#############################################################################
##
#W  tmmath.tom           GAP table of marks library           Thomas Merkwitz
##
#H  @(#)$Id: tmmath.tom,v 4.3 2001/07/05 07:05:41 gap Exp $
##
#Y  Copyright (C)  1997,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
#Y  (C) 1998 School Math and Comp. Sci., University of St.  Andrews, Scotland
##
##  This file contains the table of marks of the Mathieu groups excluding
##  $M24$.
##
#H  tomlib history
#H  --------------
#H  $Log: tmmath.tom,v $
#H  Revision 4.3  2001/07/05 07:05:41  gap
#H  first revision for tomlib
#H
#H
#H  tom history (GAP 4)
#H  -------------------
#H  (Rev. 4.3 of tomlib coincides with Rev. 4.2 of tom in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tom/tmmath.tom,v
#H  Working file: tmmath.tom
#H  head: 4.2
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H  	GAP4R2: 4.2.0.10
#H  	GAP4R2PRE2: 4.2.0.8
#H  	GAP4R2PRE1: 4.2.0.2
#H  	GAP4R1: 4.2.0.6
#H  	GAP4B5: 4.2.0.4
#H  	dec16-98b: 4.2
#H  	GAP4b4: 4.2
#H  	version-14-apr: 4.2
#H  	version-15-jun: 4.2
#H  keyword substitution: kv
#H  total revisions: 3;	selected revisions: 3
#H  description:
#H  ----------------------------
#H  revision 4.2
#H  date: 1998/03/27 15:21:41;  author: gap;  state: Exp;  lines: +16 -2
#H  added some more fusions
#H  T.Merkwitz
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/11/20 11:53:12;  author: gap;  state: Exp;  lines: +2 -2
#H  changed revision number to 4.1
#H  ----------------------------
#H  revision 1.1
#H  date: 1997/11/19 13:20:55;  author: gap;  state: Exp;
#H  added new table of marks library files
#H  ==========================================================================
#H
Revision.tmmath_tom :=
    "@(#)$Id: tmmath.tom,v 4.3 2001/07/05 07:05:41 gap Exp $";

SetActualLibFileName("tmmath");
LIBTOM( "M11",
[[1],[1,2],[1,3],[1,2,4],[1,2,5],[1,6],[1,2,3,7],[1,2,3,8],[1,2,3,9],[1,2,5,
10],[1,2,5,11],[1,2,4,5,12],[1,3,13],[1,2,6,14],[1,15],[1,2,3,4,16],[1,2,3,4,
7,8,9,17],[1,2,4,5,10,11,12,18],[1,2,3,8,13,19],[1,2,3,7,9,13,20],[1,2,5,6,14,
21],[1,2,3,5,9,10,22],[1,2,3,4,5,8,12,16,23],[1,2,3,5,8,13,19,24],[1,2,3,5,8,
13,19,25],[1,2,3,4,7,8,9,13,17,19,20,26],[1,2,3,4,5,7,8,9,10,11,12,17,18,22,
27],[1,6,15,28],[1,2,3,4,6,7,14,16,29],[1,2,3,4,6,8,14,16,30],[1,2,3,5,8,10,
13,19,24,25,31],[1,2,3,4,5,7,8,9,12,13,17,19,20,24,26,32],[1,2,3,5,8,11,13,19,
24,33],[1,2,3,4,5,6,7,8,9,12,14,16,17,21,23,29,34],[1,2,3,4,5,7,8,9,10,11,12,
13,17,18,19,20,24,25,26,31,32,33,35],[1,2,3,4,5,6,8,12,13,14,16,19,23,25,30,
36],[1,2,3,4,6,7,8,9,14,15,16,17,28,29,30,37],[1,2,3,4,5,6,8,10,11,12,13,14,
16,18,19,21,23,24,25,30,31,36,38],[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]],
0,[[1],[1,1],[1,1],[1,3,1],[1,1,1],[1,1],[1,3,1,1],[1,3,1,1],[1,1,1,1],[1,1,3,
1],[1,1,1,1],[1,5,2,1,1],[1,4,1],[1,5,1,1],[1,1],[1,3,4,1,1],[1,7,1,3,1,1,1,
1],[1,5,2,3,1,1,1,1],[1,9,4,12,1,1],[1,3,4,1,3,1,1],[1,5,5,1,1,1],[1,1,4,3,4,
1,1],[1,9,4,4,3,4,3,1,1],[1,9,4,9,12,1,1,1],[1,9,4,9,12,1,1,1],[1,15,4,9,2,12,
6,1,6,1,2,1],[1,13,4,6,3,4,4,4,1,3,3,4,3,1,1],[1,11,1,1],[1,15,10,5,6,10,6,5,
1],[1,15,10,5,6,10,6,5,1],[1,9,4,27,12,9,1,1,1,2,1],[1,21,4,18,9,4,12,12,9,1,
12,1,4,1,2,1],[1,9,4,9,12,9,1,1,1,1],[1,25,10,20,15,6,10,10,10,15,6,5,10,6,5,
1,1],[1,21,4,18,27,4,12,12,9,9,9,1,12,9,1,4,1,2,2,1,1,1,1],[1,45,40,30,45,36,
120,45,10,36,30,10,30,10,12,1],[1,55,55,55,66,55,55,55,66,12,55,55,12,11,11,
1],[1,45,40,30,135,36,120,45,45,45,10,36,30,45,10,36,30,10,20,12,10,1,1],[1,
165,220,330,495,396,220,660,660,165,495,495,55,396,144,330,660,495,55,220,396,
165,330,55,110,110,165,144,66,132,55,55,55,66,55,11,12,11,1]],
[1,2,3,4,4,5,6,6,6,8,8,8,9,10,11,12,12,16,18,18,20,24,24,36,36,36,48,55,60,60,
72,72,72,120,144,360,660,720,7920],
[39,27,26,23,18,21,26,17,17,27,18,18,35,21,28,23,17,18,35,26,21,27,23,35,31,
32,27,28,34,30,35,35,35,34,35,38,37,38,39],
[1,1,1,1,1,1,3,3,1,2,1,2,1,6,1,4,3,5,13,3,6,10,16,13,13,13,22,15,29,30,19,19,
13,29,24,36,37,36,39],
[( 1, 2)( 3, 5)( 4, 9)( 6,10),( 1, 3, 4, 7)( 2,12,10,11)],
[[[[]]],[[[2,-2],[3,1,1,1,2,-2,1,1,3,1]]],[[[1,1,2,1],[1,1,3,-1,2,1,1,1,2,-1,
3,1]]],[[[2,1,1,1,2,-2,1,1,2,-1]],[[1,1,2,1],[2,1,1,1,3,1,2,1,3,1]]],[[[1,1,2,
1],[3,1,2,1,3,2,1,1,2,1,1,1]]],[[[1,1,2,1],[3,1,2,1,3,1,2,1,1,1,3,-2]]],[[[1,
1]],[[1,1,2,1],[1,1,3,-1,2,1,1,1,2,-1,3,1]]],[[[2,-2],[3,1,1,1,2,-2,1,1,3,
1]],[[1,1,2,1],[1,1,3,-1,2,1,1,1,2,-1,3,1]]],[[[1,1,2,1],[3,2,1,1,2,-1,3,-1,2,
-2]]],[[[2,1,1,1],[2,1,3,2,2,1,1,1,2,1]],[[1,1,2,1],[3,1,2,1,3,2,1,1,2,1,1,
1]]],[[[1,1,2,1],[1,1,3,-1,2,1,1,1,2,-2,3,1]]],[[[1,1,2,1],[2,-2,1,1,2,-1,3,2,
2,1]],[[1,1,2,1],[2,1,1,1],[3,2,2,1,4,2,3,-1]]],[[[1,1,2,1],[1,1,3,-1,2,1,1,1,
2,-1,3,1]],[[1,1,2,1],[2,-2,3,1,2,1,1,1,2,1,3,1]]],[[[1,1,2,1],[3,2,2,-2,1,
1]],[[2,-2],[3,1,1,1,2,-2,1,1,3,1]]],[[[2,1,1,1],[1,1,2,-1,3,-2,2,-1]]],[[[2,
-2],[3,1,1,1,2,-2,1,1,3,1]],[[1,1,2,1],[1,1,2,-1,1,1,2,-1,3,-2]]],[[[1,1,2,
1],[3,2,2,-2,1,1]],[[1,1,2,1],[3,1,2,1,1,1,2,-1,3,-1,2,-2]]],[[[2,1,1,1,2,-2,
1,1,2,-1]],[[1,1,2,1],[2,1,1,1],[3,1,2,1,4,-1,3,1,1,1,4,1]]],[[[1,1,2,-1,1,1,
2,1,1,1]],[[1,1,2,1],[2,1,1,1,3,1,2,1,3,1]],[[2,-2],[3,1,1,1,2,-2,1,1,3,
1]]],[[[1,1]],[[1,1,2,1],[2,1,3,1],[3,1,4,2,3,1]]],[[[1,1,2,1],[3,2,2,-2,1,
1]],[[1,1,2,1],[3,1,2,1,3,2,2,1,1,1]]],[[[1,1,2,1],[2,1,1,1],[4,2,3,-1,2,-2,3,
1]],[[1,1,2,1],[2,-2,3,1,1,1,2,-1,3,-1,2,-1,3,-1]]],[[[2,1,1,1],[2,1,3,2,2,1,
1,1,2,1]],[[1,1,2,1],[3,2,2,1,1,1,2,-1,3,-2]]],[[[1,1,2,1],[2,1,1,1,3,1,2,1,3,
1]],[[1,1,2,1],[2,1,1,1],[3,1,4,2,3,-2]]],[[[1,1,2,-1,1,1,2,1,1,1]],[[1,1,2,
1],[3,1,2,1,3,2,2,1,1,1]]],[[[1,1,2,-1,1,1,2,1]],[[1,1,2,1],[2,1,3,1],[3,1,4,
2,3,1]]],[[[2,1,1,1],[2,1,3,1,2,-1,1,1,3,2]],[[1,1,2,1],[3,2,2,1,1,1,2,-1,3,
-2]]],[[[1,1,2,1],[2,1,3,1,1,1,2,-1,1,1,2,-1,3,1]],[[1,1,2,1],[1,1,2,-1,3,1,2,
1,1,1,2,1,3,1]]],[[[1,1,2,1],[3,2,2,-2,1,1]],[[1,1,2,1],[2,1,1,1],[4,1,3,-1,4,
2,2,-1,3,-1]]],[[[1,1,2,-1,1,1,2,1,1,1]],[[1,1,2,1],[3,2,2,-2,1,1]],[[2,-2],[
3,1,1,1,2,-2,1,1,3,1]]],[[[1,1,2,-1,1,1,2,1,1,1]],[[1,1,2,1],[2,-2,3,2,2,
1]],[[1,1,2,1],[3,1,2,1,3,2,2,1,1,1]]],[[[1,1,2,1],[3,1,2,1,3,1,2,1,1,1]],[[1,
1,2,-1,1,1,2,-1,1,1,2,-1,1,1]]],[[[1,1,2,-1,1,1,2,1,1,1]],[[2,1,1,1],[2,-2,3,
-2,2,-1,1,1]]],[[[1,1,2,1],[3,2,2,-2,1,1]],[[2,1,1,1],[1,1,2,-1,3,-1,1,1,2,-1,
1,1,3,1]]],[[[1,1,2,-1,1,1,2,1]],[[2,-2,1,1,2,-1,1,1,2,-2]]],[[[1,1,2,-1,1,
1]],[[2,-2],[3,1,2,1,1,1,3,1,1,1,2,1]]],[[[2,-2]],[[1,1,2,-2,1,1]],[[1,1,2,-1,
1,1,2,1,1,1]]],[[[1,1,2,-1,1,1]],[[1,1,2,1],[2,-1,3,2]]],[[[1,1]],[[2,1]]]]);
ACLT( "M11",
"sortperm",( 4, 7,10,15, 5, 6)( 8, 9)(11,14,12,16,18,22,24,26,25,27,30,29,28,
 13)(19,20)(31,32)(35,36,37));
ACLT( "M11",
"otherwords",[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[[[1,1,2,1],[2,1,1,1,3,1,2,1,3,
1]],[[2,1,1,1],[3,2,2,-1,1,1]]],,,[[[1,1]],[[2,1,1,1,2,-2,1,1,2,1]]],[[[1,1,2,
1],[3,1,2,1],[3,1,4,1,3,1,4,1]],[[1,1,2,1],[2,1,3,3,2,1,1,1]]]]);


LIBTOM( "M12",
[[1],[1,2],[1,3],[1,4],[1,5],[1,3,6],[1,3,7],[1,3,8],[1,2,9],[1,3,10],[1,2,3,
11],[1,12],[1,3,5,13],[1,2,4,14],[1,3,5,15],[1,2,4,16],[1,3,5,17],[1,3,4,18],[
1,3,6,19],[1,3,7,20],[1,3,7,21],[1,3,6,22],[1,2,3,9,11,23],[1,2,3,7,11,24],[1,
2,3,6,11,25],[1,3,6,7,8,26],[1,3,6,10,27],[1,2,3,6,7,11,28],[1,2,3,7,8,11,
29],[1,2,3,8,11,30],[1,2,3,6,8,11,31],[1,3,8,10,32],[1,3,7,10,33],[1,5,34],[1,
5,35],[1,4,5,36],[1,2,12,37],[1,3,12,38],[1,2,12,39],[1,40],[1,2,5,9,41],[1,2,
4,9,14,42],[1,3,4,8,43],[1,3,5,10,44],[1,2,4,9,45],[1,2,4,9,14,16,46],[1,2,3,
4,11,14,16,18,47],[1,3,5,10,13,15,17,48],[1,3,6,7,8,26,49],[1,2,3,6,7,8,10,11,
26,29,30,31,32,50],[1,2,3,6,7,8,11,22,25,26,28,31,51],[1,3,6,7,8,19,26,52],[1,
3,6,7,8,10,26,27,32,33,53],[1,2,3,6,7,8,11,21,24,26,28,29,54],[1,3,6,7,8,20,
26,55],[1,3,7,10,20,21,33,56],[1,2,3,6,7,8,9,11,23,24,25,28,29,30,31,57],[1,2,
3,6,10,11,19,25,27,58],[1,3,6,10,19,22,27,59],[1,2,3,7,10,11,20,24,33,60],[1,
3,5,17,34,61],[1,3,5,15,35,62],[1,3,5,13,15,34,63],[1,3,5,13,17,35,64],[1,3,4,
5,13,18,36,65],[1,2,3,11,12,37,38,39,66],[1,3,6,12,38,67],[1,3,7,12,38,68],[1,
2,3,4,9,11,14,16,18,23,42,46,47,69],[1,3,5,6,10,15,27,44,70],[1,2,3,4,8,11,14,
30,43,71],[1,2,3,4,7,8,11,16,29,43,72],[1,3,5,7,10,17,33,44,73],[1,3,5,8,10,
13,32,44,74],[1,3,5,7,13,21,75],[1,2,3,4,6,8,11,16,31,43,76],[1,3,5,6,13,22,
77],[1,2,3,5,9,11,13,23,41,78],[1,4,5,34,35,36,79],[1,2,3,6,7,8,10,11,26,27,
29,30,31,32,33,49,50,53,80],[1,2,3,6,7,8,9,10,11,21,22,23,24,25,26,28,29,30,
31,32,50,51,54,57,81],[1,2,3,6,7,8,10,11,19,22,25,26,27,28,31,32,33,51,52,53,
58,59,82],[1,2,3,6,7,8,10,11,20,21,24,26,27,28,29,32,33,53,54,55,56,60,83],[1,
2,3,6,7,8,11,19,21,24,26,28,29,49,52,54,84],[1,2,3,6,7,8,10,11,19,20,26,29,30,
31,32,50,52,55,85],[1,2,3,6,7,8,11,20,22,25,26,28,31,49,51,55,86],[1,3,5,6,15,
35,62,87],[1,3,5,7,17,34,61,88],[1,3,5,10,13,15,17,35,48,62,64,89],[1,3,5,10,
13,15,17,34,48,61,63,90],[1,2,4,5,9,14,36,41,42,45,91],[1,2,3,6,7,11,12,28,37,
38,39,66,67,68,92],[1,3,4,6,7,8,26,43,49,93],[1,2,3,4,6,7,8,9,11,14,16,23,24,
25,28,29,30,31,43,46,57,71,72,76,94],[1,3,5,6,10,13,15,17,19,22,27,48,59,77,
95],[1,3,5,7,10,13,15,17,20,21,33,48,56,75,96],[1,3,5,6,7,8,10,13,15,17,26,27,
32,33,44,48,53,70,73,74,97],[1,3,4,5,13,15,34,35,36,62,63,79,98],[1,3,4,5,13,
17,34,35,36,61,64,79,99],[1,3,4,5,13,15,17,18,34,35,36,63,64,65,79,100],[1,12,
40,101],[1,3,4,8,12,18,38,43,102],[1,3,5,10,12,15,38,44,103],[1,3,5,10,12,17,
38,44,104],[1,2,4,9,12,16,39,45,105],[1,2,3,6,7,8,9,10,11,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,49,50,51,52,53,54,55,56,57,58,59,60,80,81,82,83,84,
85,86,106],[1,3,5,7,17,21,34,61,88,107],[1,3,5,6,15,22,35,62,87,108],[1,3,5,7,
17,20,34,61,88,109],[1,3,5,7,10,13,15,17,33,34,48,61,63,88,90,110],[1,3,5,6,
15,19,35,62,87,111],[1,3,5,6,10,13,15,17,27,35,48,62,64,87,89,112],[1,2,3,4,5,
9,11,13,14,16,18,23,36,41,42,45,46,47,65,69,78,91,113],[1,2,3,4,6,7,8,10,11,
14,26,27,29,30,31,32,33,43,49,50,53,71,80,93,114],[1,2,3,5,6,7,8,9,10,11,13,
21,22,23,24,25,26,28,29,30,31,32,41,44,50,51,54,57,74,75,77,78,81,115],[1,2,3,
4,6,7,8,11,16,20,22,25,26,28,31,43,49,51,55,76,86,93,116],[1,2,3,4,6,7,8,11,
16,19,21,24,26,28,29,43,49,52,54,72,84,93,117],[1,3,4,5,10,13,15,17,18,34,35,
36,48,61,62,63,64,65,79,89,90,98,99,100,118],[1,2,3,4,6,8,11,12,14,16,18,31,
38,43,47,67,76,102,119],[1,2,3,4,8,11,12,14,16,18,30,37,38,39,43,47,66,71,102,