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#############################################################################
##
#W interfac.gi GAP 4 package AtlasRep Thomas Breuer
##
## This file contains the implementation part of the ''high level'' GAP
## interface to the ATLAS of Group Representations.
##
#############################################################################
##
#F AGR.Pager( <string> )
##
## Simply calling 'Pager' is not good enough, because GAP introduces
## line breaks in too long lines, and GAP does not compute the printable
## length of the line but the length as a string.
##
## If <string> is empty then the builtin pager runs into an error,
## therefore we catch this case.
##
AGR.Pager:= function( string )
if string <> "" then
Pager( rec( lines:= string, formatted:= true ) );
fi;
end;
#############################################################################
##
#F AGR.ShowOnlyASCII()
##
## Show nicer grids and symbols such as ℤ if the terminal admits this.
## Currently we do *not* do this if 'Print' is used to show the data,
## because of the automatically inserted line breaks.
##
AGR.ShowOnlyASCII:= function()
return UserPreference( "AtlasRep", "DisplayFunction" ) = "Print" or
GAPInfo.TermEncoding <> "UTF-8";
end;
#############################################################################
##
#F AGR.StringAtlasInfoOverview( <gapnames>, <conditions> )
##
AGR.StringAtlasInfoOverview:= function( gapnames, conditions )
local rep_rest_funs, only_if_rep, columns, len, type, widths, choice, i,
j, fstring, result, mid;
# Consider only those names for which actually information is available.
# (The ordering shall be the same as in the input.)
if gapnames = "all" then
gapnames:= AtlasOfGroupRepresentationsInfo.GAPnamesSortDisp;
else
gapnames:= Filtered( List( gapnames, AGR.InfoForName ),
x -> x <> fail );
fi;
if IsEmpty( gapnames ) then
return [];
fi;
# If 'conditions' restricts the representations then omit rows
# with empty representations part.
rep_rest_funs:= [ Characteristic, Dimension, Identifier, IsMatrixGroup,
IsPermGroup, IsPrimitive, IsTransitive, NrMovedPoints,
RankAction, Ring, Transitivity ];
only_if_rep:= ForAny( conditions, x -> x in rep_rest_funs );
# Compute the data of the columns.
columns:= [ [ "group", "l", List( gapnames, x -> [ x[1], false ] ) ] ];
len:= 0;
for type in AGR.DataTypes( "rep", "prg" ) do
if type[2].DisplayOverviewInfo <> fail then
Add( columns, [
type[2].DisplayOverviewInfo[1],
type[2].DisplayOverviewInfo[2],
List( gapnames,
n -> type[2].DisplayOverviewInfo[3](
Concatenation( [ n ], conditions ) ) ) ] );
if only_if_rep then
if type[3] = "rep" then
len:= Length( columns );
fi;
else
len:= Length( columns );
fi;
fi;
od;
# Initialize the column widths; the header string shall fit.
widths:= List( columns, c -> [ Length( c[1] ), c[2] ] );
# Restrict the lists to the nonempty rows.
choice:= [];
for i in [ 1 .. Length( gapnames ) ] do
if ForAny( [ 2 .. len ],
c -> columns[c][3][i][1] <> "" ) then
Add( choice, i );
# Evaluate the privacy flag.
if ForAny( columns, x -> x[3][i][2] ) then
columns[1][3][i][1]:= Concatenation( columns[1][3][i][1],
UserPreference( "AtlasRep", "AtlasRepMarkNonCoreData" ) );
fi;
for j in [ 1 .. Length( columns ) ] do
widths[j][1]:= Maximum( widths[j][1],
Length( columns[j][3][i][1] ) );
od;
fi;
od;
if IsEmpty( choice ) then
return [];
fi;
fstring:= function( string, width )
local strwidth, n, n1, n2;
strwidth:= WidthUTF8String( string );
if width[1] <= strwidth then
return string;
elif width[2] = "l" then
return Concatenation( string,
RepeatedString( ' ', width[1] - strwidth ) );
elif width[2] = "r" then
return Concatenation( RepeatedString( ' ', width[1] - strwidth ),
string );
else
n:= RepeatedString( ' ', width[1] - strwidth );
n1:= n{ [ QuoInt( Length( n ), 2 ) + 1 .. Length( n ) ] };
n2:= n{ [ 1 .. QuoInt( Length( n ), 2 ) ] };
return Concatenation( n1, string, n2 );
fi;
end;
result:= [];
# Add the header line.
if AGR.ShowOnlyASCII() then
mid:= " | ";
else
mid:= " │ ";
fi;
Add( result, JoinStringsWithSeparator( List( [ 1 .. Length( columns ) ],
j -> fstring( columns[j][1], widths[j] ) ), mid ) );
if AGR.ShowOnlyASCII() then
Add( result, JoinStringsWithSeparator( List( [ 1 .. Length( columns ) ],
j -> RepeatedString( "-", widths[j][1] ) ), "-+-" ) );
else
Add( result, JoinStringsWithSeparator( List( [ 1 .. Length( columns ) ],
j -> RepeatedUTF8String( "─", widths[j][1] ) ), "─┼─" ) );
fi;
# Add the information for each group.
for i in choice do
Add( result, JoinStringsWithSeparator( List( [ 1 .. Length( columns ) ],
j -> fstring( columns[j][3][i][1], widths[j] ) ), mid ) );
od;
return result;
end;
#############################################################################
##
#F AGR.StringAtlasInfoContents()
##
AGR.StringAtlasInfoContents:= function()
local datadir, result, mid, dir, header, table, info, n, path, subdir,
dstfile, prefix, ncols, widths, i, row, sep;
# general information
datadir:= UserPreference( "AtlasRep", "AtlasRepDataDirectory" );
if datadir = "" then
datadir:= "(no local caches available)";
fi;
result:= [];
Add( result, Concatenation( "- AtlasRepAccessRemoteFiles: ",
String( UserPreference( "AtlasRep",
"AtlasRepAccessRemoteFiles" ) ), "\n" ) );
Add( result, Concatenation( "- AtlasRepDataDirectory: ", datadir, "\n" ) );
# information per part of the database
if AGR.ShowOnlyASCII() then
mid:= " | ";
else
mid:= " │ ";
fi;
dir:= Directory( datadir );
header:= [ "ID", mid, "address, version, files" ];
table:= [];
for info in AtlasOfGroupRepresentationsInfo.notified do
n:= 0;
if info.ID = "core" then
path:= Filename( dir, "datagens" );
if IsDirectoryPath( path ) then
n:= n + Length( Difference( DirectoryContents( path ),
[ ".", "..", "dummy" ] ) );
fi;
path:= Filename( dir, "dataword" );
if IsDirectoryPath( path ) then
n:= n + Length( Difference( DirectoryContents( path ),
[ ".", "..", "dummy" ] ) );
fi;
elif StartsWith( info.DataURL, "http" ) then
# remote data extension
path:= Filename( dir, Concatenation( "dataext/", info.ID ) );
if IsDirectoryPath( path ) then
n:= n + Length( Difference( DirectoryContents( path ),
[ ".", "..", "toc.json" ] ) );
fi;
else
# local data extension (perhaps with one intermediate directory level)
path:= info.DataURL;
if IsDirectoryPath( path ) then
path:= Directory( path );
for subdir in Difference( DirectoryContents( path ),
[ ".", "..", "toc.json" ] ) do
dstfile:= Filename( path, subdir );
if IsDirectoryPath( dstfile ) then
n:= n + Length( Difference( DirectoryContents( dstfile ),
[ ".", ".." ] ) );
else
n:= n + 1;
fi;
od;
fi;
fi;
path:= info.DataURL;
if not StartsWith( path, "http" ) then
prefix:= First( List( DirectoriesLibrary( "pkg" ),
d -> Filename( d, "" ) ),
str -> StartsWith( path, str ) );
if prefix <> fail then
path:= ReplacedString( path, prefix, "" );
fi;
fi;
Add( table, [ info.ID, mid, Concatenation( path, "," ) ] );
if IsBound( info.Version ) then
Add( table, [ "", mid, Concatenation( "version ", info.Version,
"," ) ] );
fi;
Add( table, [ "", mid, Concatenation( String( n ),
" files locally available." ) ] );
od;
ncols:= Length( header );
widths:= List( header, Length );
for row in table do
for i in [ 1 .. ncols ] do
widths[i]:= Maximum( widths[i], WidthUTF8String( row[i] ) );
od;
od;
for i in [ 1, 3 ] do
widths[i]:= -widths[i];
od;
Add( result, Concatenation( List( [ 1 .. ncols ],
i -> String( header[i], widths[i] ) ) ) );
if AGR.ShowOnlyASCII() then
sep:= JoinStringsWithSeparator( List( [ 1, 3 .. ncols ],
j -> RepeatedString( "-", AbsInt( widths[j] ) ) ), "-+-" );
else
sep:= JoinStringsWithSeparator( List( [ 1, 3 .. ncols ],
j -> RepeatedUTF8String( "─", AbsInt( widths[j] ) ) ), "─┼─" );
fi;
for row in table do
if row[1] <> "" then
Add( result, sep );
fi;
Add( result,
Concatenation( List( [ 1 .. ncols ],
i -> String( row[i], widths[i] ) ) ) );
od;
return result;
end;
#############################################################################
##
#F AGR.InfoPrgs( <conditions> )
##
AGR.InfoPrgs:= function( conditions )
local gapname, groupname, name, tocs, std, argpos, stdavail, toc, record,
type, list, header, nams, sort, info, pi;
gapname:= conditions[1];
groupname:= AGR.InfoForName( gapname );
if groupname = fail then
return rec( list:= [] );
fi;
conditions:= conditions{ [ 2 .. Length( conditions ) ] };
name:= groupname[2];
tocs:= AGR.TablesOfContents( conditions );
if Length( conditions ) = 0 or
not ( IsInt( conditions[1] ) or IsList( conditions[1] ) ) then
std:= true;
argpos:= 1;
else
std:= conditions[1];
if IsInt( std ) then
std:= [ std ];
fi;
argpos:= 2;
fi;
# If the standardization is prescribed then do not mention it.
# Otherwise if all information refers to the same standardization then
# print just one line.
# Otherwise print the standardization for each entry.
stdavail:= [];
if std = true or 1 < Length( std ) then
for toc in tocs do
if IsBound( toc.( name ) ) then
record:= toc.( name );
for type in AGR.DataTypes( "prg" ) do
if IsBound( record.( type[1] ) ) then
for list in record.( type[1] ) do
if std = true or list[1] in std then
AddSet( stdavail, list[1] );
fi;
od;
fi;
od;
fi;
od;
fi;
# Create the header line.
# (Because of 'AGR.CreateHTMLInfoForGroup',
# the group name must occur as an entry of its own .)
header:= [ "Programs for G = ", groupname[1], ":" ];
if Length( stdavail ) = 1 then
Append( header, [ " (all refer to std. generators ",
String( stdavail[1] ), ")" ] );
fi;
# Collect the info lines for the scripts.
list:= [];
nams:= [];
sort:= [];
if ( Length( conditions ) = argpos and
conditions[ argpos ] = IsStraightLineProgram )
or ( Length( conditions ) = argpos + 1
and conditions[ argpos ] = IsStraightLineProgram
and conditions[ argpos + 1 ] = true )
or Length( conditions ) < argpos then
for type in AGR.DataTypes( "prg" ) do
info:= type[2].DisplayPRG( tocs, [ gapname, groupname[2] ], std,
stdavail );
Add( list, info );
if IsEmpty( info ) then
Add( sort, [ 0 ] );
elif IsString( info[2] ) then
Add( sort, [ 0, info[1] ] );
else
Add( sort, [ 1, info[1] ] );
fi;
Add( nams, type[1] );
od;
fi;
# Sort the information such that those come first for which a single
# line is given.
# (This is because 'BrowseAtlasInfo' turns the parts with more than
# one line into a subcategory which is created from the first line.)
# Inside this ordering of entries, sort the information alphabetically.
pi:= Sortex( sort );
return rec( header := header,
list := Permuted( list, pi ),
nams := Permuted( nams, pi ) );
end;
#############################################################################
##
#F AGR.EvaluateMinimalityCondition( <gapname>, <conditions> )
##
## Evaluate conditions involving '"minimal"':
## Replace the string '"minimal"' by the number in question if known,
## return 'true' in this case and 'false' otherwise.
## (In the 'false' case, an info message is printed.)
##
AGR.EvaluateMinimalityCondition:= function( gapname, conditions )
local pos, info, pos2;
pos:= Position( conditions, "minimal" );
if pos <> fail and pos <> 1 then
if IsIdenticalObj( conditions[ pos-1 ], NrMovedPoints ) then
# ..., NrMovedPoints, "minimal", ...
info:= MinimalRepresentationInfo( gapname, NrMovedPoints );
if info = fail then
Info( InfoAtlasRep, 1,
"minimal perm. repr. of '", gapname, "' not known" );
return false;
fi;
conditions[ pos ]:= info.value;
elif IsIdenticalObj( conditions[ pos-1 ], Dimension ) then
pos2:= Position( conditions, Characteristic );
if pos2 <> fail and pos2 < Length( conditions ) then
# ..., Characteristic, <p>, ..., Dimension, "minimal", ...
info:= MinimalRepresentationInfo( gapname,
Characteristic, conditions[ pos2+1 ] );
if info = fail then
Info( InfoAtlasRep, 1,
"minimal matrix repr. of '", gapname,
"' in characteristic ", conditions[ pos2+1 ],
" not known" );
return false;
fi;
conditions[ pos ]:= info.value;
else
pos2:= Position( conditions, Ring );
if pos2 <> fail and pos2 < Length( conditions )
and IsField( conditions[ pos2+1 ] )
and IsFinite( conditions[ pos2+1 ] ) then
# ..., Ring, <R>, ..., Dimension, "minimal", ...
info:= MinimalRepresentationInfo( gapname,
Size, Size( conditions[ pos2+1 ] ) );
if info = fail then
Info( InfoAtlasRep, 1,
"minimal matrix repr. of '", gapname,
"' over '", conditions[ pos2+1 ], "' not known" );
return false;
fi;
conditions[ pos ]:= info.value;
fi;
fi;
fi;
fi;
return true;
end;
#############################################################################
##
#F AGR.InfoReps( <conditions> )
##
## This function is used by 'AGR.StringAtlasInfoGroup' and
## 'BrowseData.AtlasRepGroupInfoTable'.
##
AGR.InfoReps:= function( conditions )
local info, stdavail, header, list, types, r, type, entry;
info:= CallFuncList( AllAtlasGeneratingSetInfos, conditions );
# If all information refers to the same standardization then
# print just one line.
# Otherwise print the standardization for each entry.
stdavail:= Set( List( info, x -> x.standardization ) );
# Construct the header line.
# (Because of 'AGR.CreateHTMLInfoForGroup',
# 'gapname' must occur as an entry of its own .)
header:= [ "Representations for G = ", AGR.GAPName( conditions[1] ),
":" ];
if Length( stdavail ) = 1 then
Add( header, Concatenation(
" (all refer to std. generators ", String( stdavail[1] ),
")" ) );
fi;
list:= [];
types:= AGR.DataTypes( "rep" );
for r in info do
type:= First( types, t -> t[1] = r.type );
entry:= type[2].DisplayGroup( r );
if IsString( entry ) then
entry:= [ entry ];
fi;
entry:= [ [ String( r.repnr ), ":" ], [ entry[1], "" ],
entry{ [ 2 .. Length( entry ) ] } ];
if not ( IsString( r.identifier[2] ) or
ForAll( r.identifier[2], IsString ) ) then
entry[2][2]:= UserPreference( "AtlasRep", "AtlasRepMarkNonCoreData" );
fi;
if 1 < Length( stdavail ) then
Add( entry, [ ", w.r.t. std. gen. ", String( r.standardization ) ] );
fi;
Add( list, entry );
od;
return rec( header := header,
list := list );
end;
#############################################################################
##
#F AGR.StringAtlasInfoGroup( <conditions> )
##
## Deal with the detailed overview for one group.
##
AGR.StringAtlasInfoGroup:= function( conditions )
local result, screenwidth, inforeps, list, line, len1, len2, indent,
underline, bullet, bulletlength, i, prefix, entry, infoprgs, j,
colsep;
result:= [];
screenwidth:= SizeScreen()[1] - 1;
# 'DisplayAtlasInfo( <gapname>[, <std>][, <conditions>] )'
inforeps:= AGR.InfoReps( conditions );
if not IsEmpty( inforeps.list ) then
list:= List( inforeps.list, line -> Concatenation(
[ Concatenation( line[1] ), Concatenation( line[2] ) ],
Concatenation( line{ [ 3 .. Length( line ) ] } ) ) );
len1:= Maximum( List( list, x -> WidthUTF8String( x[1] ) ) );
len2:= Maximum( List( list, x -> WidthUTF8String( x[2] ) ) );
indent:= 0;
line:= Concatenation( inforeps.header{ [ 1 .. 3 ] } );
if AGR.ShowOnlyASCII() then
underline:= RepeatedString( "-", Sum( List(
inforeps.header{ [ 1 .. 3 ] }, Length ) ) );
else
underline:= RepeatedUTF8String( "─", Sum( List(
inforeps.header{ [ 1 .. 3 ] }, Length ) ) );
fi;
for i in [ 4 .. Length( inforeps.header ) ] do
if WidthUTF8String( line ) + WidthUTF8String( inforeps.header[i] )
>= screenwidth
and WidthUTF8String( line ) <> indent then
Add( result, line );
Add( result, underline );
underline:= "";
line:= "";
fi;
Append( line, inforeps.header[i] );
od;
if line <> "" then
Add( result, line );
fi;
if underline <> "" then
Add( result, underline );
fi;
indent:= len1 + len2 + 2;
if indent >= screenwidth then
indent:= 1;
fi;
prefix:= RepeatedString( " ", indent );
for entry in list do
# right-aligned number, left-aligned description
line:= Concatenation( String( entry[1], len1 ), " ",
entry[2],
RepeatedString( " ", len2
- WidthUTF8String( entry[2] ) ),
" " );
for i in [ 3 .. Length( entry ) ] do
if WidthUTF8String( line ) + WidthUTF8String( entry[i] )
>= screenwidth
and Length( line ) <> indent then
Add( result, line );
line:= ShallowCopy( prefix );
fi;
Append( line, entry[i] );
od;
Add( result, line );
od;
fi;
# 'DisplayAtlasInfo( <gapname>[, <std>][, IsStraightLineProgram] )'
infoprgs:= AGR.InfoPrgs( conditions );
if ForAny( infoprgs.list, x -> not IsEmpty( x ) ) then
if IsBound( inforeps ) and not IsEmpty( inforeps.list ) then
Add( result, "" );
fi;
indent:= 0;
# Format the header.
line:= Concatenation( infoprgs.header{ [ 1 .. 3 ] } );
if AGR.ShowOnlyASCII() then
underline:= RepeatedString( "-", Sum( List(
infoprgs.header{ [ 1 .. 3 ] }, Length ) ) );
bullet:= "- ";
else
underline:= RepeatedUTF8String( "─", Sum( List(
infoprgs.header{ [ 1 .. 3 ] }, Length ) ) );
bullet:= "• ";
fi;
bulletlength:= 2;
for i in [ 4 .. Length( infoprgs.header ) ] do
if WidthUTF8String( line ) + WidthUTF8String( infoprgs.header[i] )
>= screenwidth
and WidthUTF8String( line ) <> indent then
Add( result, line );
Add( result, underline );
underline:= "";
line:= "";
fi;
Append( line, infoprgs.header[i] );
od;
if line <> "" then
Add( result, line );
fi;
if underline <> "" then
Add( result, underline );
fi;
# Format the info list. Each entry is a list of the following type:
# - empty or
# - consists of two strings (corresponding to table columns),
# plus a program identifier, or
# - has a string at position 1
# and non-string lists of length 3 at the other positions,
# each representing the columns of a table row,
# plus a program identifier.
len1:= 0;
len2:= 0;
for i in infoprgs.list do
if not IsEmpty( i ) then
if IsString( i[2] ) then
# This happens if only one program is available,
# and if the type is not "automorphisms", "kernels", or "maxes".
len1:= Maximum( len1, WidthUTF8String( i[1] ) );
if Length( i ) = 2 then
len2:= Maximum( len2, WidthUTF8String( i[2] ) );
fi;
else
# This happens for "automorphisms", "kernels", and "maxes",
# and whenever more than one program is available for a type.
len1:= Maximum( len1, WidthUTF8String( i[1] ) + 1 );
for j in [ 2 .. Length( i ) ] do
len1:= Maximum( len1, WidthUTF8String( i[j][1] ) );
len2:= Maximum( len2, WidthUTF8String( i[j][2] ) );
od;
fi;
fi;
od;
# The two columns shall be left aligned.
len1:= -len1;
len2:= -len2;
colsep:= " ";
indent:= RepeatedString( " ", bulletlength );
for i in infoprgs.list do
if not IsEmpty( i ) then
if IsString( i[2] ) then
Add( result, Concatenation( bullet,
String( i[1], len1 ),
colsep,
String( i[2], len2 ) ) );
else
Add( result, Concatenation( bullet, i[1], ":" ) );
for j in [ 2 .. Length( i ) ] do
Add( result, Concatenation( indent,
String( i[j][1], len1 ),
colsep,
String( i[j][2], len2 ) ) );
od;
fi;
fi;
od;
fi;
return result;
end;
#############################################################################
##
#F DisplayAtlasInfo( [<listofnames>][,][<std>][,]["contents", <sources>]
#F [, IsPermGroup[, true]]
#F [, NrMovedPoints, <n>]
#F [, IsTransitive[, <bool>]]
#F [, Transitivty[, <n>]]
#F [, IsPrimitive[, <bool>]]
#F [, RankAction[, <n>]]
#F [, IsMatrixGroup[, true]]
#F [, Characteristic, <p>][, Dimension, <n>]
#F [, Ring, <R>]
#F [, Position, <n>]
#F [, Character, <chi>]
#F [, Identifier, <id>] )
#F DisplayAtlasInfo( <gapname>[, <std>][, "contents", <sources>]
#F [, IsPermGroup[, true]]
#F [, NrMovedPoints, <n>]
#F [, IsTransitive[, <bool>]]
#F [, Transitivty[, <n>]]
#F [, IsPrimitive[, <bool>]]
#F [, RankAction[, <n>]]
#F [, IsMatrixGroup[, true]]
#F [, Characteristic, <p>][, Dimension, <n>]
#F [, Ring, <R>]
#F [, Position, <n>]
#F [, Character, <chi>]
#F [, Identifier, <id>]
#F [, IsStraightLineProgram[, true]] )
#F DisplayAtlasInfo( "contents" )
##
#T support DisplayAtlasInfo( <tbl> ) for a character table <tbl>
#T with admissible Identifier value
##
InstallGlobalFunction( DisplayAtlasInfo, function( arg )
local result, width, fun;
# Distinguish the summary overview for at least one group
# from the detailed overview for exactly one group.
if Length( arg ) = 0 then
result:= AGR.StringAtlasInfoOverview( "all", arg );
elif Length( arg ) = 1 and arg[1] = "contents" then
result:= AGR.StringAtlasInfoContents();
elif IsList( arg[1] ) and ForAll( arg[1], IsString ) then
result:= AGR.StringAtlasInfoOverview( arg[1],
arg{ [ 2 .. Length( arg ) ] } );
elif not IsString( arg[1] ) or arg[1] = "contents" then
result:= AGR.StringAtlasInfoOverview( "all", arg );
else
result:= AGR.StringAtlasInfoGroup( arg );
fi;
width:= SizeScreen()[1] - 2;
if AGR.ShowOnlyASCII() then
result:= List( result,
l -> InitialSubstringUTF8String( l, width, "*" ) );
else
result:= List( result,
l -> InitialSubstringUTF8String( l, width, "⋯" ) );
fi;
Add( result, "" );
fun:= EvalString( UserPreference( "AtlasRep", "DisplayFunction" ) );
fun( JoinStringsWithSeparator( result, "\n" ) );
end );
#############################################################################
##
#F AtlasGenerators( <gapname>, <repnr>[, <maxnr>] )
#F AtlasGenerators( <identifier> )
#F AtlasGenerators( <inforecord> )
##
## <identifier> is a list containing at the first position the string
## <gapname>,
## at the second position a string or a list of strings
## (describing filenames),
## at the third position a positive integer denoting the standardization of
## the representation,
## at the fourth position a positive integer describing the common ring of
## the generators,
## and at the fifth position, if bound, a positive integer denoting the
## number of the maximal subgroup to which the representation is restricted.
##
InstallGlobalFunction( AtlasGenerators, function( arg )
local identifier, gapname, id, maxnr, rep, repnr, reps, prog, filenames,
i, groupname, type, gens, result;
if Length( arg ) = 1 then
# 'AtlasGenerators( <identifier> )'
identifier:= arg[1];
if IsRecord( identifier ) and IsBound( identifier.identifier ) then
identifier:= identifier.identifier;
fi;
gapname:= identifier[1];
id:= identifier;
if IsBound( identifier[5] ) then
maxnr:= identifier[5];
id:= identifier{ [ 1 .. 4 ] };
fi;
rep:= First( AGR.MergedTableOfContents( "all", gapname ),
r -> r.identifier = id );
elif ( Length( arg ) = 2 and IsString( arg[1] ) and IsPosInt( arg[2] ) )
or ( Length( arg ) = 3 and IsString( arg[1] ) and IsPosInt( arg[2] )
and IsPosInt( arg[3] ) ) then
# 'AtlasGenerators( <gapname>, <repnr>[, <maxnr>] )'
gapname:= arg[1];
repnr:= arg[2];
reps:= AGR.MergedTableOfContents( "all", gapname );
rep:= First( reps, r -> r.repnr = repnr );
if rep = fail then
return fail;
fi;
identifier:= ShallowCopy( rep.identifier );
if IsBound( arg[3] ) then
maxnr:= arg[3];
identifier[5]:= maxnr;
fi;
else
Error( "usage: AtlasGenerators( <gapname>,<repnr>[,<maxnr>] ) or\n",
" AtlasGenerators( <identifier> )" );
fi;
# If the restriction to a subgroup is required then
# try to fetch the program (w.r.t. the correct standardization)
# *before* reading the generators;
# if we do not get the program then the generators are not needed.
if IsBound( maxnr ) then
prog:= AtlasProgram( gapname, identifier[3], maxnr );
if prog = fail then
return fail;
fi;
fi;
filenames:= identifier[2];
if IsString( filenames ) then
filenames:= [ [ "datagens", filenames ] ];
else
filenames:= ShallowCopy( filenames );
for i in [ 1 .. Length( filenames ) ] do
if IsString( filenames[i] ) then
filenames[i]:= [ "datagens", filenames[i] ];
fi;
od;
fi;
# Access the data file(s).
groupname:= AGR.InfoForName( gapname );
if groupname = fail then
Info( InfoAtlasRep, 1,
"AtlasGenerators: no group with GAP name '", gapname, "'" );
return fail;
fi;
type:= First( AGR.DataTypes( "rep" ), l -> l[1] = rep.type );
if IsRecord( arg[1] ) then
PushOptions( rec( inforecord:= arg[1] ) );
fi;
gens:= AGR.FileContents( filenames, type );
if IsRecord( arg[1] ) then
PopOptions();
fi;
if gens = fail then
return fail;
fi;
result:= ShallowCopy( rep );
if IsRecord( arg[1] ) then
if IsBound( arg[1].givenRing ) then
result.givenRing:= arg[1].givenRing;
fi;
if IsBound( arg[1].constructingFilter ) then
result.constructingFilter:= arg[1].constructingFilter;
fi;
fi;
if IsBound( maxnr ) then
result.identifier:= identifier;
# Evaluate the straight line program.
result.generators:= ResultOfStraightLineProgram( prog.program, gens );
# Add/adjust info.
if IsBound( groupname[3].sizesMaxes )
and IsBound( groupname[3].sizesMaxes[ maxnr ] ) then
result.size:= groupname[3].sizesMaxes[ maxnr ];
fi;
if IsBound( groupname[3].structureMaxes )
and IsBound( groupname[3].structureMaxes[ maxnr ] ) then
result.groupname:= groupname[3].structureMaxes[ maxnr ];
fi;
else
result.generators:= gens;
fi;
# Return the result.
return Immutable( result );
end );
#############################################################################
##
#F AGR.MergedTableOfContents( <tocid>, <gapname> )
##
## 'AGR.MergedTableOfContents' returns a list of the known representations
## for the group with name <gapname>.
## This list is sorted by types and for each type by its 'SortTOCEntries'
## function.
## The list is cached in the component <gapname> of the global record
## 'AtlasOfGroupRepresentationsInfo.TableOfContents.merged'.
## When a new table of contents is notified with
## 'AtlasOfGroupRepresentationsNotifyPrivateDirectory' then the cache is
## cleared.
##
AGR.MergedTableOfContents:= function( tocid, gapname )
local merged, label, groupname, result, tocs, type, typeresult, sortkeys,
toc, record, id, i, repname, oneresult, types, r, loc;
merged:= AtlasOfGroupRepresentationsInfo.TableOfContents.merged;
if IsString( tocid ) then
tocid:= [ tocid ];
fi;
label:= Concatenation( JoinStringsWithSeparator( tocid, "|" ),
"|", gapname );
if IsBound( merged.( label ) ) then
return merged.( label );
fi;
groupname:= AGR.InfoForName( gapname );
if groupname = fail then
return [];
elif tocid = [ "all" ] then
result:= [];
# collect all representations, sort them for each type.
tocs:= AGR.TablesOfContents( [ "contents", "all" ] );
for type in AGR.DataTypes( "rep" ) do
typeresult:= [];
sortkeys:= [];
for toc in tocs do
if IsBound( toc.( groupname[2] ) ) then
record:= toc.( groupname[2] );
if IsBound( record.( type[1] ) ) then
for i in record.( type[1] ) do
repname:= i[ Length(i) ];
if not IsString( repname ) then
repname:= repname[1];
fi;
repname:= repname{ [ 1 .. Position( repname, '.' )-1 ] };
id:= i[ Length(i) ];
if toc.TocID <> "core" then
if IsString( id ) then
id:= [ [ toc.TocID, id ] ];
else
id:= List( id, x -> [ toc.TocID, x ] );
fi;
fi;
oneresult:= rec( groupname := gapname,
identifier := [ gapname, id,
i[1], i[2] ],
repname := repname,
standardization := i[1],
type := type[1],
contents := toc.TocID );
type[2].AddDescribingComponents( oneresult, type );
Add( typeresult, oneresult );
Add( sortkeys, type[2].SortTOCEntries( i ) );
od;
fi;
fi;
od;
SortParallel( sortkeys, typeresult );
Append( result, typeresult );
od;
if IsBound( groupname[3].size ) then
for i in result do
i.size:= groupname[3].size;
od;
fi;
for i in [ 1 .. Length( result ) ] do
result[i].repnr:= i;
od;
elif tocid = [ "local" ] then
types:= AGR.DataTypes( "rep" );
result:= [];
for r in AGR.MergedTableOfContents( "all", gapname ) do
type:= First( types, x -> x[1] = r.type );
if r.contents <> "core" then
loc:= AtlasOfGroupRepresentationsLocalFilename(
r.identifier[2], type );
elif IsString( r.identifier[2] ) then
loc:= AtlasOfGroupRepresentationsLocalFilename(
[ [ "datagens", r.identifier[2] ] ], type );
else
loc:= AtlasOfGroupRepresentationsLocalFilename(
List( r.identifier[2], x -> [ "datagens", x ] ), type );
fi;
if not IsEmpty( loc ) and ForAll( loc[1][2], x -> x[2] ) then
Add( result, r );
fi;
od;
else
# Now we know that we have to filter a list which we can compute.
if "local" in tocid then
result:= AGR.MergedTableOfContents( "local", gapname );
else
result:= AGR.MergedTableOfContents( "all", gapname );
fi;
tocid:= Difference( tocid, [ "all", "local" ] );
result:= Filtered( result, r -> r.contents in tocid );
fi;
merged.( label ):= result;
return result;
end;
#############################################################################
##
#F AGR.EvaluateCharacterCondition( <gapname>, <conditions>, <reps> )
##
## Evaluate conditions involving 'Character'.
## The list <conditions> is changed in place such that the first occurrence
## of 'Character' and the subsequent entry (the condition on the character)
## are removed.
## The return value is the sublist of those entries in <reps> that satisfy
## the condition.
##
AGR.EvaluateCharacterCondition:= function( gapname, conditions, reps )
local pos, map, pos2, p, chars, primes, consts, i, chi, tbl, ordtbl, dec,
const, j, repnames, mapi, len;
# If 'Character' does not occur then we need not work.
pos:= Position( conditions, Character );
if pos = fail then
return reps;
elif pos = Length( conditions ) then
return [];
fi;
map:= AtlasOfGroupRepresentationsInfo.characterinfo;
if not IsBound( map.( gapname ) ) then
Info( InfoAtlasRep, 1,
"no character information for ", gapname, " known" );
return [];
fi;
map:= map.( gapname );
# Check whether also 'Characteristic' is specified.
pos2:= Position( conditions, Characteristic );
if pos2 = fail then
p:= "?";
elif pos2 = Length( conditions ) then
return [];
else
p:= conditions[ pos2+1 ];
if IsInt( p ) then
p:= [ p ];
fi;
fi;
# Interpret the character(s).
chars:= conditions[ pos+1 ];
if IsClassFunction( chars ) then
chars:= [ chars ];
fi;
if IsList( chars ) and ForAll( chars, IsClassFunction ) then
# The characters are explicitly given.
# Compute the positions of their irreducible constituents.
primes:= [];
consts:= [];
for i in [ 1 .. Length( chars ) ] do
chi:= chars[i];
tbl:= UnderlyingCharacterTable( chi );
if IsOrdinaryTable( tbl ) then
ordtbl:= tbl;
else
ordtbl:= OrdinaryCharacterTable( tbl );
fi;
if gapname = Identifier( ordtbl ) and
( p = "?" or
( IsFunction( p ) and p( UnderlyingCharacteristic( tbl ) ) = true ) or
( IsList( p ) and UnderlyingCharacteristic( tbl ) in p ) ) then
if IsOrdinaryTable( tbl ) then
dec:= MatScalarProducts( tbl, Irr( tbl ), [ chi ] )[1];
else
dec:= Decomposition( Irr( tbl ), [ chi ], "nonnegative" )[1];
fi;
const:= [];
if dec <> fail and ForAll( dec, x -> IsInt( x ) and 0 <= x ) then
AddSet( primes, UnderlyingCharacteristic( tbl ) );
for j in [ 1 .. Length( dec ) ] do
if dec[j] = 1 then
Add( const, j );
elif 1 < dec[j] then
Add( const, [ j, dec[j] ] );
fi;
od;
if Length( const ) = 1 and IsInt( const[1] ) then
const:= const[1];
fi;
Add( consts, const );
fi;
fi;
od;
p:= primes;
chi:= consts;
elif not ( IsPosInt( chars ) or IsString( chars ) ) then
#T perhaps admit a list of positions or strings?
return [];
else
# The position in the list of irreducibles or the name is given.
if p = "?" then
# No characteristic is specified, this means *ordinary* character.
p:= [ 0 ];
fi;
chi:= chars;
fi;
# Look for the character(s) in the info lists.
repnames:= [];
for i in [ 1 .. Length( map ) ] do
if IsBound( map[i] ) and
( ( IsFunction( p ) and ( ( i = 1 and p( 0 ) = true ) or
( 1 < i and p( i ) = true ) ) ) or
( IsList( p ) and ( ( i = 1 and 0 in p ) or i in p ) ) ) then
mapi:= map[i];
for j in [ 1 .. Length( mapi[1] ) ] do
if ( IsPosInt( chi ) and mapi[1][j] = chi ) or
( IsString( chi ) and mapi[3][j] = chi ) or
( IsList( chi ) and mapi[1][j] in chi ) then
# We have found a character that matches.
Add( repnames, mapi[2][j] );
fi;
od;
fi;
od;
if Length( repnames ) = 0 then
return [];
fi;
# We will return a nonempty list. Remove 'Character' from 'conditions'.
for i in [ pos .. Length( conditions )-2 ] do
conditions[i]:= conditions[ i+2 ];
od;
Remove( conditions );
Remove( conditions );
return Filtered( reps, r -> r.repname in repnames );
end;
#############################################################################
##
#F AGR.AtlasGeneratingSetInfo( <conditions>, "one" )
#F AGR.AtlasGeneratingSetInfo( <conditions>, "all" )
#F AGR.AtlasGeneratingSetInfo( <conditions>, <types> )
##
## This function does the work for 'OneAtlasGeneratingSetInfo',
## 'AllAtlasGeneratingSetInfos', and 'AGR.InfoReps'.
## The first entry in <conditions> can be a group name
## or a list of group names.
##
AGR.AtlasGeneratingSetInfo:= function( conditions, mode )
local pos, tocid, gapnames, types, std, filter, givenRing, position,
result, gapname, reps, cond, info, type, F;
# Ignore the condition that no straight line programs are wanted.
pos:= Position( conditions, IsStraightLineProgram );
if pos <> fail and
pos < Length( conditions ) and conditions[ pos + 1 ] = false then
conditions:= Concatenation( conditions{ [ 1 .. pos-1 ] },
conditions{ [ pos+2 .. Length( conditions ) ] } );
fi;
# Restrict the sources.
pos:= Position( conditions, "contents" );
if pos <> fail then
tocid:= conditions[ pos+1 ];
conditions:= Concatenation( conditions{ [ 1 .. pos-1 ] },
conditions{ [ pos+2 .. Length( conditions ) ] } );
else
tocid:= "all";
fi;
# The first argument (if there is one) is a group name,
# or a list of group names,
# or an integer (denoting a standardization),
# or a function (denoting the first condition).
if Length( conditions ) = 0 or IsInt( conditions[1] )
or IsFunction( conditions[1] ) then
# The group is not restricted.
gapnames:= List( AtlasOfGroupRepresentationsInfo.GAPnamesSortDisp,
pair -> pair[1] );
elif IsString( conditions[1] ) then
# Only one group is considered.
gapnames:= [ AGR.GAPName( conditions[1] ) ];
conditions:= conditions{ [ 2 .. Length( conditions ) ] };
elif IsList( conditions[1] ) and ForAll( conditions[1], IsString ) then
# A list of group names is prescribed.
gapnames:= List( conditions[1], AGR.GAPName );
conditions:= conditions{ [ 2 .. Length( conditions ) ] };
else
Error( "invalid first argument ", conditions[1] );
fi;
types:= AGR.DataTypes( "rep" );
# Deal with a prescribed standardization.
if 1 <= Length( conditions ) and
( IsInt( conditions[1] ) or
( IsList( conditions[1] ) and ForAll( conditions[1], IsInt ) ) ) then
std:= conditions[1];
if IsInt( std ) then
std:= [ std ];
fi;
conditions:= conditions{ [ 2 .. Length( conditions ) ] };
else
std:= true;
fi;
# Extract a prescribed 'ConstructingFilter'.
filter:= fail;
pos:= Position( conditions, ConstructingFilter );
if pos <> fail then
if pos = Length( conditions ) or not IsFilter( conditions[ pos+1 ] ) then
Error( "condition 'ConstructingFilter' must be followed by a filter" );
fi;
filter:= conditions[ pos+1 ];
conditions:= Concatenation( conditions{ [ 1 .. pos-1 ] },
conditions{ [ pos+2 .. Length( conditions ) ] } );
fi;
# Extract a prescribed ring (but leave it in 'conditions').
givenRing:= fail;
pos:= Position( conditions, Ring );
if pos <> fail then
if pos = Length( conditions ) or not ( IsRing( conditions[ pos+1 ] )
#T admit a list of rings!
or IsFunction( conditions[ pos+1 ] )
or conditions[ pos+1 ] = fail ) then
Error( "condition 'Ring' must be followed by a ring" );
elif IsRing( conditions[ pos+1 ] ) then
givenRing:= conditions[ pos+1 ];
fi;
fi;
# A prescribed ring prescribes also a characteristic.
if givenRing <> fail and Position( conditions, Characteristic ) = fail then
conditions:= Concatenation( conditions,
[ Characteristic, Characteristic( givenRing ) ] );
fi;
# Deal with a prescribed representation number.
pos:= Position( conditions, Position );
if pos <> fail then
if pos = Length( conditions ) or not IsPosInt( conditions[ pos+1 ] ) then
Error( "condition 'Position' must be followed by a pos. integer" );
fi;
position:= conditions[ pos+1 ];
conditions:= Concatenation( conditions{ [ 1 .. pos-1 ] },
conditions{ [ pos+2 .. Length( conditions ) ] } );
fi;
result:= [];
for gapname in gapnames do
reps:= AGR.MergedTableOfContents( tocid, gapname );
# Evaluate the 'Position' condition.
if pos <> fail then
reps:= Filtered( reps, r -> r.repnr = position );
fi;
cond:= ShallowCopy( conditions );
# Evaluate conditions involving '"minimal"' (modify 'cond' in place).
if AGR.EvaluateMinimalityCondition( gapname, cond ) then
# Evaluate the 'Character' condition.
if Character in cond then
reps:= AGR.EvaluateCharacterCondition( gapname, cond, reps );
fi;
# Loop over the relevant representations.
for info in reps do
type:= First( types, t -> t[1] = info.type );
if ( std = true or info.standardization in std ) and
type[2].AccessGroupCondition( info, ShallowCopy( cond ) ) then
# Hack:
# Store the desired ring/field if there is one,
# in order to create the matrices over the correct ring/field.
if givenRing <> fail and IsBound( info.ring )
and not IsIdenticalObj( givenRing, info.ring ) then
info:= ShallowCopy( info );
info.givenRing:= givenRing;
fi;
if filter <> fail then
info:= ShallowCopy( info );
#T twice copy?
info.constructingFilter:= filter;
fi;
if mode = "one" then
return info;
else
Add( result, info );
fi;
fi;
od;
fi;
od;
# We have checked all available representations.
if mode = "one" then
return fail;
else
return result;
fi;
end;
#############################################################################
##
#F OneAtlasGeneratingSetInfo( [<gapname>][, <std>] )
#F OneAtlasGeneratingSetInfo( [<gapname>][, <std>], IsPermGroup[, true] )
#F OneAtlasGeneratingSetInfo( [<gapname>][, <std>], NrMovedPoints, <n> )
#F OneAtlasGeneratingSetInfo( [<gapname>][, <std>], IsMatrixGroup[, true] )
#F OneAtlasGeneratingSetInfo( [<gapname>][, <std>][, Characteristic, <p>]
#F [, Dimension, <m>] )
#F OneAtlasGeneratingSetInfo( [<gapname>][, <std>][, Ring, <R>]
#F [, Dimension, <m>] )
#F OneAtlasGeneratingSetInfo( [<gapname>,][ <std>,] Position, <n> )
##
InstallGlobalFunction( OneAtlasGeneratingSetInfo, function( arg )
return AGR.AtlasGeneratingSetInfo( arg, "one" );
end );
#############################################################################
##
#F AllAtlasGeneratingSetInfos( [<gapname>][, <std>] )
#F AllAtlasGeneratingSetInfos( [<gapname>][, <std>], IsPermGroup[, true] )
#F AllAtlasGeneratingSetInfos( [<gapname>][, <std>], NrMovedPoints, <n> )
#F AllAtlasGeneratingSetInfos( [<gapname>][, <std>], IsMatrixGroup[, true] )
#F AllAtlasGeneratingSetInfos( [<gapname>][, <std>][, Characteristic, <p>]
#F [, Dimension, <m>] )
#F AllAtlasGeneratingSetInfos( [<gapname>][, <std>][, Ring, <R>]
#F [, Dimension, <m>] )
##
InstallGlobalFunction( AllAtlasGeneratingSetInfos, function( arg )
return AGR.AtlasGeneratingSetInfo( arg, "all" );
end );
#############################################################################
##
#M AtlasRepInfoRecord( <gapname> )
##
InstallMethod( AtlasRepInfoRecord,
[ "IsString" ],
function( gapname )
local info, result, comp, groupname, name, maxes, maxstd, toc, record, i;
# Make sure that the file 'gap/types.g' is already loaded.
IsRecord( AtlasOfGroupRepresentationsInfo );
if not IsBound( AGR.GAPnamesRec.( gapname ) ) then
return rec();
fi;
info:= AGR.GAPnamesRec.( gapname )[3];
result:= rec( name:= gapname );
for comp in [ "size", "nrMaxes", "sizesMaxes", "structureMaxes" ] do
if IsBound( info.( comp ) ) then
result.( comp ):= StructuralCopy( info.( comp ) );
fi;
od;
groupname:= AGR.InfoForName( gapname );
name:= groupname[2];
maxes:= [];
maxstd:= [];
for toc in AGR.TablesOfContents( "all" ) do
if IsBound( toc.( name ) ) then
record:= toc.( name );
if IsBound( record.maxes ) then
for i in record.maxes do
if i[2] in maxes then
AddSet( maxstd[ Position( maxes, i[2] ) ], i[1] );
else
Add( maxes, i[2] );
Add( maxstd, [ i[1] ] );
fi;
od;
fi;
fi;
od;
if IsBound( info.maxext ) then
for i in info.maxext do
if i[2] in maxes then
AddSet( maxstd[ Position( maxes, i[2] ) ], i[1] );
else
Add( maxes, i[2] );
Add( maxstd, [ i[1] ] );
fi;
od;
fi;
if not IsEmpty( maxes ) then
SortParallel( maxes, maxstd );
ConvertToRangeRep( maxes );
result.slpMaxes:= [ maxes, maxstd ];
fi;
return result;
end );
#############################################################################
##
#F AtlasGroup( [<gapname>[, <std>]] )
#F AtlasGroup( [<gapname>[, <std>]], IsPermGroup[, true] )
#F AtlasGroup( [<gapname>[, <std>]], NrMovedPoints, <n> )
#F AtlasGroup( [<gapname>[, <std>]], IsMatrixGroup[, true] )
#F AtlasGroup( [<gapname>[, <std>]][, Characteristic, <p>]
#F [, Dimension, <m>] )
#F AtlasGroup( [<gapname>[, <std>]][, Ring, <R>][, Dimension, <m>] )
#F AtlasGroup( [<gapname>[, <std>]], Position, <n> )
#F AtlasGroup( <identifier> )
##
InstallGlobalFunction( AtlasGroup, function( arg )
local info, identifier, gapname, gens, result;
if Length( arg ) = 1 and IsRecord( arg[1] ) then
info:= arg[1];
elif Length( arg ) = 1 and IsList( arg[1] ) and not IsString( arg[1] ) then
# Find the info record with this identifier.
identifier:= arg[1];
gapname:= identifier[1];
info:= First( AGR.MergedTableOfContents( "all", gapname ),
r -> r.identifier = identifier );
else
info:= CallFuncList( OneAtlasGeneratingSetInfo, arg );
fi;
if info <> fail then
gens:= AtlasGenerators( info );
if gens <> fail then
result:= GroupWithGenerators( gens.generators );
if IsBound( gens.isPrimitive ) then
SetIsPrimitive( result, gens.isPrimitive );
fi;
# Note that it would *not* be safe to set 'NrMovedPoints'
# or 'LargestMovedPoint' to 'gens.p'.
if IsBound( gens.rankAction ) then
SetRankAction( result, gens.rankAction );
fi;
if IsBound( gens.size ) then
SetSize( result, gens.size );
fi;
if IsBound( gens.transitivity ) then
SetTransitivity( result, gens.transitivity );
SetIsTransitive( result, gens.transitivity > 0 );
fi;
#T Set known info about the *group* (IsSimple etc., not stored in 'gens')!
SetAtlasRepInfoRecord( result, info );
return result;
fi;
fi;
return fail;
end );
#############################################################################
##
#F AtlasSubgroup( <gapname>[, <std>], <maxnr> )
#F AtlasSubgroup( <gapname>[, <std>], IsPermGroup[, true], <maxnr> )
#F AtlasSubgroup( <gapname>[, <std>], NrMovedPoints, <n>, <maxnr> )
#F AtlasSubgroup( <gapname>[, <std>], IsMatrixGroup[, true], <maxnr> )
#F AtlasSubgroup( <gapname>[, <std>][, Characteristic, <p>]
#F [, Dimension, <m>], <maxnr> )
#F AtlasSubgroup( <gapname>[, <std>][, Ring, <R>]
#F [, Dimension, <m>], <maxnr> )
#F AtlasSubgroup( <gapname>[, <std>], Position, <n>, <maxnr> )
#F AtlasSubgroup( <G>, <maxnr> )
#F AtlasSubgroup( <identifier>, <maxnr> )
##
#T ... or the same with '<maxnr>' replaced by '"maxes", <maxnr>, <maxstd>'
##
InstallGlobalFunction( AtlasSubgroup, function( arg )
local maxnr, info, groupname, std, prog, result, inforec;
maxnr:= arg[ Length( arg ) ];
if not IsPosInt( maxnr ) then
Error( "<maxnr> must be a positive integer" );
fi;
if Length( arg ) = 2 and IsRecord( arg[1] ) then
info:= arg[1];
groupname:= info.groupname;
elif Length( arg ) = 2 and IsGroup( arg[1] ) then
if not HasAtlasRepInfoRecord( arg[1] ) then
Error( "the 'AtlasRepInfoRecord' value is not set for the group" );
fi;
info:= AtlasRepInfoRecord( arg[1] );
groupname:= info.groupname;
elif Length( arg ) = 2 and IsList( arg[1] ) and not IsString( arg[1] ) then
info:= rec( identifier:= arg[1], standardization:= arg[1][3] );
groupname:= arg[1][1];
elif 1 < Length( arg ) then
info:= CallFuncList( OneAtlasGeneratingSetInfo,
arg{ [ 1 .. Length( arg ) - 1 ] } );
groupname:= arg[1];
else
info:= fail;
fi;
if info = fail then
return fail;
fi;
std:= info.standardization;
prog:= AtlasProgram( groupname, std, "maxes", maxnr );
if prog = fail then
return fail;
fi;
if Length( arg ) = 2 and IsGroup( arg[1] ) then
# We need not load the generators from files.
result:= GroupWithGenerators( ResultOfStraightLineProgram( prog.program,
GeneratorsOfGroup( arg[1] ) ) );
else
result:= AtlasGenerators( info );
if result = fail then
return fail;
fi;
result:= GroupWithGenerators( ResultOfStraightLineProgram( prog.program,
result.generators ) );
fi;
if IsBound( prog.size ) then
SetSize( result, prog.size );
fi;
inforec:= rec( identifier:= Concatenation( info.identifier,
[ maxnr ] ),
standardization:= std );
if IsBound( info.repnr ) then
inforec.repnr:= info.repnr;
fi;
if IsBound( prog.subgroupname ) then
inforec.groupname:= prog.subgroupname;
fi;
if IsBound( prog.size ) then
inforec.size:= prog.size;
fi;
SetAtlasRepInfoRecord( result, inforec );
return result;
end );
#############################################################################
##
#M ConjugacyClasses( <G> )
##
## For a group with stored 'AtlasRepInfoRecord' value,
## there may be a straight line program that computes class representatives.
## If yes then use it, otherwise give up.
##
## Note that the 'ccls' straight line programs output the representatives
## in Atlas ordering, in particular the identity element comes first.
##
#T Is there a way to express that a group constructed with 'AtlasSubgroup'
#T does in fact have standard generators,
#T such that class representatives can be computed with this method?
##
InstallMethod( ConjugacyClasses,
[ "IsGroup and IsFinite and HasAtlasRepInfoRecord" ],
OVERRIDENICE + RankFilter( IsPermGroup ), # adjust to other uprankings
function( G )
local info, prg, reps;
info:= AtlasRepInfoRecord( G );
if info.groupname <> info.identifier[1] then
# The group is just a subgroup of an Atlas group.
TryNextMethod();
fi;
prg:= AtlasProgram( info.groupname, info.standardization, "classes" );
if prg = fail then
# We do not know a straight line program for computing class reps.
TryNextMethod();
fi;
reps:= ResultOfStraightLineProgram( prg.program,
GeneratorsOfGroup( G ) );
return List( reps, x -> ConjugacyClass( G, x ) );
end );
#############################################################################
##
#F AtlasProgramInfo( <gapname>[, <std>][, "maxes"], <maxnr> )
#F AtlasProgramInfo( <gapname>[, <std>], "maxes", <maxnr>[, <std2>] )
#F AtlasProgramInfo( <gapname>[, <std>], "maxstd", <maxnr>, <vers>, <substd> )
#F AtlasProgramInfo( <gapname>[, <std>], "kernel", <factname> )
#F AtlasProgramInfo( <gapname>[, <std>], "classes" )
#F AtlasProgramInfo( <gapname>[, <std>], "cyclic" )
#F AtlasProgramInfo( <gapname>[, <std>], "cyc2ccl"[, <vers>] )
#F AtlasProgramInfo( <gapname>[, <std>], "automorphism", <autname> )
#F AtlasProgramInfo( <gapname>[, <std>], "check" )
#F AtlasProgramInfo( <gapname>[, <std>], "presentation" )
#F AtlasProgramInfo( <gapname>[, <std>], "find" )
#F AtlasProgramInfo( <gapname>, <std>, "restandardize", <std2> )
#F AtlasProgramInfo( <gapname>[, <std>], "other", <descr> )
##
InstallGlobalFunction( AtlasProgramInfo, function( arg )
local identifier, gapname, groupname, type, result, std, argpos,
conditions, tocs, toc, id;
if Length( arg ) = 1 then
# 'AtlasProgramInfo( <identifier> )'
identifier:= arg[1];
gapname:= identifier[1];
groupname:= AGR.InfoForName( gapname );
if groupname = fail then
return fail;
fi;
for type in AGR.DataTypes( "prg" ) do
result:= type[2].AtlasProgramInfo( type, identifier, groupname[2] );
if result <> fail then
result.groupname:= gapname;
result.version:= AGR.VersionOfSLP( identifier[2] );
return Immutable( result );
fi;
od;
return fail;
elif Length( arg ) = 0 or not IsString( arg[1] ) then
Error( "the first argument must be the GAP name of a group" );
fi;
# Now handle the cases of more than one argument.
gapname:= arg[1];
groupname:= AGR.InfoForName( gapname );
if groupname = fail then
Info( InfoAtlasRep, 1,
"AtlasProgramInfo: no group with GAP name '", gapname, "'" );
return fail;
fi;
if IsInt( arg[2] ) and 2 < Length( arg ) then
std:= [ arg[2] ];
argpos:= 3;
elif IsBool( arg[2] ) and 2 < Length( arg ) then
std:= true;
argpos:= 3;
else
std:= true;
argpos:= 2;
fi;
conditions:= arg{ [ argpos .. Length( arg ) ] };
# Restrict to a prescribed selection of tables of contents.
tocs:= AGR.TablesOfContents( conditions );
# 'AtlasProgramInfo( <gapname>[, <std>][, "maxes"], <maxnr> )'
if ( Length( conditions ) = 1 and IsInt( conditions[1] ) ) or
( Length( conditions ) = 3 and IsInt( conditions[1] )
and conditions[2] = "version" ) then
conditions:= Concatenation( [ "maxes" ], conditions );
fi;
for toc in tocs do
# Note that 'toc.( groupname[2] )' need not be bound
# if database extensions provide straight line pograms.
for type in AGR.DataTypes( "prg" ) do
id:= type[2].AccessPRG( toc, groupname[2], std, conditions );
if id <> fail then
# The table of contents provides a program as is required.
return AtlasProgramInfo( Concatenation( [ groupname[1] ], id ) );
fi;
od;
od;
# No program was found.
Info( InfoAtlasRep, 2,
"no program for conditions ", conditions, "\n",
"#I of the group with GAP name '", groupname[1], "'" );
return fail;
end );
#############################################################################
##
#F AtlasProgram( <gapname>[, <std>][, "maxes"], <maxnr> )
#F AtlasProgram( <gapname>[, <std>], "maxes", <maxnr>[, <std2>] )
#F AtlasProgram( <gapname>[, <std>], "maxstd", <maxnr>, <vers>, <substd> )
#F AtlasProgram( <gapname>[, <std>], "kernel", <factname> )
#F AtlasProgram( <gapname>[, <std>], "classes" )
#F AtlasProgram( <gapname>[, <std>], "cyclic" )
#F AtlasProgram( <gapname>[, <std>], "cyc2ccl"[, <vers>] )
#F AtlasProgram( <gapname>[, <std>], "automorphism", <autname> )
#F AtlasProgram( <gapname>[, <std>], "check" )
#F AtlasProgram( <gapname>[, <std>], "presentation" )
#F AtlasProgram( <gapname>[, <std>], "find" )
#F AtlasProgram( <gapname>, <std>, "restandardize", <std2> )
#F AtlasProgram( <gapname>[, <std>], "other", <descr> )
#F AtlasProgram( <identifier> )
##
## <identifier> is a list containing at the first position the string
## <gapname>,
## at the second position a string or a list of strings
## (describing the filenames involved),
## and at the third position a positive integer denoting the standardization
## of the program.
##
InstallGlobalFunction( AtlasProgram, function( arg )
local identifier, gapname, groupname, type, result, info;
if Length( arg ) = 1 then
# 'AtlasProgram( <identifier> )'
identifier:= arg[1];
gapname:= identifier[1];
groupname:= AGR.InfoForName( gapname );
if groupname = fail then
return fail;
fi;
for type in AGR.DataTypes( "prg" ) do
result:= type[2].AtlasProgram( type, identifier, groupname[2] );
if result <> fail then
result.groupname:= groupname[1];
result.version:= AGR.VersionOfSLP( identifier[2] );
return Immutable( result );
fi;
od;
return fail;
elif Length( arg ) = 0 or not IsString( arg[1] ) then
Error( "the first argument must be the GAP name of a group" );
fi;
# Now handle the cases of more than one argument.
info:= CallFuncList( AtlasProgramInfo, arg );
if info = fail then
return fail;
fi;
return AtlasProgram( info.identifier );
end );
#############################################################################
##
#M EvaluatePresentation( <G>, <gapname>[, <std>] )
#M EvaluatePresentation( <gens>, <gapname>[, <std>] )
##
InstallMethod( EvaluatePresentation,
[ "IsGroup", "IsString" ],
{ G, gapname } -> EvaluatePresentation( GeneratorsOfGroup( G ), gapname, 1 ) );
InstallMethod( EvaluatePresentation,
[ "IsHomogeneousList", "IsString" ],
{ gens, gapname } -> EvaluatePresentation( gens, gapname, 1 ) );
InstallMethod( EvaluatePresentation,
[ "IsGroup", "IsString", "IsPosInt" ],
{ G, gapname, std } -> EvaluatePresentation( GeneratorsOfGroup( G ), gapname, std ) );
InstallMethod( EvaluatePresentation,
[ "IsHomogeneousList", "IsString", "IsPosInt" ],
function( gens, gapname, std )
local prg;
prg:= AtlasProgram( gapname, std, "presentation" );
if prg = fail then
return fail;
elif NrInputsOfStraightLineDecision( prg.program )
<> Length( gens ) then
Error( "presentation for \"", gapname, "\" has ",
NrInputsOfStraightLineDecision( prg.program ),
" generators but ", Length( gens ),
" generators were given" );
fi;
prg:= StraightLineProgramFromStraightLineDecision( prg.program );
return ResultOfStraightLineProgram( prg, gens );
end );
#############################################################################
##
#M StandardGeneratorsData( <G>, <gapname>[, <std>] )
#M StandardGeneratorsData( <gens>, <gapname>[, <std>] )
##
InstallMethod( StandardGeneratorsData,
[ "IsGroup", "IsString" ],
function( G, gapname )
return StandardGeneratorsData( GeneratorsOfGroup( G ), gapname, 1 );
end );
InstallMethod( StandardGeneratorsData,
[ "IsHomogeneousList", "IsString" ],
{ gens, gapname } -> StandardGeneratorsData( gens, gapname, 1 ) );
InstallMethod( StandardGeneratorsData,
[ "IsGroup", "IsString", "IsPosInt" ],
function( G, gapname, std )
return StandardGeneratorsData( GeneratorsOfGroup( G ), gapname, std );
end );
InstallMethod( StandardGeneratorsData,
[ "IsHomogeneousList", "IsString", "IsPosInt" ],
function( gens, gapname, std )
local prg, options, mgens, res;
prg:= AtlasProgram( gapname, std, "find" );
if prg = fail then
return fail;
fi;
prg:= prg.program;
if ValueOption( "projective" ) = true then
# This is supported only for FFE matrix groups.
# We do not check this condition,
# 'ProjectiveOrder' will run into an error if it is not satisfied.
options:= rec( orderfunction:= mat -> ProjectiveOrder( mat )[1] );
else
options:= rec();
fi;
mgens:= GeneratorsWithMemory( gens );
res:= ResultOfBBoxProgram( prg, GroupWithGenerators( mgens ),
options );
if res = "timeout" then
return "timeout";
elif res = fail then
# The program has detected that 'gens' cannot belong to 'gapname'.
return fail;
fi;
return rec( gapname:= gapname,
givengens:= gens,
stdgens:= StripMemory( res ),
givengenstostdgens:= SLPOfElms( res ),
std:= std );
end );
#############################################################################
##
#E
[ 0.71Quellennavigators
Projekt
]
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