tcond(1) - f32

1tcond(1)                         User Commands                        tcond(1)
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NAME

6       tcond - tensor product condensation
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SYNOPSIS

9       tcond [OPTIONS] <Info> <A> <B> <Result>
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DESCRIPTION

12       This program performs the final steps of the tensor condensation proce‐
13       dure.  It calculates, for one or more elements  a_1,  a_2,  ...  ,  the
14       action of e_H·a_i·e_H on the condensed tensor product (M⊗N)e_H.
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16       As input, the program expects the action of a_i on M and N with respect
17       to the same basis as the generators of the condensation subgroup H that
18       were  fed into precond before.  The program also needs the semisimplic‐
19       ity basis calculated by pwkond, and the P and Q matrices calculated  by
20       precond.
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22       If  the  generators are already given with repect to the semisimplicity
23       basis, you can use the -n option  to  tell  tcond  to  skip  the  basis
24       change.
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26       The  outputs  are NGen matrices describing the action of e_H·a_i·e_H on
27       (M⊗N)e_H.  These matrices are written to Result.1, Result.2,  ....   If
28       you use the -t option, tcond also calculates the action of a_i on M and
29       N with respect to the semisimplicity basis.  This option cannot be used
30       together with -n.
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32       The  following  sequence  of  commands shows the complete procedure for
33       condensing a tensor product.  To make things simpler,  we  assume  that
34       M=N.   The  condensation subgroup shall be given by three generators in
35       the files "sub.1", "sub.2", and "sub.3".  The generators of  the  group
36       shall be "g.1" and "g.2".
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38         chop -g 3 sub
39         pwkond -tb sub
40         precond tp sub sub
41         tcond -g 2 tp g g result
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43       After these commands are completed, the action of the condensed genera‐
44       tors is in "result.1", "result.2", and "result.3".
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OPTIONS

47       -Q     Quiet, no messages.
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49       -V     Verbose, more messages.
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51       -T <MaxTime>
52              Set CPU time limit
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54       -g <NGen>
55              Set the number of generators.  Default: 2.
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57       -t     Write transformed generators of <A> and <B>.
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59       -n     No basis change.  Assume that generators  on  <A>  and  <B>  are
60              already in semisimplicity basis.
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IMPLEMENTATION DETAILS

63       The  algorithm  used by this program is described in Markus Wiegelmann,
64       "Fixpunktkondensation von Tensorproduktmoduln", Diplomarbeit, Lehrstuhl
65       D für Mathematik der RWTH Aachen, 1994.
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INPUT FILES

68       Info.tki
69              Tensor condensation information, made by precond(1).
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71       A.{1,2,...}
72              Generators of the left factor.
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74       B.{1,2,...}
75              Generators of the right factor.
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77       A.ssb  Semisimplicity basis for A, made by pwkond(1).
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79       B.ssb  Semisimplicity basis for B, made by pwkond(1).
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81       Info.q.{1,2,...}
82              Basis matrices for constituents.
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84       Info.p.{1,2,...}
85              Projection matrices for constituents.
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OUTPUT FILES

88       Result.{1,2,...}
89              Condensed matrices.
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91       A.ss.{1,2,...}
92              Transformed generators (with -t).
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94       B.ss.{1,2,...}
95              Transformed generators (with -t).
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