This file is indexed.

/usr/share/gap/lib/matblock.gi is in gap-libs 4r6p5-3.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
#############################################################################
##
#W  matblock.gi                 GAP Library                  Alexander Hulpke
##
##
#Y  Copyright (C)  1997,  Lehrstuhl D für Mathematik,  RWTH Aachen,  Germany
#Y  (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y  Copyright (C) 2002 The GAP Group
##
##  This file contains the implementation of methods for block matrices.
##


#############################################################################
##
#R  IsBlockMatrixRep( <mat> )
##
##  A matrix in this representation is described by the following data.
##
##  \beginitems
##  `blocks' &
##       an ordered list of triples $[ i, j, m ]$ where $m$ is a matrix
##       (possibly again a block matrix) with `rb' rows and `cb' columns
##       that is in the $i$-th row block and in the $j$-th column block
##       of the matrix <mat>,
##
##  `nrb' &
##       number of row blocks,
##
##  `ncb' &
##       number of column blocks,
##
##  `rpb' &
##       rows per block,
##
##  `cpb' &
##       columns per block,
##
##  `zero' &
##       the zero element that is stored in all places of the matrix
##       outside the blocks in `blocks'.
##  \enditems
##
DeclareRepresentation( "IsBlockMatrixRep",
    IsComponentObjectRep,
    [ "blocks", "zero", "nrb", "ncb", "rpb", "cpb" ] );


#############################################################################
##
#F  BlockMatrix( <blocks>, <nrb>, <ncb> )
#F  BlockMatrix( <blocks>, <nrb>, <ncb>, <rpb>, <cpb>, <zero> )
##
InstallGlobalFunction( BlockMatrix, function( arg )
    local blocks, nrb, ncb, rpb, cpb, zero, dims, newblocks, block, i;

    # Check and get the arguments.
    if Length( arg ) < 3 or not
       ( IsList( arg[1] ) and IsInt( arg[2] ) and IsInt( arg[3] ) ) then
      Error( "need at least <blocks>, <nrb>, <ncb>" );
    fi;

    blocks := arg[1];
    nrb    := arg[2];
    ncb    := arg[3];

    if Length( arg ) = 3 then
      if IsEmpty( blocks ) then
        Error( "need <rpb>, <cpb>, <zero> if <blocks> is empty" );
      fi;
      rpb  := Length( blocks[1][3] );
      cpb  := Length( blocks[1][3][1] );
      zero := Zero( blocks[1][3][1][1] );
    elif Length( arg ) = 6 then
      rpb  := arg[4];
      cpb  := arg[5];
      zero := arg[6];
    else
      Error("usage: BlockMatrix(<blocks>,<nrb>,<ncb>[,<rpb>,<cpb>,<zero>])");
    fi;

    if not ( IsInt(rpb) and IsInt(cpb) and IsInt(nrb) and IsInt(ncb) ) then
      Error( "block matrices must be finite" );
    fi;
    dims:= [ rpb, cpb ];

    # Remove zero blocks, and sort the list of blocks.
    newblocks:= [];
    for block in blocks do
      if IsBlockMatrixRep( block[3] ) or not IsZero( block[3] ) then
        if DimensionsMat( block[3] ) <> dims then
          Error( "all blocks must have the same dimensions" );
        fi;
        Add( newblocks, block );
      fi;
    od;
    Sort( newblocks, IsLexicographicallyLess );
    i:=1;
    while i+1<=Length(newblocks) do
      if newblocks[i][1] = newblocks[ i+1 ][1] and
         newblocks[i][2] = newblocks[ i+1 ][2] then

        #Error( "two blocks for position [", newblocks[i][1], "][",
        #       newblocks[i][2], "]" );
	newblocks:=Concatenation(newblocks{[1..i-1]},
	     [[newblocks[i][1],newblocks[i][2],
	       newblocks[i][3]+newblocks[i+1][3]]],
	     newblocks{[i+2..Length(newblocks)]});
      else
	i:=i+1;
      fi;
    od;

    # Construct and return the block matrix.
    return Objectify( NewType( CollectionsFamily( CollectionsFamily(
                                   FamilyObj( zero ) ) ),
                                   IsOrdinaryMatrix
                               and IsMultiplicativeGeneralizedRowVector
                               and IsBlockMatrixRep
                               and IsCopyable
                               and IsFinite ),
                      rec( blocks := Immutable( newblocks ),
                           zero   := zero,
                           nrb    := nrb,
                           ncb    := ncb,
                           rpb    := rpb,
                           cpb    := cpb ) );
end );


#############################################################################
##
#M  Length( <blockmat> )  . . . . . . . . . . . . . . . .  for a block matrix
##
InstallMethod( Length,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ],
    blockmat -> blockmat!.nrb * blockmat!.rpb );


#############################################################################
##
#M  \[\]( <blockmat>, <n> ) . . . . . . . . . . . . . . .  for a block matrix
##
InstallMethod( \[\],
    "for an ordinary block matrix and a positive integer",
    [ IsOrdinaryMatrix and IsBlockMatrixRep, IsPosInt ],
    function( blockmat, n )
    local qr, i, ii, row, block, j;

    # `n-1 = qr[1] * blockmat!.rpb + qr[2]'.
    qr:= QuotientRemainder( Integers, n-1, blockmat!.rpb );
    i:= qr[1] + 1;
    ii:= qr[2] + 1;

    row:= ListWithIdenticalEntries( blockmat!.cpb * blockmat!.ncb,
                                    blockmat!.zero );
    for block in blockmat!.blocks do
      if block[1] = i then
        j:= block[2];
        row{ [ (j-1)*blockmat!.cpb + 1 .. j*blockmat!.cpb ] }:= block[3][ii];
      elif i < block[1] then
        break;
      fi;
    od;

    return row;
    end );


#############################################################################
##
#M  TransposedMat( <blockmat> ) . . . . . . . . . . . . .  for a block matrix
##
InstallMethod( TransposedMat,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ],
    m -> BlockMatrix( List( m!.blocks, i -> [ i[2], i[1],
                                              TransposedMat( i[3] ) ] ),
                      m!.ncb,
                      m!.nrb,
                      m!.cpb,
                      m!.rpb,
                      m!.zero ) );


#############################################################################
##
#M  MatrixByBlockMatrix( <blockmat> ) . . . create matrix from (block) matrix
##
InstallMethod( MatrixByBlockMatrix,
    [ IsMatrix ],
    function( blockmat )
    local mat, block, i, j;

    if not IsOrdinaryMatrix( blockmat ) then
      Error( "<blockmat> must be an ordinary matrix" );
    elif not IsBlockMatrixRep( blockmat ) then
      mat:= blockmat;
    else

      mat:= NullMat( blockmat!.nrb * blockmat!.rpb,
                     blockmat!.ncb * blockmat!.cpb,
                     blockmat!.zero );
      for block in blockmat!.blocks do
        i:= block[1];
        j:= block[2];
        mat{ [ (i-1)*blockmat!.rpb+1 .. i*blockmat!.rpb ] }{
             [ (j-1)*blockmat!.cpb+1 .. j*blockmat!.cpb ] }:=
              MatrixByBlockMatrix( block[3] );
      od;

    fi;

    return mat;
end );


#############################################################################
##
#F  AsBlockMatrix( <m>, <nrb>, <ncb> )  . . . create block matrix from matrix
##
InstallGlobalFunction( AsBlockMatrix, function( mat, nrb, ncb )
    local rpb, cpb, blocks, i, ii, j, jj, block;

    if not IsOrdinaryMatrix( mat ) or IsEmpty( mat ) then
      Error( "<mat> must be a nonempty ordinary matrix" );
    fi;

    rpb:= Length( mat ) / nrb;
    cpb:= Length( mat[1] ) / ncb;
    if not ( IsInt( rpb ) and IsInt( cpb ) ) then
      Error( "<nrb> and <ncb> must divide the dimensions of <mat>" );
    fi;

    blocks:= [];
    for i in [ 1 .. nrb ] do
      ii:= (i-1) * rpb;
      for j in [ 1 .. ncb ] do
        jj:= (j-1) * cpb;
        block:= mat{ [ ii+1 .. ii+cpb ] }{ [ jj+1 .. jj+rpb ] };
        if not IsZero( block ) then
          Add( blocks, [ i, j, block ] );
        fi;
      od;
    od;

    return BlockMatrix( blocks, nrb, ncb, rpb, cpb, Zero( mat[1][1] ) );
end );


#############################################################################
##
##  arithmetic operations for block matrices
##

#############################################################################
##
#M  \=( <bm1>, <bm2> )  . . . . . . . . . . . . . . .  for two block matrices
##
InstallMethod( \=,
    "for two ordinary block matrices",
    IsIdenticalObj,
    [ IsOrdinaryMatrix and IsBlockMatrixRep,
      IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( bm1, bm2 )
    if     bm1!.nrb = bm2!.nrb
       and bm1!.ncb = bm2!.ncb
       and bm1!.rpb = bm2!.rpb
       and bm1!.cpb = bm2!.cpb then
      return bm1!.blocks = bm2!.blocks;
    else
      TryNextMethod();
    fi;
    end );


#############################################################################
##
#M  \+( <bm1>, <bm2> )  . . . . . . . . . . . . . . .  for two block matrices
##
InstallMethod( \+,
    "for two ordinary block matrices",
    IsIdenticalObj,
    [ IsOrdinaryMatrix and IsBlockMatrixRep,
      IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( bm1, bm2 )
    local blocks, pos, i;

    if     bm1!.nrb = bm2!.nrb
       and bm1!.ncb = bm2!.ncb
       and bm1!.rpb = bm2!.rpb
       and bm1!.cpb = bm2!.cpb then

      blocks:= Concatenation( bm1!.blocks, bm2!.blocks );
      Sort( blocks, IsLexicographicallyLess );
      pos:= 1;
      i:= 1;
      while i < Length( blocks ) do
        blocks[ pos ]:= blocks[i];
        if blocks[i][1] = blocks[ i+1 ][1] and
           blocks[i][2] = blocks[ i+1 ][2] then
          blocks[ pos ]:= ShallowCopy( blocks[ pos ] );
          blocks[ pos ][3]:= blocks[i][3] + blocks[ i+1 ][3];
          i:= i+1;
        fi;
        i:= i+1;
        pos:= pos+1;
      od;
      if i = Length( blocks ) then
        blocks[ pos ]:= blocks[i];
        pos:= pos+1;
      fi;
      for i in [ pos .. Length( blocks ) ] do
        Unbind( blocks[i] );
      od;
      return BlockMatrix( blocks, bm1!.nrb, bm1!.ncb, bm1!.rpb, bm1!.cpb,
                          bm1!.zero );

    else
      TryNextMethod();
    fi;
    end );


#############################################################################
##
#M  \+( <bm>, <grv> ) . . . . . . . . . . . . . . .  for block matrix and grv
#M  \+( <grv>, <bm> ) . . . . . . . . . . . . . . .  for grv and block matrix
##
InstallOtherMethod( \+,
    "for an ordinary block matrix, and a grv",
    IsIdenticalObj,
    [ IsOrdinaryMatrix and IsBlockMatrixRep, IsGeneralizedRowVector ],
    function( bm, grv )
    return MatrixByBlockMatrix( bm ) + grv;
    end );

InstallOtherMethod( \+,
    "for a grv, and an ordinary block matrix",
    IsIdenticalObj,
    [ IsGeneralizedRowVector, IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( grv, bm )
    return grv + MatrixByBlockMatrix( bm );
    end );


#############################################################################
##
#M  AdditiveInverseOp( <blockmat> ) . . . . . . . . . . .  for a block matrix
##
##  We can't do better than the default method for AdditiveInverseOp,
##  since that has to produce a mutable result
##
InstallMethod( AdditiveInverseOp,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ],
    bm -> BlockMatrix( List( bm!.blocks,
                             b -> [ b[1], b[2], AdditiveInverse( b[3] ) ] ),
                       bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, bm!.zero ) );


#############################################################################
##
#M  \*( <bm1>, <bm2> )  . . . . . . . . . . . . . . .  for two block matrices
#M  \*( <bm>, <vec> ) . . . . . . . . . . . . . . for block matrix and vector
#M  \*( <vec>, <bm> ) . . . . . . . . . . . . . . for vector and block matrix
#M  \*( <bm>, <c> ) . . . . . . . . . . . . for block matrix and ring element
#M  \*( <c>, <bm> ) . . . . . . . . . . . . for ring element and block matrix
##
InstallMethod( \*,
    "for two ordinary block matrices",
    IsIdenticalObj,
    [ IsOrdinaryMatrix and IsBlockMatrixRep,
      IsOrdinaryMatrix and IsBlockMatrixRep ], 6,
    # being a block matrix is better than being a small list
    function( bm1, bm2 )
    local blocks, b1, b2, pos, i;

    if     bm1!.ncb = bm2!.nrb and bm1!.cpb = bm2!.rpb then

      # Get the blocks of the product.
      blocks:= [];
      for b1 in bm1!.blocks do
        for b2 in bm2!.blocks do
          if b1[2] = b2[1] then
            Add( blocks, [ b1[1], b2[2], b1[3] * b2[3] ] );
          fi;
        od;
      od;

      # Put blocks at the same position together.
      pos:= 1;
      i:= 1;
      while i < Length( blocks ) do
        blocks[ pos ]:= blocks[i];
        if blocks[i][1] = blocks[ i+1 ][1] and
           blocks[i][2] = blocks[ i+1 ][2] then
          blocks[ pos ]:= ShallowCopy( blocks[ pos ] );
          blocks[ pos ][3]:= blocks[i][3] + blocks[ i+1 ][3];
          i:= i+1;
        fi;
        i:= i+1;
        pos:= pos+1;
      od;
      if i = Length( blocks ) then
        blocks[ pos ]:= blocks[i];
        pos:= pos+1;
      fi;
      for i in [ pos .. Length( blocks ) ] do
        Unbind( blocks[i] );
      od;

      # Return the result.
      return BlockMatrix( blocks, bm1!.nrb, bm2!.ncb, bm1!.rpb, bm2!.cpb,
                          bm1!.zero );

    else
      TryNextMethod();
    fi;
    end );

InstallMethod( \*,
    "for ordinary block matrix and vector",
    IsCollsElms,
    [ IsOrdinaryMatrix and IsBlockMatrixRep, IsRowVector ],
    function( bm, vec )
    local cpb, rpb, ncols, nrows, vector, block, i, j;

    cpb:= bm!.cpb;
    rpb:= bm!.rpb;
    ncols:= bm!.ncb * cpb;
    nrows:= bm!.nrb * rpb;
    if Length( vec ) < ncols then
      vec:= Concatenation( vec,
              ListWithIdenticalEntries( ncols - Length( vec ), bm!.zero ) );
#T yes, this can be optimized ...
    fi;

    vector:= ListWithIdenticalEntries( nrows, bm!.zero );
    for block in bm!.blocks do
      i:= block[1];
      j:= block[2];
      vector{ [ (i-1)*rpb+1 .. i*rpb ] }:=
                        vector{ [ (i-1)*rpb+1 .. i*rpb ] } +
                        block[3] * vec{ [ (j-1)*cpb+1 .. j*cpb ] };
    od;

    return vector;
    end );

InstallMethod( \*,
    "for vector and ordinary block matrix",
    IsElmsColls,
    [ IsRowVector, IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( vec, bm )
    local cpb, rpb, ncols, nrows, vector, block, i, j;

    cpb:= bm!.cpb;
    rpb:= bm!.rpb;
    ncols:= bm!.ncb * cpb;
    nrows:= bm!.nrb * rpb;
    if Length( vec ) < nrows then
      vec:= Concatenation( vec,
              ListWithIdenticalEntries( nrows - Length( vec ), bm!.zero ) );
#T yes, this can be optimized ...
    fi;

    vector:= ListWithIdenticalEntries( ncols, bm!.zero );
    for block in bm!.blocks do
      i:= block[1];
      j:= block[2];
      vector{ [ (j-1)*cpb+1 .. j*cpb ] }:=
                        vector{ [ (j-1)*cpb+1 .. j*cpb ] } +
                        vec{ [ (i-1)*rpb+1 .. i*rpb ] } * block[3];
    od;

    return vector;
    end );

InstallMethod( \*,
    "for ordinary block matrix and ring element",
    IsCollCollsElms,
    [ IsOrdinaryMatrix and IsBlockMatrixRep, IsRingElement ],
    function( bm, c )
    return BlockMatrix( List( bm!.blocks,
                              b -> [ b[1], b[2], b[3] * c ] ),
                        bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, bm!.zero );
    end );

InstallMethod( \*,
    "for ring element and ordinary block matrix",
    IsElmsCollColls,
    [ IsRingElement, IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( c, bm )
    return BlockMatrix( List( bm!.blocks,
                              b -> [ b[1], b[2], c * b[3] ] ),
                        bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, bm!.zero );
    end );


#############################################################################
##
#M  \*( <bm>, <n> ) . . . . . . . . . . . . . .  for block matrix and integer
#M  \*( <n>, <bm> ) . . . . . . . . . . . . . .  for integer and block matrix
##
InstallMethod( \*,
    "for ordinary block matrix and integer",
    [ IsOrdinaryMatrix and IsBlockMatrixRep, IsInt ],
    function( bm, n )
    return BlockMatrix( List( bm!.blocks,
                              b -> [ b[1], b[2], b[3] * n ] ),
                        bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, bm!.zero );
    end );

InstallMethod( \*,
    "for integer and ordinary block matrix",
    [ IsInt, IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( n, bm )
    return BlockMatrix( List( bm!.blocks,
                              b -> [ b[1], b[2], n * b[3] ] ),
                        bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, bm!.zero );
    end );


#############################################################################
##
#M  \*( <bm>, <z> ) . . . . . . . . . . . .  for integer block matrix and ffe
#M  \*( <z>, <bm> ) . . . . . . . . . . . .  for ffe and integer block matrix
##
InstallMethod( \*,
    "for ordinary block matrix of integers and ffe",
    [ IsOrdinaryMatrix and IsBlockMatrixRep and IsCyclotomicCollColl,
      IsFFE ],
    function( bm, z )
    return BlockMatrix( List( bm!.blocks,
                              b -> [ b[1], b[2], b[3] * z ] ),
                        bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, Zero( z ) );
    end );

InstallMethod( \*,
    "for ffe and ordinary block matrix of integers",
    [ IsFFE,
      IsOrdinaryMatrix and IsBlockMatrixRep and IsCyclotomicCollColl ],
    function( z, bm )
    return BlockMatrix( List( bm!.blocks,
                              b -> [ b[1], b[2], z * b[3] ] ),
                        bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, Zero( z ) );
    end );


#############################################################################
##
#M  \*( <bm>, <mgrv> )  . . . . . . . . . . . . . . for block matrix and mgrv
#M  \*( <mgrv>, <bm> )  . . . . . . . . . . . . . . for mgrv and block matrix
##
InstallOtherMethod( \*,
    "for an ordinary block matrix, and a mgrv",
    IsIdenticalObj,
    [ IsOrdinaryMatrix and IsBlockMatrixRep,
      IsMultiplicativeGeneralizedRowVector ],
    function( bm, grv )
    return MatrixByBlockMatrix( bm ) * grv;
    end );

InstallOtherMethod( \*,
    "for a mgrv, and an ordinary block matrix",
    IsIdenticalObj,
    [ IsMultiplicativeGeneralizedRowVector,
      IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( grv, bm )
    return grv * MatrixByBlockMatrix( bm );
    end );


#############################################################################
##
#M  OneOp( <bm> )  . . . . . . . . . . . . . . . . . . . . for a block matrix
##
InstallOtherMethod( OneOp,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ], 3,
    # being a block matrix is better than being a small list
    function( bm )
    local mat;
    if bm!.nrb = bm!.ncb and bm!.rpb = bm!.cpb then
      if IsEmpty( bm!.blocks ) then
        mat:= Immutable( IdentityMat( bm!.rpb, bm!.zero ) );
      else
        mat:= One( bm!.blocks[1][3] );
      fi;
      return BlockMatrix( List( [ 1 .. bm!.nrb ], i -> [ i, i, mat ] ),
                          bm!.nrb, bm!.ncb, bm!.rpb, bm!.cpb, bm!.zero );
    else
      TryNextMethod();
    fi;
    end );


#############################################################################
##
#M  InverseOp( <bm> )  . . . . . . . . . . . . . . . . . . for a block matrix
##
InstallOtherMethod( InverseOp,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ],
function( bm )
  return AsBlockMatrix(InverseOp(MatrixByBlockMatrix(bm)),bm!.nrb,bm!.ncb);
end );

#############################################################################
##
#M  \^
##
InstallMethod( \^,"for block matrix and integer",
    [ IsOrdinaryMatrix and IsBlockMatrixRep,IsInt ],POW_OBJ_INT);

#############################################################################
##
#M  ViewObj( <blockmat> ) . . . . . . . . . . . . . . . .  for a block matrix
##
InstallMethod( ViewObj,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( m )
    Print( "<block matrix of dimensions (", m!.nrb, "*", m!.rpb,
           ")x(", m!.ncb, "*", m!.cpb, ")>" );
    end );


#############################################################################
##
#M  PrintObj( <blockmat> )  . . . . . . . . . . . . . . .  for a block matrix
##
InstallMethod( PrintObj,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ],
    function( m )
    Print( "BlockMatrix( ", m!.blocks, ",", m!.nrb, ",", m!.ncb,
           ",", m!.rpb, ",", m!.cpb, ",", m!.zero, " )" );
    end );


#############################################################################
##
#M  DimensionsMat( <blockmat> ) . . . . . . . . . . . . .  for a block matrix
##
InstallMethod( DimensionsMat,
    "for an ordinary block matrix",
    [ IsOrdinaryMatrix and IsBlockMatrixRep ],
    m -> [ m!.nrb * m!.rpb, m!.ncb * m!.cpb ] );


#############################################################################
##
#E