi;
# Check matrix representations over fields in characteristic zero.
known:= AllAtlasGeneratingSetInfos( grpname, Ring, IsField );
knownzero:= Filtered( known,
r -> IsBound( r.ring ) and not IsFinite( r.ring ) );
if not IsEmpty( knownzero ) then
deg:= Minimum( List( knownzero, r -> r.dim ) );
mindeg:= MinimalRepresentationInfo( grpname, Characteristic, 0,
"lookup" );
if mindeg = fail then
if verbose then
Print( "#I `", grpname, "': degree ", deg, " char. 0 ",
"matrix repr. known but no minimality info stored\n" );
fi;
elif deg < mindeg.value then
Print( "#E `", grpname, "': smaller char. 0 matrix repr. (", deg,
") than minimal degree (", mindeg.value, ")\n" );
result:= false;
fi;
fi;
# Check matrix representations over finite fields.
knownfinite:= Filtered( known, r -> IsFinite( r.ring ) );
chars_and_sizes:= [];
for size in Set( List( knownfinite, r -> Size( r.ring ) ) ) do
p:= SmallestRootInt( size );
info:= First( chars_and_sizes, pair -> pair[1] = p );
if info = fail then
Add( chars_and_sizes, [ p, [ size ] ] );
else
Add( info[2], size );
fi;
od;
for info in chars_and_sizes do
p:= info[1];
knowncharp:= Filtered( knownfinite,
r -> Characteristic( r.ring ) = p );
deg:= Minimum( List( knowncharp, r -> r.dim ) );
mindeg:= MinimalRepresentationInfo( grpname, Characteristic, p,
"lookup" );
if mindeg = fail then
if verbose then
Print( "#I `", grpname, "': degree ", deg, " char. ", p,
" matrix repr. known but no minimality info stored\n" );
fi;
elif deg < mindeg.value then
Print( "#E `", grpname, "': smaller char. ", p, " matrix repr. (",
deg, ") than minimal degree (", mindeg.value, ")\n" );
result:= false;
fi;
for q in info[2] do
knownsizeq:= Filtered( knownfinite,
r -> Size( r.ring ) = q );
deg:= Minimum( List( knownsizeq, r -> r.dim ) );
mindeg:= MinimalRepresentationInfo( grpname, Size, q,
"lookup" );
if mindeg = fail then
if verbose then
Print( "#I `", grpname, "': degree ", deg, " size ", q,
" matrix repr. known but no minimality info stored\n" );
fi;
elif deg < mindeg.value then
Print( "#E `", grpname, "': smaller size ", q,
" matrix repr. (", deg, ") than minimal degree (",
mindeg.value, ")\n" );
result:= false;
fi;
od;
od;
od;
return result;
end;
if not IsPackageMarkedForLoading( "TomLib", "" ) then
Unbind( HasStandardGeneratorsInfo );
Unbind( IsStandardGeneratorsOfGroup );
Unbind( LIBTOMKNOWN );
Unbind( StandardGeneratorsInfo );
fi;
if not IsPackageMarkedForLoading( "CTblLib", "" ) then
Unbind( ConstructionInfoCharacterTable );
Unbind( HasConstructionInfoCharacterTable );
Unbind( LibInfoCharacterTable );
fi;
#############################################################################
##
#E
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