mkcycl(1)

1mkcycl(1)                        User Commands                       mkcycl(1)
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NAME

6       mkcycl - find cyclic subspaces of a condensed module
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SYNOPSIS

9       mkcycl [OPTIONS] <Name>
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DESCRIPTION

12       This program is invoked after pwkond(1) has calculated the condensation
13       with respect to the peak words.  Mkcycl calculates, for each  condensed
14       module,  its  1-dimensional subspaces.  The output is a list of vectors
15       (in matrix form) for each irreducible constituent, which  generate  all
16       cyclic  submodules.   For example, if "X10a" is the constituent's name,
17       the list of vectors is written to "X10a.v".
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OPTIONS

20       -Q     Quiet, no messages.
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22       -V     Verbose, more messages.
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24       -T <MaxTime>
25              Set CPU time limit
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27       -G     Produce output in GAP format.  This option implies -Q.
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IMPLEMENTATION DETAILS

30       Mkcycl uses a very simple approach: it spins up  every  vector  in  the
31       condensed  module  (avoiding scalar multiples, though), and maintains a
32       list of all cyclic submodules found.  As the dimension of the condensed
33       module  grows,  the  number  of vectors to spin up quickly becomes very
34       large.  This poses an upper limit on the dimension  of  condensed  mod‐
35       ules,  i.e.,  on  the  multiplicity  of irreducible constituents.  Over
36       GF(2), for example, a 16-dimensional condensed module requires about 20
37       hours of CPU time on a standard workstation.
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39       A second limit concerns the number of cyclic submodules.  Usually there
40       are much less cyclic submodules than 1-spaces.  Sometimes, however,  it
41       may  happen that the peak word found in the second step is "bad" in the
42       sense that the condensed generators commute.  In such a case one  finds
43       a large number of cyclic submodules and the following steps will proba‐
44       bly take too much time.  For this reason, the pwkond(1) program has  an
45       option  to  exclude  one  or more specified peak words from the search.
46       So, if the peak word turns out to be "bad", you can try another one.
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INPUT FILES

49       Name.cfinfo
50              Constituent info file.
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52       Name<Cf>.{1,2,...}k
53              Generators on condensed modules.
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55       Name<Cf>.np
56              Condensed peak words.
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OUTPUT FILES

59       Name<Cf>.v
60              Cyclic submodules.
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