zts(1) - f31

1zts(1)                           User Commands                          zts(1)
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NAME

6       zts - tensor spin of modules
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SYNOPSIS

9       zts [OPTIONS] <M> <N> <Seed> [<Sub>]
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DESCRIPTION

12       This  program  is similar to zsp, but it works on the tensor product of
13       two modules, M⊗N.  Zts spins up one or  more  vectors,  and  optionally
14       calculates  a matrix representation corresponding to the invariant sub‐
15       space.  The program does not use the matrix representation of the  gen‐
16       erators  on  M⊗N, which would be too large in many cases.  This program
17       is used, for example, to spin up vectors  that  have  been  uncondensed
18       with tuc.
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20       The  action  of  the generators on both M and N must be given as square
21       matrices, see "INPUT FILES" below.  You can use the -g option to  spec‐
22       ify the number of generators.  The default is two generators.
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24       Seed  vectors  are  read from Seed.  They must be given with respect to
25       the lexicographically ordered basis explained below.
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27       If the Sub argument is given, zts writes a basis of the invariant  sub‐
28       space  to Sub, calculates the action of the generators on the invariant
29       subspace, and writes it to Sub.1, Sub.2, ....
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OPTIONS

32       -Q     Quiet, no messages.
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34       -V     Verbose, more messages.
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36       -T <MaxTime>
37              Set CPU time limit
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39       -g <#Gens>
40              Set number of generators.  Default: 2.
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42       -n, --no-action
43              Output only Sub, do not calculate Sub.1, ....
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IMPLEMENTATION DETAILS

46       Let B=(b_1,...,b_m) be a basis of M, C=(c_1,...,c_n) a basis of N,  and
47       denote  by  B⊗C  the lexicographically ordered basis (b_1⊗c_1, b_1⊗c_2,
48       ..., b_m⊗c_n).  For vϵM⊗N, the coordinate row m(v,B⊗C) has  mn  entries
49       which  can  be arranged as a m×n matrix (top to bottom, left to right).
50       Let M(B,v,C) denote this matrix.  Then
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52         M(B,va,C) = m(B,a|_M,B)^trM(B,v,C)m(C,a|_N,C) for all aϵA,vϵM⊗N
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54       Using this relation, we can calculate the image  of  any  vector  vϵM⊗N
55       under an algebra element a, and thus spin up a vector without using the
56       matrix representation of a on vϵM⊗N.
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INPUT FILES

59       M.{1,2,...}
60              Generators on the left representation.
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62       N.{1,2,...}
63              Generators on the right representation.
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65       Seed   Seed vectors.
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OUTPUT FILES

68       Sub    Invariant subspace.
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70       Sub.{1,2,...}
71              Action on the invariant subspace.
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