zmo(1) - f30

1zmo(1)                           User Commands                          zmo(1)
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NAME

6       zmo - make orbits under a set of permutations
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SYNOPSIS

9       zmo [OPTIONS] <Perm> <Orbits>
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DESCRIPTION

12       This  program  calculates  the  orbits under a set of permutations.  By
13       default, the program works with two permutations which  are  read  from
14       Perm.1  and  Perm.2.   Using  the -g option you can specify a different
15       number of permutations (using the  same  file  name  convention).   For
16       example,
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18         zmo -g 3 p orbs
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20       reads three permutations from p.1, p.2, and p.3.  All permutations must
21       have the same degree.
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23       The result is written to Orbits and consists of two parts:
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25       · The orbit number table.  This is an integer matrix with one row and N
26         columns, where N is the degree of the permutations.  The ith entry in
27         this table contains the orbit number of point i.  Note: Orbit numbers
28         start with 0.
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30       · The  orbit sizes table.  This is an integer matrix with one row and K
31         columns, where K is the number of orbits.  The ith entry contains the
32         size of the orbit number i.
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34       This  file  can  be fed into zkd(1) or zuk(1).  At the end, the program
35       prints a message containing the orbit sizes.  Note that at most 20 dif‐
36       ferent orbit sizes are shown here.
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OPTIONS

39       -Q     Quiet, no messages.
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41       -V     Verbose, more messages.
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43       -T <MaxTime>
44              Set CPU time limit
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46       -g <#Perms>
47              Set number of permutations.  Default: 2.
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49       -s <Seed>
50              Set seed point.  Default: 1.
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IMPLEMENTATION DETAILS

53       The  algorithm  uses a fixed size stack to store points.  At the begin‐
54       ning, a seed point is searched which has not yet assigned an orbit num‐
55       ber.   This  point is assigned the next orbit number (beginning with 0)
56       and put on the stack.  The main part consists of taking  a  point  from
57       the stack and applying all generators.  Any new points obtained in this
58       way are assigned the same orbit number and put on the stack.  This step
59       is  repeated  until  the  stack is empty, i.e., the orbit is exhausted.
60       Then, the next seed point is seached, and its orbit is calculated,  and
61       so on, until all orbits are found.  By default, the first seed point is
62       1.  A different seed point may be selected with the -s option.
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64       The number of permutations must be less than 50.  All permutations must
65       fit  into  memory  at the same time.  Also the stack size is limited to
66       100000 positions.
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INPUT FILES

69       Perm.{1,2,...}
70              Permutations
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OUTPUT FILES

73       Orbits Orbit table and sizes.
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