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Display for a character table optionally shows the degrees of the character fields #5047

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Sep 15, 2022
Merged

Display for a character table optionally shows the degrees of the character fields #5047

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5 changes: 5 additions & 0 deletions lib/ctbl.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -3421,6 +3421,11 @@ DeclareGlobalFunction( "ConvertToLibraryCharacterTableNC" );
## centralizer orders in a style similar to that used in the
## &ATLAS; of Finite Groups&nbsp;<Cite Key="CCN85"/>,
## </Item>
## <Mark><C>characterField</C></Mark>
## <Item>
## <K>true</K> to show the degrees of the character fields over the prime
## field, in a column with header <C>d</C>,
## </Item>
## <Mark><C>chars</C></Mark>
## <Item>
## an integer or a list of integers to select a sublist of the
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37 changes: 32 additions & 5 deletions lib/ctbl.gi
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Expand Up @@ -4803,11 +4803,13 @@ BindGlobal( "CharacterTableDisplayDefault", function( tbl, options )
ncols, # total number of columns
linelen, # line length
q, # quadratic cyc / powermap entry
field_degrees, # list of degrees of character fields
indicator, # list of primes
OD, # show a column with orthog. discriminants
iw, # width of indicator columns
indic, # indicator values
oddata, # orthog. discriminants
p, # characteristic
ind2, # 2nd indicator
iwsum, # total width of (OD and) indicator columns
entry, # run over 'oddata'
Expand Down Expand Up @@ -5005,6 +5007,17 @@ BindGlobal( "CharacterTableDisplayDefault", function( tbl, options )
fi;
od;

# print degrees of character fields?
field_degrees:= false;
for record in options do
if IsBound( record.characterField ) then
if record.characterField = true then
field_degrees:= true;
fi;
break;
fi;
od;

# print Frobenius-Schur indicators?
indicator:= [];
for record in options do
Expand Down Expand Up @@ -5071,15 +5084,29 @@ BindGlobal( "CharacterTableDisplayDefault", function( tbl, options )
fi;
indicator:= Concatenation( [ "OD" ], indicator );
fi;
if field_degrees then
indicator:= Concatenation( [ "d" ], indicator );
fi;
if indicator <> [] then
for i in [ 1 .. Length( indicator ) ] do
if indicator[i] = "OD" then
indic[1]:= ListWithIdenticalEntries( Length( cnr ), "" );
if indicator[i] = "d" then
p:= UnderlyingCharacteristic( tbl );
if p = 0 then
indic[i]:= List( chars,
x -> String( Dimension( Field( Rationals, x ) ) ) );
else
indic[i]:= List( chars,
x -> String( Length( Factors( SizeOfFieldOfDefinition(
ClassFunction( tbl, x ), p ) ) ) ) );
fi;
iw[i]:= Maximum( 2, Maximum( List( indic[i], Length ) ) ) + 1;
elif indicator[i] = "OD" then
indic[i]:= ListWithIdenticalEntries( Length( cnr ), "" );
if IsBoundGlobal( "OrthogonalDiscriminants" ) then
oddata:= ValueGlobal( "OrthogonalDiscriminants" )( tbl );
for j in [ 1 .. Length( cnr ) ] do
if IsBound( oddata[ cnr[j] ] ) then
indic[1][j]:= oddata[ cnr[j] ];
indic[i][j]:= oddata[ cnr[j] ];
fi;
od;
else
Expand All @@ -5088,11 +5115,11 @@ BindGlobal( "CharacterTableDisplayDefault", function( tbl, options )
for j in [ 1 .. Length( cnr ) ] do
if ( not ind2[ cnr[j] ] in [ -1, 0 ] ) and
Irr( tbl )[ cnr[j] ][1] mod 2 = 0 then
indic[1][j]:= "?";
indic[i][j]:= "?";
fi;
od;
fi;
iw[i]:= Maximum( 2, Maximum( List( indic[1], Length ) ) ) + 1;
iw[i]:= Maximum( 2, Maximum( List( indic[i], Length ) ) ) + 1;
else
if chars_from_irr and
IsBound( ComputedIndicators( tbl )[ indicator[i] ] ) then
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14 changes: 14 additions & 0 deletions tst/testinstall/ctbl.tst
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Expand Up @@ -252,6 +252,20 @@ CT2
X.1 1 -1 1
X.2 2 . -1
X.3 1 1 1
gap> Display( t,
> rec( characterField:= true ) );
CT2

2 1 1 .
3 1 . 1

1a 2a 3a
2P 1a 1a 3a
3P 1a 2a 1a
d
X.1 1 1 -1 1
X.2 1 2 . -1
X.3 1 1 1 1

# viewing and printing of character tables with stored groups
gap> t:= CharacterTable( DihedralGroup( 8 ) );;
Expand Down