1mktree(1)                        User Commands                       mktree(1)
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NAME

6       mktree - enumerate elements of a finitely generated matrix group
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SYNOPSIS

9       mksub [OPTIONS] <Name>
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DESCRIPTION

12       This  program  enumerates  all  elements of a finitely generated matrix
13       group.  By default, the program assumes that the group has two  genera‐
14       tors,  which  are  read  from Name.1 and Name.2.  A different number of
15       generators can be specified with -g.
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17       Unless the -n option is used, the program writes the  element  tree  to
18       Name.elt.   The  element  tree  describes how the group elements can be
19       calculated as products of generators.  It is actually a matrix with two
20       columns and one row for each group element.  The ith row of this matrix
21       describes how the ith element is calculated:
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23       · The row (-1,-1) represents the unit element.  This row appears  first
24         in the output.
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26       · (0,k)  means  that  this element is the kth generator.  Note that the
27         generator number starts with 0, i.e., the first generator has k=0.
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29       · (s,k) means that the corresponding element is obtained by multiplying
30         the  sth element from the right by the kth generator.  Both generator
31         and element numbers start with 0.  Thus,  the  (0,k)  lines  decribed
32         above are actually a special case of the general (s,k) lines.
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34       The following example shows the output for a group of the order 10 with
35       two generators, a and b:
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37       Line   Contents   Meaning
38         1    -1    -1   identity matrix
39         2     0     0   a
40         3     0     1   b
41         4     1     0   aa
42         5     1     1   ab
43         6     3     0   aaa
44         7     3     1   aab
45         8     5     0   aaaa
46         9     5     1   aaab
47        10     7     1   aaaab
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OPTIONS

50       -Q     Quiet, no messages.
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52       -V     Verbose, more messages.
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54       -T <MaxTime>
55              Set CPU time limit
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57       -g <NGen>
58              Set the number of generators.  Default: 2.
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60       -n     Don't write the element file, just print the order.
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IMPLEMENTATION DETAILS

63       The program holds all group elements in memory.  This limits the appli‐
64       cation  of  the  program  to fairly small groups and representations of
65       small degree.
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INPUT FILES

68       Name.{1,2,...}
69              Generators
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OUTPUT FILES

72       Name.elt
73              Element tree.
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77MeatAxe                             2.4.24                           mktree(1)