mkhom(1) - f31

1mkhom(1)                         User Commands                        mkhom(1)
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NAME

6       mkhom - calculate homomorphisms between modules
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SYNOPSIS

9       mkhom [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 writes the spinning basis of M to
19       M.std, and a k-basis of the homomorphism space to  Hom.1,  Hom.2,  ....
20       The  latter  are  given with respect to the spinning 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 uses peak words of the first module.  Thus, before using the pro‐
26       gram, 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 spinning basis.
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38       -s     When M=N, calculate endomorphisms in the spinning basis.
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40       -l     When  M=N,  find  a  generating set of End(M), and calculate the
41              left regular representation.
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43       -r     When M=N, find a generating set of  End(M),  and  calculate  the
44              right regular representation.
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46       -b     For big endorings, with -r or -l, save memory.
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48       -H <Dim>
49              If the radical is given, Dim is the dimension of the head.
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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       M.{1,2,...}
58              Generators in representation M.
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60       N.{1,2,...}
61              Generators in representation N.
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63       M.cfinfo
64              Constituent info file for M.
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66       N.cfinfo
67              Constituent info file for N.
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69       M.rad  Generators for the head of M (with -H).
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71       M<Cf>.k
72              Uncondense matrix, produced by pwkond(1).
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OUTPUT FILES

75       M.std  The spinning basis for M.
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77       Hom.{1,2,...}
78              A k-basis of Hom(M,N).
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80       M.std.{1,2,...}
81              Generators in the spinning basis (with -t).
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