1discgrp(5gv)               Geometry Project Programs              discgrp(5gv)
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NAME

6       discrete group file formats
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SYNOPSIS

9       An ascii file representation of a discrete geometric group.
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SUMMARY

12       This  file  format  applies  to a wide variety of groups encountered in
13       topology and geometry.  At the beginning of the file is the string DIS‐
14       CGRP,  in  conformity  with other OOGL file formats (see oogl(5)).  The
15       remainder of the file is a series of parenthesized expressions.
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17       The file format is based on an expandable set of key markers  and  val‐
18       ues.  A typical entry would be
19              (group  borromean )
20       where parentheses enclose the expression.  The string 'group' is called
21       the key marker.  The remaining text contains a value, in  this  case  a
22       character string which is the name of the group.  Key markers currently
23       recognized and their values include:
24              group     A name for this group.
25              comment An arbitrary comment [maximum length 256 bytes]
26                    [must be enclosed in double quotes]
27              attribute One of a several keyword identifiers including:
28                      euclidean       is a euclidean group
29                   hyperbolic      is a hyperbolic group
30                   spherical       is a spherical group
31                   transposed      the matrices are transposed
32                   finite          this is a finite group
33              model     In the case that 'hyperbolic' is an attribute, and the dimension is
34              three, this keyword sets the model that is
35              expected for reading subsequent isometries, i.e., expects elements of
36              SL(2,C) if the model is upperhalfspace or conformalball and O(3,1,R) if it is
37              projective.
38                   projective     default
39                   upperhalfspace
40                   conformalball  [not currently implemented]
41              display These values set characteristics of the the display of the discrete
42              group.
43                   centercam keeps the camera centered in central dirichlet domain.
44                   zcull          removes tiles which lie behind the camera.
45                   showcam        if centercam is set, displays camgeom, if provided (see below).
46              dimn    The dimension of the space.
47              ngens   Number of generators.
48              gens    List of generators.
49              nels    Number of group elements.
50              els     List of group elements.
51              wafile    Word acceptor file (in DEAGL format version 2.2)
52              camgeom An OOGL-format geometry description to represent the observer.
53              geom An OOGL-format geometry description. Will replace the default Dirichlet domain computation.
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55       String-matching of key markers and attribute  values  is  case-insensi‐
56       tive.
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58       Currently all matrices must be 4x4 real matrices.  Hence the only valid
59       dimensions are 2,3, or 4.  The typical case is dimension 3 where  there
60       are  projective  models for hyperbolic, euclidean, and spherical geome‐
61       try.  Dimension 2 groups should leave the z-coordinate unchanged.
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63       Matrices are considered transposed if they are  considered  to  act  on
64       column vectors as in: M.v = v'.  This is the usual mathematical conven‐
65       tion convention. So, if you use this  convention  you  must  mark  your
66       matrices as being transposed.
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68       Group  elements  are specified by an optional character string followed
69       by a list of 16 real numbers.  For the case of generators, the  charac‐
70       ter  string represents the name of that generator. Its main use is with
71       the automatic group software: the name used here should match  that  of
72       the  generator in the word acceptor file.  It should, for example, be a
73       single character for the software to work reliably. For composite  ele‐
74       ments,  the  string  is the word in the generators which describes this
75       group element.
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77       OOGL libraries expect discrete group files to use the '.dgp' suffix.
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79       A file which describes the group of the three  dimensional  torus  fol‐
80       lows:
81              DISCGRP
82              (group 3torus )
83              (comment "  This is a test of the new discrete group library.  " )
84              (attribute Euclidean )
85              (display centercam )
86              (enumdepth 3 )      # look at all words of length 3 or less in generators
87              (enumdist 10.0 )    # and which don't move the origin more than 10.0
88              (dimn 3 )
89              (ngens 3 )
90              (gens
91              a
92                           1             0             0             0
93                           0             1             0             0
94                           0             0             1             0
95                           1             0          -0.1             1
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97              b
98                           1             0             0             0
99                           0             1             0             0
100                           0             0             1             0
101                         0.1             1             0             1
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103              c
104                           1             0             0             0
105                           0             1             0             0
106                           0             0             1             0
107                           0           0.2             1             1
108
109              )
110              (cpoint 0.000000 0.000000 0.000000 1.000000 )
111              (camgeom
112              { = OFF
113              5 2 5
114
115              0 0 0
116              -0.1 0 0.5
117              0.1 0 0.5
118              0 -0.1 0.5
119              0 0.1 0.5
120
121              3     0 1 2    200 200 0 .8
122              3     0 3 4    0 200 200 .8
123              }
124              )
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FILES

127       Example   group   files  are  to  be  found  in  the  OOGL  release  in
128       ${GEOM}/data/groups, where e.g., GEOM = /u/gcg/ngrap.  See  also  disc‐
129       grp(3) and automata(1).
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AUTHORS

132       Charlie Gunn.
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BUGS

135       For dimension 2, the code should read and write 3 x 3 matrices.
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139                                Date: 92/08/26                    discgrp(5gv)
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