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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346#############################################################################
##
#W brmindeg.g GAP 4 package AtlasRep Thomas Breuer
##
#Y Copyright (C) 2007, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
##
## This file contains a Browse application for showing the minimal degree
## data in a table.
##
#############################################################################
##
#F BrowseMinimalDegrees( [<groupnames>] )
##
## <#GAPDoc Label="BrowseMinimalDegrees">
## <ManSection>
## <Func Name="BrowseMinimalDegrees" Arg='[groupnames]'/>
##
## <Returns>
## the list of info records for the clicked representations.
## </Returns>
## <Description>
## If the &GAP; package <Package>Browse</Package> (see <Cite Key="Browse"/>)
## is loaded then this function is available.
## It opens a browse table whose rows correspond to the groups for which the
## <Package>ATLAS</Package> of Group Representations contains
## some information about minimal degrees,
## whose columns correspond to the characteristics that occur,
## and whose entries are the known minimal degrees.
## <P/>
## <Example><![CDATA[
## gap> if IsBound( BrowseMinimalDegrees ) then
## > down:= NCurses.keys.DOWN;; DOWN:= NCurses.keys.NPAGE;;
## > right:= NCurses.keys.RIGHT;; END:= NCurses.keys.END;;
## > enter:= NCurses.keys.ENTER;; nop:= [ 14, 14, 14 ];;
## > # just scroll in the table
## > BrowseData.SetReplay( Concatenation( [ DOWN, DOWN, DOWN,
## > right, right, right ], "sedddrrrddd", nop, nop, "Q" ) );
## > BrowseMinimalDegrees();;
## > # restrict the table to the groups with minimal ordinary degree 6
## > BrowseData.SetReplay( Concatenation( "scf6",
## > [ down, down, right, enter, enter ] , nop, nop, "Q" ) );
## > BrowseMinimalDegrees();;
## > BrowseData.SetReplay( false );
## > fi;
## ]]></Example>
## <P/>
## If an argument <A>groupnames</A> is given then it must be a list of
## group names of the <Package>ATLAS</Package> of Group Representations;
## the browse table is then restricted to the rows corresponding to these
## group names and to the columns that are relevant for these groups.
## A perhaps interesting example is the subtable with the data concerning
## sporadic simple groups and their covering groups,
## which has been published in <Cite Key="Jan05"/>.
## This table can be shown as follows.
## <P/>
## <Example><![CDATA[
## gap> if IsBound( BrowseMinimalDegrees ) then
## > # just scroll in the table
## > BrowseData.SetReplay( Concatenation( [ DOWN, DOWN, DOWN, END ],
## > "rrrrrrrrrrrrrr", nop, nop, "Q" ) );
## > BrowseMinimalDegrees( BibliographySporadicSimple.groupNamesJan05 );;
## > fi;
## ]]></Example>
## <P/>
## The browse table does not contain rows for the groups
## <M>6.M_{22}</M>, <M>12.M_{22}</M>, <M>6.Fi_{22}</M>.
## Note that in spite of the title of <Cite Key="Jan05"/>, the entries in
## Table 1 of this paper are in fact the minimal degrees of faithful
## <E>irreducible</E> representations, and in the above three cases,
## these degrees are larger than the minimal degrees of faithful
## representations.
## The underlying data of the browse table is about the minimal faithful
## (but not necessarily irreducible) degrees.
## <P/>
## The return value of <Ref Func="BrowseMinimalDegrees"/> is the list of
## <Ref Func="OneAtlasGeneratingSetInfo"/> values for those representations
## that have been <Q>clicked</Q> in visual mode.
## <P/>
## The variant without arguments of this function is also available
## in the menu shown by <Ref Func="BrowseGapData" BookName="Browse"/>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
BindGlobal( "BrowseMinimalDegrees", function( arg )
local data, name, char, lastj, labelsrow, mat, src, i, entry, pos, j,
perm, info, file, parse, keys, modes, newactions, showaction, mode,
table, result;
if Length( arg ) = 0 then
data:= MinimalRepresentationInfoData.datalist;
elif Length( arg ) = 1 and IsList( arg[1] ) then
data:= [];
for name in arg[1] do
Append( data, Filtered( MinimalRepresentationInfoData.datalist,
x -> x[1] = name ) );
od;
if IsEmpty( data ) then
return [];
fi;
else
Error( "usage: BrowseMinimalDegrees( [<groupnames>] )" );
fi;
char:= Set( List( Filtered( data, x -> x[2][1] = "Characteristic" ),
x -> x[2][2] ) );
lastj:= Length( char ) + 1;
labelsrow:= [];
mat:= [];
src:= [];
for i in [ 1 .. Length( data ) ] do
entry:= data[i];
pos:= Position( labelsrow, entry[1] );
if pos = fail then
pos:= Length( labelsrow ) + 1;
labelsrow[ pos ]:= entry[1];
mat[ pos ]:= [];
src[ pos ]:= [];
fi;
if entry[2][1] = "Characteristic" and IsInt( entry[3] ) then
j:= Position( char, entry[2][2] );
if OneAtlasGeneratingSetInfo( labelsrow[ pos ],
Characteristic, entry[2][2], Dimension, entry[3] ) = fail then
mat[ pos ][j]:= String( entry[3] );
else
mat[ pos ][j]:= rec( rows:= [ [ NCurses.attrs.BOLD, true,
NCurses.ColorAttr( "blue", -1 ), true,
String( entry[3] ) ] ], align:= "r" );
fi;
if not IsBound( src[ pos ][j] ) then
src[ pos ][j]:= [];
fi;
AddSet( src[ pos ][j], entry[4] );
elif entry[2] = "NrMovedPoints" then
if OneAtlasGeneratingSetInfo( labelsrow[ pos ],
NrMovedPoints, entry[3] ) = fail then
mat[ pos ][ lastj ]:= String( entry[3] );
else
mat[ pos ][ lastj ]:= rec( rows:= [ [ NCurses.attrs.BOLD, true,
NCurses.ColorAttr( "blue", -1 ), true,
String( entry[3] ) ] ], align:= "r" );
fi;
if not IsBound( src[ pos ][ lastj ] ) then
src[ pos ][ lastj ]:= [];
fi;
AddSet( src[ pos ][ lastj ], entry[4] );
fi;
od;
if Length( arg ) = 0 then
# Sort the rows.
perm:= Sortex( List( labelsrow,
BrowseData.SplitStringIntoNumbersAndNonnumbers ) );
#T really better than BrowseData.CompareAsNumbersAndNonnumbers?
labelsrow:= Permuted( labelsrow, perm );
mat:= Permuted( mat, perm );
src:= Permuted( src, perm );
fi;
# Fill missing entries with a question mark.
for i in [ 1 .. Length( mat ) ] do
info:= First( AtlasOfGroupRepresentationsInfo.GAPnames,
x -> x[1] = labelsrow[i] );
for j in [ 1 .. Length( char ) ] do
if not IsBound( mat[i][j] ) then
if char[j] = 0 or ( IsList( info ) and IsBound( info[3].size )
and info[3].size mod char[j] = 0 ) then
mat[i][j]:= "?";
fi;
fi;
od;
# perm. degree
if not IsBound( mat[i][ lastj ] ) then
mat[i][ lastj ]:= "?";
fi;
od;
# Load the bibliographic data.
file:= Filename( DirectoriesPackageLibrary( "atlasrep", "bibl" ),
"mindegbib.xml" );
parse:= ParseBibXMLextFiles( file );
keys:= List( parse.entries,
e -> RecBibXMLEntry( e, "Text", parse.strings ).Label );
# Construct the extended modes if necessary.
if not IsBound( BrowseData.defaults.work.customizedModes.brmindeg ) then
# Create a shallow copy of each default mode for `Browse', and add
# new actions to those modes where an entry is selected:
# - vb: Show BibTeX format of the selected entry in a pager
# - vh: Show HTML format of the selected entry in a pager
# - vt: Show text format of the selected entry in a pager
modes:= List( BrowseData.defaults.work.availableModes,
BrowseData.ShallowCopyMode );
BrowseData.defaults.work.customizedModes.brmindeg:= modes;
newactions:= [ [ "vb", "BibTeX" ],
[ "vh", "HTML" ],
[ "vt", "Text" ] ];
showaction:= pair -> [ [ pair[1] ],
rec( helplines:= [ Concatenation( "show ", pair[2],
" format of bibl. info" ),
"for the selected entry in a pager" ],
action:= function( t )
local row, col, disp, i, pos;
if t.dynamic.selectedEntry <> [ 0, 0 ] then
row:= t.dynamic.indexRow[ t.dynamic.selectedEntry[1] ] / 2;
col:= t.dynamic.indexCol[ t.dynamic.selectedEntry[2] ] / 2;
if IsBound( src[ row ][ col ] ) then
disp:= [];
for i in src[ row ][ col ] do
pos:= Position( keys, i );
if pos <> fail then
Add( disp, parse.entries[ pos ] );
fi;
od;
if not IsEmpty( disp ) then
NCurses.hide_panel( t.dynamic.statuspanel );
NCurses.Pager( JoinStringsWithSeparator( List( disp,
e -> BrowseData.SimplifiedString(
StringBibXMLEntry( e, pair[2],
parse.strings ) ) ), "\n" ) );
NCurses.show_panel( t.dynamic.statuspanel );
fi;
fi;
fi;
t.dynamic.changed:= true;
end ) ];
newactions:= List( newactions, showaction );
for mode in modes do
if mode.name in [ "select_entry", "select_row_and_entry",
"select_column_and_entry" ] then
BrowseData.SetActions( mode, newactions );
fi;
od;
else
modes:= BrowseData.defaults.work.customizedModes.brmindeg;
fi;
# Construct the browse table.
table:= rec(
work:= rec(
availableModes:= modes,
align:= "ct",
header:= t -> BrowseData.HeaderWithRowCounter( t,
"Minimal Degrees of Representations",
Length( mat ) ),
footer:= rec(
# Show the sources of the data.
select_entry:= function( t )
local entry, e, pos;
entry:= "";
if t.dynamic.selectedEntry <> [ 0, 0 ] then
e:= src[ t.dynamic.indexRow[ t.dynamic.selectedEntry[1] ] / 2 ];
pos:= t.dynamic.indexCol[ t.dynamic.selectedEntry[2] ] / 2;
if IsBound( e[ pos ] ) and not IsEmpty( e[ pos ] ) then
entry:= Concatenation( "source: ",
JoinStringsWithSeparator( e[ pos ], ", " ) );
fi;
fi;
return [ entry ];
end ),
footerLength:= rec(
select_entry:= 1 ),
CategoryValues:= function( t, i, j )
local val;
val:= t.work.main[ i/2 ][ j/2 ];
if NCurses.IsAttributeLine( val ) then
val:= NCurses.SimpleString( val );
else
val:= Concatenation( List( val.rows, NCurses.SimpleString ) );
fi;
if 2 * Length( char ) < j then
return [ Concatenation( "min. perm. degree = ", val ) ];
else
return [ Concatenation( "char. ", String( char[ j/2 ] ), ": ",
val ) ];
fi;
end,
main:= mat,
labelsRow:= List( labelsrow,
x -> [ rec( rows:= [ x ], align:= "l" ) ] ),
labelsCol:= [ Concatenation( List( char,
x -> rec( rows:= [ String( x ) ], align:= "r" ) ),
[ "perm. degree" ] ) ],
sepLabelsRow:= "|",
sepLabelsCol:= "|",
sepRow:= "-",
sepCol:= Concatenation( [ "| " ],
List( [ 1 .. Length( char ) ], x -> " | " ), [ " |" ] ),
SpecialGrid:= BrowseData.SpecialGridLineDraw,
Click:= rec(
select_entry:= rec(
helplines:= [ "add the representation to the result list" ],
action:= function( t )
local i, j, entry;
if t.dynamic.selectedEntry <> [ 0, 0 ] then
i:= t.dynamic.indexRow[ t.dynamic.selectedEntry[1] ] / 2;
j:= t.dynamic.indexCol[ t.dynamic.selectedEntry[2] ] / 2;
if IsBound( mat[i][j] ) then
entry:= mat[i][j];
if IsRecord( entry ) then
entry:= First( entry.rows[1], IsString );
fi;
if j <= Length( char ) then
info:= OneAtlasGeneratingSetInfo( labelsrow[i],
Characteristic, char[j],
Dimension, Int( entry ) );
else
info:= OneAtlasGeneratingSetInfo( labelsrow[i],
NrMovedPoints, Int( entry ) );
fi;
if not info in t.dynamic.Return then
Add( t.dynamic.Return, info );
fi;
fi;
fi;
end ),
),
),
dynamic:= rec(
sortFunctionsForColumns:= List( [ 0 .. Length( char ) ],
x -> BrowseData.CompareLenLex ),
Return:= [],
activeModes:= [ First( modes, x -> x.name = "browse" ) ],
),
);
# Show the browse table.
result:= NCurses.BrowseGeneric( table );
# Construct the return value.
return result;
end );
#############################################################################
##
## Add the Browse application to the list shown by `BrowseGapData'.
##
BrowseGapDataAdd( "Minimal Degrees of Representations",
BrowseMinimalDegrees, true, "\
the list of known minimal degrees for the groups of the \
Atlas of Group Representations, \
shown in a browse table with one column for each characteristic \
plus a column for the minimal permutation degree; \
available representations are shown in boldface blue, \
clicking on the table cell of such a representation adds the \
info record for it to the result list; \
the inputs vb, vh, vt open a pager showing the bibliographic sources \
of the selected entry if available; \
try ?BrowseMinimalDegrees for details" );
#############################################################################
##
#E