mkhom_old(1)

1mkhom_old(1)                     User Commands                    mkhom_old(1)
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NAME

6       mkhom_old - calculate homomorphisms between modules
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SYNOPSIS

9       mkhom_old [OPTIONS] <M> <N> <Hom>
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DESCRIPTION

12       This  program  calculates a basis for the vector space of homomorphisms
13       between two kG-modules, Hom_kG(M,N).   In  the  case  M=N  the  program
14       optionally  finds  a  generating  set for the algebra of endomoprhisms,
15       End_kG(M), and calculates the corresponding left or right regular  rep‐
16       resentation.
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18       If  used  without any options, mkhom_old writes the standard basis of M
19       to M.std, and a k-basis of the homomorphism space to Hom.1, Hom.2, ....
20       The  latter  are  given with respect to the standard basis of M and the
21       original basis of N.  To get the  homomorphisms  with  respect  to  the
22       original  bases of M and N]fP, multiply the matrices from the left with
23       the inverse of Hom.
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25       Mkhom_old uses peak words of the first module.  Thus, before using  the
26       program, chop(1) and pwkond(1) must have been run on the first module.
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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       -t     Calculate generators for <M> in the standard basis.
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38       -s     When M=N, calculate endomorphisms in the standard basis.
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40       -r <Side>
41              When  M=N,  find  a  generating set of End(M), and calculate the
42              left (Side=1) or right (Side=2) regular representation.
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44       -b <Mode>
45              Save memory, Mode=0..2.
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47       -H <Dim>
48              If the radical is given, Dim is the dimension of the head.
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IMPLEMENTATION DETAILS

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

56       M.{1,2,...}
57              Generators in representation M.
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59       N.{1,2,...}
60              Generators in representation N.
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62       M.cfinfo
63              Constituent info file for M.
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65       N.cfinfo
66              Constituent info file for N.
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68       M.rad  Generators for the head of M (with -H).
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70       M<Cf>.k
71              Uncondense matrix, produced by pwkond(1).
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OUTPUT FILES

74       M.std  The standard basis for M.
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76       Hom.{1,2,...}
77              A k-basis of Hom(M,N).
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79       M.std.{1,2,...}
80              Generators in the standard basis (with -t).
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