soc(1) - f32

1soc(1)                           User Commands                          soc(1)
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NAME

6       soc - Socle series
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SYNOPSIS

9       soc [OPTIONS] <Name>
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DESCRIPTION

12       This  program determines the Loewy structure of a module by calculating
13       the socles.  Before  using  the  program,  you  must  run  chop(1)  and
14       pwkond(1) with the -t option.  For example,
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16         chop m11
17         pwkond -t m11
18         soc m11
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20       For  each  layer  of the socle series, the program prints the dimension
21       and the multiplicities of the irreducible constituents in  this  layer.
22       This  information  is  also  written to the cfinfo file.  The following
23       example shows the relevant portion of the cfinfo file:
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25         CFInfo.NSocles := 5;
26         CFInfo.Socles := [[1,0,0],[0,1,1],[2,0,0],[0,1,1],[1,0,0]];
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28       The numbers in CFInfo.socles are the multiplicities of the  irreducible
29       constituents for each layer of the socle series.
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31       Using the -l option, you can specify a maximum length.  After MaxLength
32       socles have been calculated, the program prints a warning and stops.
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34       A basis basis reflecting the Loewy structure of the module  is  written
35       to  Name.soc.   Note:  soc always writes a basis of the full space.  If
36       the socle series is  not  calculated  completely  because  the  maximum
37       length  has  been  reached,  the partial basis found so far is extended
38       with random vectors to form a complete basis.
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OPTIONS

41       -Q     Quiet, no messages.
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43       -V     Verbose, more messages.
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45       -T <MaxTime>
46              Set CPU time limit
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48       -l <length>
49              Calculate only the first<length> layers.
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IMPLEMENTATION DETAILS

52       The algorithm used by this program was developed by Magdolna Szöke; see
53       "Examining  Green  Correspondents of Weight Modules", Aachener Beiträge
54       zur Mathematik, Band 24, Wissenschaftsverlag Mainz, Aachen, 1998.
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INPUT FILES

57       Name.cfinfo
58              Constituent info file.
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60       Name<Cf>.std.{1,2,...}
61              Generators on constituents.
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63       Name<Cf>.op
64              Spin-up script for the standard basis.
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66       Name<Cf>.k
67              Uncondense matrix.
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OUTPUT FILES

70       Name.cfinfo
71              Constituent info file.
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73       Name.soc
74              Matrix for basis change.
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