1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
|
#############################################################################
##
#W ctbltoct.g GAP 4 package CTblLib Thomas Breuer
##
#Y Copyright (C) 2011, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
##
## This file contains functions for collecting information about a
## character table contained in the GAP Character Table Library,
## and for turning this information into an overview string.
##
## Functions for creating Browse overviews are in the file `ctbltocb.g'.
#T mention HTML file creation!
##
## 0. Some utilities for collecting information
## 1. Transform the info into a plain string.
##
#############################################################################
##
## 0. Some utilities for collecting information
##
#############################################################################
##
## CTblLib.TableValue( <groupname>, <attrname> )
##
## helper: access attribute values
##
CTblLib.TableValue:= function( groupname, attrname )
local enum, attrs, attr, tbl;
enum:= CTblLib.Data.IdEnumerator;
if not groupname in enum.identifiers then
enum:= CTblLib.Data.IdEnumeratorExt;
fi;
if groupname in enum.identifiers then
attrs:= enum.attributes;
if IsBound( attrs.( attrname ) ) then
attr:= attrs.( attrname );
return attr.attributeValue( attr, groupname );
fi;
fi;
if attrname = "FusionsTo" then
return Set( List( ComputedClassFusions( CharacterTable( groupname ) ),
r -> r.name ) );
elif attrname = "Maxes" then
tbl:= CharacterTable( groupname );
if HasMaxes( tbl ) then
return Maxes( tbl );
else
return fail;
fi;
elif IsBoundGlobal( attrname ) then
# We assume that there is a (default) value.
return ValueGlobal( attrname )( CharacterTable( groupname ) );
else
# We have no idea what to do.
return fail;
fi;
end;
#############################################################################
##
#F CTblLib.CompareAsNumbersAndNonnumbers( <nam1>, <nam2> )
##
## This is a copy of `BrowseData.CompareAsNumbersAndNonnumbers'.
##
CTblLib.CompareAsNumbersAndNonnumbers:= function( nam1, nam2 )
local len1, len2, len, digit, comparenumber, i;
len1:= Length( nam1 );
len2:= Length( nam2 );
len:= len1;
if len2 < len then
len:= len2;
fi;
digit:= false;
comparenumber:= 0;
for i in [ 1 .. len ] do
if nam1[i] in DIGITS then
if nam2[i] in DIGITS then
digit:= true;
if comparenumber = 0 then
# first digit of a number, or previous digits were equal
if nam1[i] < nam2[i] then
comparenumber:= 1;
elif nam1[i] <> nam2[i] then
comparenumber:= -1;
fi;
fi;
else
# if digit then the current number in `nam2' is shorter,
# so `nam2' is smaller;
# if not digit then a number starts in `nam1' but not in `nam2',
# so `nam1' is smaller
return not digit;
fi;
elif nam2[i] in DIGITS then
# if digit then the current number in `nam1' is shorter,
# so `nam1' is smaller;
# if not digit then a number starts in `nam2' but not in `nam1',
# so `nam2' is smaller
return digit;
else
# both characters are non-digits
if digit then
# first evaluate the current numbers (which have the same length)
if comparenumber = 1 then
# nam1 is smaller
return true;
elif comparenumber = -1 then
# nam2 is smaller
return false;
fi;
digit:= false;
fi;
# now compare the non-digits
if nam1[i] <> nam2[i] then
return nam1[i] < nam2[i];
fi;
fi;
od;
if digit then
# The suffix of the shorter string is a number.
# If the longer string continues with a digit then it is larger,
# otherwise the first digits of the number decide.
if len < len1 and nam1[ len+1 ] in DIGITS then
# nam2 is smaller
return false;
elif len < len2 and nam2[ len+1 ] in DIGITS then
# nam1 is smaller
return true;
elif comparenumber = 1 then
# nam1 is smaller
return true;
elif comparenumber = -1 then
# nam2 is smaller
return false;
fi;
fi;
# Now the longer string is larger.
return len1 < len2;
end;
##############################################################################
##
#F CTblLib.MaxesInfoTable( <groupname>, <zero> )
##
## `CTblLib.MaxesInfoTable' returns a "datatable" record
## with information about the available character tables of
## maximal subgroups of the group <groupname>.
## If the `Maxes' info for <groupname> is not available then the names of
## the form `<groupname>M<i>' are considered.
##
CTblLib.MaxesInfoTable := function( groupname, zero )
local maxes, size, matrix, title, i, maxname, maxsize;
maxes:= CTblLib.TableValue( groupname, "Maxes" );
size:= CTblLib.TableValue( groupname, "Size" );
matrix:= [];
if maxes = fail then
# List those maxes that are known as such.
title:= "Some maximal subgroups";
for i in [ 1 .. 100 ] do
maxname:= Concatenation( groupname, "M", String( i ) );
maxname:= LibInfoCharacterTable( maxname );
if maxname <> fail then
maxname:= maxname.firstName;
maxsize:= CTblLib.TableValue( maxname, "Size" );
Add( matrix, [
String( i ),
String( maxsize ),
String( size / maxsize ),
rec( type:= "linkedtext",
display:= StructureDescriptionCharacterTableName(
maxname ),
target:= [ "details page", [ maxname, 0 ] ] ),
rec( type:= "linkedtext",
display:= maxname,
target:= [ "details page", [ maxname, 0 ] ] ) ] );
fi;
od;
else
# Loop over the maxes.
title:= "Maximal subgroups";
for maxname in maxes do
maxsize:= CTblLib.TableValue( maxname, "Size" );
Add( matrix, [ String( Length( matrix ) + 1 ),
String( maxsize ),
String( size / maxsize ),
rec( type:= "linkedtext",
display:= StructureDescriptionCharacterTableName(
maxname ),
target:= [ "details page", [ maxname, 0 ] ] ),
rec( type:= "linkedtext",
display:= maxname,
target:= [ "details page", [ maxname, 0 ] ] ) ] );
od;
fi;
if IsEmpty( matrix ) then
return fail;
fi;
return rec( type:= "datatable",
title:= title,
header:= [ "", "Order", "Index", "Structure", "Name" ],
matrix:= matrix,
colalign:= [ "right", "right", "right", "left", "left" ] );
end;
##############################################################################
##
#F CTblLib.SylowNormalizerInfoTable( <groupname>, <zero> )
##
## `CTblLib.SylowNormalizerInfoTable' returns a "datatable" record
## with information about the available character tables of
## Sylow normalizers of the group <groupname>.
##
CTblLib.SylowNormalizerInfoTable := function( groupname, zero )
local size, matrix, p, name, sylnosize;
size:= CTblLib.TableValue( groupname, "Size" );
matrix:= [];
# Get the tables of the known Sylow normalizers.
for p in PrimeDivisors( size ) do
name:= LibInfoCharacterTable(
Concatenation( groupname, "N", String( p ) ) );
if name <> fail then
name:= name.firstName;
sylnosize:= CTblLib.TableValue( name, "Size" );
Add( matrix, [ String( p ),
String( sylnosize ),
String( size / sylnosize ),
rec( type:= "linkedtext",
display:= StructureDescriptionCharacterTableName(
name ),
target:= [ "details page", [ name, 0 ] ] ),
rec( type:= "linkedtext",
display:= name,
target:= [ "details page", [ name, 0 ] ] ) ] );
fi;
od;
if IsEmpty( matrix ) then
return fail;
fi;
return rec( type:= "datatable",
title:= "Stored Sylow p normalizers",
header:= [ "p", "Order", "Index", "Structure", "Name" ],
matrix:= matrix,
colalign:= [ "right", "right", "right", "left", "left" ] );
end;
##############################################################################
##
#F CTblLib.BrauerTableInfoTable( <groupname>, <zero> )
##
## `CTblLib.BrauerTableInfoTable' returns a "datatable" record
## with information about the available Brauer character tables of
## the group <groupname>.
##
CTblLib.BrauerTableInfoTable:= function( groupname, zero )
local size, matrix, t, p, modtbl;
size:= CTblLib.TableValue( groupname, "Size" );
matrix:= [];
t:= CharacterTable( groupname );
# Get the tables of the available Brauer tables.
for p in PrimeDivisors( size ) do
modtbl:= t mod p;
if modtbl <> fail then
Add( matrix, [
String( p ),
rec( type:= "linkedtext",
display:= "details",
target:= [ "details page", [ groupname, p ] ] ),
rec( type:= "linkedtext",
display:= "show table",
target:= [ "show table", [ groupname, p ] ] ),
rec( type:= "linkedtext",
display:= "show dec. matrix",
target:= [ "dec. matrix", [ groupname, p, 0 ] ] ) ] );
fi;
od;
if IsEmpty( matrix ) then
return fail;
fi;
return rec( type:= "datatable",
title:= "Available Brauer tables",
header:= [ "p", "", "", "" ],
matrix:= matrix,
colalign:= [ "right", "left", "left", "left" ] );
end;
##############################################################################
##
#F CTblLib.AtlasRepInfoLink( <groupname>, <zero> )
##
## `CTblLib.AtlasRepInfoLink' returns a "linkedtext" record if the package
## `AtlasRep' is available and provides representations of <groupname>;
## the purpose is to allow one to navigate to the AtlasRep overview.
##
CTblLib.AtlasRepInfoLink:= function( groupname, zero )
local func, n;
if not IsBoundGlobal( "AllAtlasGeneratingSetInfos" ) then
return fail;
fi;
func:= ValueGlobal( "AllAtlasGeneratingSetInfos" );
n:= Length( CallFuncList( func, [ groupname ] ) );
if n = 0 then
return fail;
fi;
return rec( type:= "linkedtext",
title:= "Atlas representations",
display:= Concatenation( String( n ), " available" ),
target:= [ "AtlasRep overview", [ groupname ] ] );
end;
##############################################################################
##
#F CTblLib.GroupInfoList( <groupname>, <zero> )
##
## `CTblLib.GroupInfoList' returns a "datalist" record
## with information about the known group constructions of
## the group <groupname>.
##
CTblLib.GroupInfoList:= function( groupname, zero )
local grps, i, factors, genericnam, genericfun, entry, pos;
grps:= GroupInfoForCharacterTable( groupname );
if IsEmpty( grps ) then
return fail;
fi;
grps:= ShallowCopy( grps );
for i in [ 1 .. Length( grps ) ] do
if grps[i][1] = "DirectProductByNames" then
factors:= [];
genericnam:= [ "Cyclic", "Alternating", "Symmetric", "Dihedral" ];
genericfun:= [ "C", "A", "S", "D" ];
for entry in grps[i][2] do
if Length( entry ) = 1 then
Add( factors, entry[1] );
elif Length( entry ) = 2 and IsPosInt( entry[2] ) then
pos:= Position( genericnam, entry[1] );
if pos = fail then
Add( factors, fail );
else
Add( factors,
Concatenation( genericfun[ pos ], String( entry[2] ) ) );
fi;
else
Add( factors, fail );
fi;
od;
if fail in factors then
Unbind( grps[i] );
else
grps[i]:= [ "DirectProduct", factors ];
fi;
fi;
od;
grps:= Compacted( grps );
Sort( grps ); # sort here in order to get increasing degrees etc.
grps:= List( grps, x -> [ x[1], String( x[2] ) ] );
grps:= List( grps, x -> Concatenation( x[1], "(",
x[2]{ [ 2 .. Length( x[2] )-1 ] }, ")" ) );
return rec( type:= "datalist",
title:= "Group constructions in GAP",
list:= grps,
colalign:= [ "left" ] );
end;
##############################################################################
##
#F CTblLib.FromFusionsInfoList( <groupname>, <zero> )
##
## `CTblLib.FromFusionsInfoList' returns a "datalist" record
## with information about the known class fusions
## from the character table of the group <groupname> to other tables.
##
CTblLib.FromFusionsInfoList:= function( groupname, zero )
local fusions, list, name;
# Get the fusion info.
fusions:= CTblLib.TableValue( groupname, "FusionsTo" );
if IsEmpty( fusions ) then
return fail;
fi;
fusions:= ShallowCopy( fusions );
Sort( fusions, CTblLib.CompareAsNumbersAndNonnumbers );
list:= [];
# Loop over the fusions.
for name in fusions do
Add( list, rec( type:= "linkedtext",
display:= name,
target:= [ "details page", [ name, 0 ] ] ) );
od;
return rec( type:= "datalist",
title:= "Stored class fusions from this table",
list:= list );
end;
##############################################################################
##
#F CTblLib.NamesOfFusionSourcesInfoList( <groupname>, <zero> )
##
## `CTblLib.NamesOfFusionSourcesInfoList' returns a "datalist" record
## with information about the known class fusions
## from other character tables to that of the group <groupname>.
##
CTblLib.NamesOfFusionSourcesInfoList:= function( groupname, zero )
local fusions, list, name;
# Get the fusion info.
fusions:= CTblLib.TableValue( groupname, "NamesOfFusionSources" );
if IsEmpty( fusions ) then
return fail;
fi;
fusions:= ShallowCopy( fusions );
Sort( fusions, CTblLib.CompareAsNumbersAndNonnumbers );
list:= [];
# Loop over the fusions.
for name in fusions do
Add( list, rec( type:= "linkedtext",
display:= name,
target:= [ "details page", [ name, 0 ] ] ) );
od;
return rec( type:= "datalist",
title:= "Stored class fusions to this table",
list:= list );
end;
##############################################################################
##
#F CTblLib.BlocksInfoTable( <groupname>, <p> )
##
## `CTblLib.BlocksInfoTable' returns a "datatable" record
## with information about the <p>-blocks of the group <groupname>.
##
CTblLib.BlocksInfoTable:= function( groupname, p )
local matrix, t, modtbl, info, i, row;
matrix:= [];
t:= CharacterTable( groupname );
modtbl:= t mod p;
if modtbl = fail then
#T we could show the numbers of ordinary/Brauer characters per block
return fail;
fi;
info:= BlocksInfo( modtbl );
for i in [ 1 .. Length( info ) ] do
row:= [ String( i ), String( info[i].defect ) ];
if info[i].defect = 0 then
row[3]:= Concatenation( "chi_", String( info[i].ordchars[1] ),
", phi_", String( info[i].modchars[1] ) );
else
row[3]:= rec( type:= "linkedtext",
display:= Concatenation(
String( Length( info[i].ordchars ) ), " x ",
String( Length( info[i].modchars ) ) ),
target:= [ "dec. matrix", [ groupname, p, i ] ] );
fi;
Add( matrix, row );
od;
return rec( title:= "p-blocks",
type:= "datatable",
header:= [ "nr", "defect", "matrix" ],
matrix:= matrix,
colalign:= [ "right", "right", "left" ] );
end;
##############################################################################
##
#V CTblLib.OrdinaryTableInfo
#V CTblLib.BrauerTableInfo
##
## `CTblLib.OrdinaryTableInfo' is a list of functions that describe the
## parts of information shown by `BrowseCTblLibInfo' and
## `StringCTblLibInfo'.
#T and also by the HTML file generator `HTMLCreateGroupInfoFile'
##
CTblLib.OrdinaryTableInfo:= [
# The group order shall be displayed as number and in factored form.
function( groupname, zero )
return rec( title:= "Group order",
type:= "factored order",
value:= CTblLib.TableValue( groupname, "Size" ) );
end,
# The number of classes shall be displayed.
function( groupname, zero )
return rec( title:= "Number of classes",
type:= "string",
value:= String( CTblLib.TableValue( groupname,
"NrConjugacyClasses" ) ) );
end,
# The `InfoText' value shall be displayed.
function( groupname, zero )
return rec( title:= "InfoText value",
type:= "string",
value:= CTblLib.TableValue( groupname, "InfoText" ) );
end,
# Display info about maximal subgroups if available.
CTblLib.MaxesInfoTable,
# Display info about Sylow normalizers if available.
CTblLib.SylowNormalizerInfoTable,
# Display the available Brauer tables.
CTblLib.BrauerTableInfoTable,
# Display the link to AtlasRep if available.
CTblLib.AtlasRepInfoLink,
# Display the GroupInfo values.
CTblLib.GroupInfoList,
# The fusions on this table shall be mentioned.
CTblLib.FromFusionsInfoList,
# The fusions to this table shall be mentioned.
CTblLib.NamesOfFusionSourcesInfoList,
];
CTblLib.BrauerTableInfo:= [
# The group order shall be displayed as number and in factored form.
function( groupname, p )
return rec( title:= "Group order",
type:= "factored order",
value:= CTblLib.TableValue( groupname, "Size" ) );
end,
# The number of p-regular classes shall be displayed.
function( groupname, p )
local t;
t:= CharacterTable( groupname );
return rec( title:= "Number of p-regular classes",
type:= "string",
value:= Concatenation( String( Length(
Filtered( OrdersClassRepresentatives( t ),
x -> x mod p <> 0 ) ) ),
" out of ",
String( NrConjugacyClasses( t ) ) ) );
end,
# Information about p-blocks shall be displayed.
CTblLib.BlocksInfoTable,
];
#############################################################################
##
## 1. Transform the info into a plain string.
##
##############################################################################
##
#F StringStandardTable( <obj> )
##
StringStandardTable:= function( obj )
local width, colwidths, row, j, totalwidth, hlines, hlinem, hlinee,
str, left, mid, right, n, res, header, matrix, frow;
width:= function( entry )
if IsString( entry ) then
return Length( entry );
else
return Length( entry.display );
fi;
end;
# Compute column widths.
if IsBound( obj.header ) then
colwidths:= List( obj.header, width );
else
colwidths:= ListWithIdenticalEntries( Length( obj.matrix[1] ), 0 );
fi;
for row in obj.matrix do
for j in [ 1 .. Length( row ) ] do
colwidths[j]:= Maximum( colwidths[j], width( row[j] ) );
od;
od;
totalwidth:= Sum( colwidths, 0 ) + 4 + 3 * ( Length( colwidths ) - 1 );
n:= Length( colwidths );
if not CTblLib.ShowOnlyASCII() then
mid:= List( colwidths, i -> RepeatedUTF8String( "─", i ) );
hlines:= Concatenation( "┌─",
JoinStringsWithSeparator( mid, "─┬─" ), "─┐" );
hlinem:= Concatenation( "├─",
JoinStringsWithSeparator( mid, "─┼─" ), "─┤" );
hlinee:= Concatenation( "└─",
JoinStringsWithSeparator( mid, "─┴─" ), "─┘" );
left:= "│ ";
mid:= " │ ";
right:= " │";
else
hlines:= RepeatedString( '-', totalwidth );
hlinem:= hlines;
hlinee:= hlines;
left:= "| ";
mid:= " | ";
right:= " |";
fi;
for j in [ 1 .. n ] do
if obj.colalign[j] = "left" then
colwidths[j]:= -colwidths[j];
fi;
od;
res:= [ hlines ];
if IsBound( obj.header ) then
header:= List( [ 1 .. n ],
i -> String( CTblLib.StringRender( obj.header[i] ),
colwidths[i] ) );
Add( res, Concatenation( left,
JoinStringsWithSeparator( header, mid ), right ) );
Add( res, hlinem );
fi;
for row in obj.matrix do
frow:= List( [ 1 .. n ],
i -> String( CTblLib.StringRender( row[i] ),
colwidths[i] ) );
Add( res, Concatenation( left,
JoinStringsWithSeparator( frow, mid ), right ) );
od;
Add( res, hlinee );
return res;
end;
##############################################################################
##
#F CTblLib.StringRender( <obj> )
##
CTblLib.StringRender:= function( obj )
local len, list, str, pos, i, entry, lentry;
if IsString( obj ) then
return obj;
elif not ( IsRecord( obj ) and IsBound( obj.type ) ) then
Error( "<obj> must be a string or a record with the component `type'" );
fi;
if obj.type = "string" then
return obj.value;
elif obj.type = "linkedtext" then
# Ignore the link information.
return obj.display;
elif obj.type = "datalist" then
# Break the list into lines.
# (In each line, add at least one entry, then fill up.
# Note that `FormatParagraph' would be allowed to add line breaks
# inside entries.)
len:= SizeScreen()[1] - 5;
list:= [];
str:= Concatenation( CTblLib.StringRender( obj.list[1] ), "," );
pos:= Length( str );
for i in [ 2 .. Length( obj.list ) ] do
entry:= CTblLib.StringRender( obj.list[i] );
lentry:= Length( entry ) + 2;
if pos + lentry > len then
Add( list, str );
str:= "";
pos:= 0;
fi;
if pos <> 0 then
Append( str, " " );
pos:= pos + 1;
fi;
Append( str, entry );
Append( str, "," );
pos:= pos + lentry - 1;
od;
Unbind( str[ pos ] );
Add( list, str );
return list;
elif obj.type = "datatable" then
return StringStandardTable( obj );
elif obj.type = "factored order" then
return Concatenation( String( obj.value ), " = ",
StringPP( obj.value ) );
else
Error( "unknown type `", obj.type, "'" );
fi;
end;
##############################################################################
##
#F DisplayCTblLibInfo( <tbl> )
#F DisplayCTblLibInfo( <name>[, <p>] )
#F StringCTblLibInfo( <tbl> )
#F StringCTblLibInfo( <name>[, <p>] )
##
## <#GAPDoc Label="DisplayCTblLibInfo">
## <ManSection>
## <Func Name="DisplayCTblLibInfo" Arg='tbl' Label="for a character table"/>
## <Func Name="DisplayCTblLibInfo" Arg='name[, p]' Label="for a name"/>
## <Func Name="StringCTblLibInfo" Arg='tbl' Label="for a character table"/>
## <Func Name="StringCTblLibInfo" Arg='name[, p]' Label="for a name"/>
##
## <Description>
## When <Ref Func="DisplayCTblLibInfo" Label="for a character table"/>
## is called with an ordinary or modular character table <A>tbl</A> then
## an overview of the information available for this character table
## is shown via the function that is given by the user preference
## <Ref Subsect="subsect:displayfunction"/>.
## When <Ref Func="DisplayCTblLibInfo" Label="for a name"/>
## is called with a string <A>name</A> that is an admissible name for
## an ordinary character table then the overview for this character table
## is shown.
## If a prime integer <A>p</A> is entered in addition to <A>name</A> then
## information about the <A>p</A>-modular character table is shown instead.
## <P/>
## An interactive variant of
## <Ref Func="DisplayCTblLibInfo" Label="for a name"/> is
## <Ref Func="BrowseCTblLibInfo"/>.
## <P/>
## The string that is shown by
## <Ref Func="DisplayCTblLibInfo" Label="for a name"/> can be computed using
## <Ref Func="StringCTblLibInfo" Label="for a name"/>,
## with the same arguments.
## <P/>
## <Example><![CDATA[
## gap> StringCTblLibInfo( CharacterTable( "A5" ) );;
## gap> StringCTblLibInfo( CharacterTable( "A5" ) mod 2 );;
## gap> StringCTblLibInfo( "A5" );;
## gap> StringCTblLibInfo( "A5", 2 );;
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
BindGlobal( "StringCTblLibInfo", function( arg )
local groupname, p, name, title, attr, str, info, fun, val, str2;
if Length( arg ) = 1 and IsCharacterTable( arg[1] ) then
groupname:= Identifier( arg[1] );
p:= UnderlyingCharacteristic( arg[1] );
if p <> 0 then
name:= PartsBrauerTableName( groupname );
if name <> fail then
groupname:= name.ordname;
fi;
fi;
elif Length( arg ) = 1 and IsString( arg[1] ) then
groupname:= arg[1];
p:= 0;
elif Length( arg ) = 2 and IsString( arg[1] ) and IsPosInt( arg[2] ) then
groupname:= arg[1];
p:= arg[2];
else
Error( "usage: StringCTblLibInfo( <tbl> ) or\n",
" StringCTblLibInfo( <name>[, <p>] )" );
fi;
name:= LibInfoCharacterTable( groupname );
if name = fail then
return "";
fi;
groupname:= name.firstName;
# Construct the information about `groupname'.
title:= Concatenation( "Character Table info for ", groupname );
if p <> 0 then
Append( title, Concatenation( " mod ", String( p ) ) );
fi;
# header line
attr:= IsBound( TextAttr ) and IsRecord( TextAttr );
if attr then
str:= ShallowCopy( TextAttr.underscore );
else
str:= "";
fi;
Append( str, title );
if attr then
Append( str, TextAttr.reset );
fi;
Append( str, "\n\n" );
if p = 0 then
info:= CTblLib.OrdinaryTableInfo;
else
info:= CTblLib.BrauerTableInfo;
fi;
for fun in info do
val:= fun( groupname, p );
if val <> fail then
if attr then
Append( str, TextAttr.bold );
fi;
Append( str, val.title );
Append( str, ":" );
if attr then
Append( str, TextAttr.reset );
fi;
Append( str, "\n " );
str2:= CTblLib.StringRender( val );
if IsString( str2 ) then
str2:= ReplacedString( str2, "\n", "\n " );
else
str2:= JoinStringsWithSeparator( str2, "\n " );
fi;
Append( str, str2 );
Append( str, "\n\n" );
fi;
od;
return str;
end );
BindGlobal( "DisplayCTblLibInfo", function( arg )
local str, width, fun;
str:= CallFuncList( StringCTblLibInfo, arg );
if str <> "" then
width:= SizeScreen()[1] - 2;
if CTblLib.ShowOnlyASCII() then
str:= List( SplitString( str, "\n" ),
l -> InitialSubstringUTF8String( l, width, "*" ) );
else
str:= List( SplitString( str, "\n" ),
l -> InitialSubstringUTF8String( l, width, "⋯" ) );
fi;
fun:= EvalString( UserPreference( "AtlasRep", "DisplayFunction" ) );
fun( JoinStringsWithSeparator( str, "\n" ) );
fi;
end );
#############################################################################
##
#E
|
