1zor(1)                           User Commands                          zor(1)
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NAME

6       zor - calculate the order of a matrix or permutation
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SYNOPSIS

9       zor [OPTIONS] <File>
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DESCRIPTION

12       This  program reads a file, containing either permutations, or a square
13       matrix, and calculates the order(s) and prints the message:
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15         ORDER IS xxxx
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17       There are two options to reduce the run time of the program.  Using the
18       -m  option  you  can  specify  a maximal expected order. If, during the
19       algorithm described below, the order reaches this  limit,  the  program
20       will  stop  and  print  an appropriate message.  The second option, -q,
21       makes zor stop if the dimension of W (see below) reaches  1/10  of  the
22       dimension of the whole space.  In this case, the message is
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24         ORDER IS A MULTIPLE OF NNN
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26       Note: The -q and -m options have no effect for permutations.
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OPTIONS

29       -Q     Quiet, no messages.
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31       -V     Verbose, more messages.
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33       -T <MaxTime>
34              Set CPU time limit
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36       -m <MaxOrder>
37              Set an upper limit for the order of cyclic subspaces.
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39       -q     Quick mode: find a lower bound for the order.
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41       -G     Produce output in GAP format.
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IMPLEMENTATION DETAILS

44       If  the input is a matrix, the order is found by calculating the orders
45       on cyclic subspaces and taking the least common  multiple.   The  algo‐
46       rithm works as follows:
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48       · Let  A  be  the given matrix and V the space A acts upon.  Set W:={0}
49         (the trivial subspace) and o:=1.
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51       · (NEXT) Choose a vector v not in W.  Calculate the cyclic  subspace  C
52         generated by v and the order o' of A on C.
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54       · Set o:=lcm(o,o')
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56       · W:=W  +  C.   If W=V, o is the order of A and the program terminates.
57         Otherwise, continue with (NEXT).
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59       Gaussian elimination is used to maintain a basis of W in echelon  form.
60       In  order to avoid infinite loops, there is a limit on o'.  If the vec‐
61       tor does not return after 1000 multiplications the order is assumed  to
62       be  infinite and the program stops with an error message.  This happens
63       also if the value of o exceeds 100000.
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65       If the input file contains permutations, each one is read  in  and  its
66       order  is  calculated  as the least common multiple of the orbit sizes.
67       The result is printed in the format
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69         ELEMENT nn HAS ORDER nnn
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71       The whole matrix plus a second matrix of the same size  must  fit  into
72       memory.   In  the case of permutations, there must be enough memory for
73       one permutation.
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77MeatAxe                             2.4.24                              zor(1)
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