bionic (5) discgrp.5gv.gz

Provided by: geomview_1.9.5-2_amd64 bug

NAME

       discrete group file formats

SYNOPSIS

       An ascii file representation of a discrete geometric group.

SUMMARY

       This  file  format  applies  to  a  wide  variety of groups encountered in topology and geometry.  At the
       beginning of the file is the string DISCGRP, in conformity with other OOGL file  formats  (see  oogl(5)).
       The remainder of the file is a series of parenthesized expressions.

       The file format is based on an expandable set of key markers and values.  A typical entry would be
              (group  borromean )
       where  parentheses  enclose  the expression.  The string 'group' is called the key marker.  The remaining
       text contains a value, in this case a character string which is the  name  of  the  group.   Key  markers
       currently recognized and their values include:
              group     A name for this group.
              comment An arbitrary comment [maximum length 256 bytes]
                    [must be enclosed in double quotes]
              attribute One of a several keyword identifiers including:
                      euclidean       is a euclidean group
                   hyperbolic      is a hyperbolic group
                   spherical       is a spherical group
                   transposed      the matrices are transposed
                   finite          this is a finite group
              model     In the case that 'hyperbolic' is an attribute, and the dimension is
              three, this keyword sets the model that is
              expected for reading subsequent isometries, i.e., expects elements of
              SL(2,C) if the model is upperhalfspace or conformalball and O(3,1,R) if it is
              projective.
                   projective     default
                   upperhalfspace
                   conformalball  [not currently implemented]
              display These values set characteristics of the the display of the discrete
              group.
                   centercam keeps the camera centered in central dirichlet domain.
                   zcull          removes tiles which lie behind the camera.
                   showcam        if centercam is set, displays camgeom, if provided (see below).
              dimn    The dimension of the space.
              ngens   Number of generators.
              gens    List of generators.
              nels    Number of group elements.
              els     List of group elements.
              wafile    Word acceptor file (in DEAGL format version 2.2)
              camgeom An OOGL-format geometry description to represent the observer.
              geom An OOGL-format geometry description. Will replace the default Dirichlet domain computation.

       String-matching of key markers and attribute values is case-insensitive.

       Currently  all  matrices  must be 4x4 real matrices.  Hence the only valid dimensions are 2,3, or 4.  The
       typical case is dimension 3 where there are projective models for hyperbolic,  euclidean,  and  spherical
       geometry.  Dimension 2 groups should leave the z-coordinate unchanged.

       Matrices are considered transposed if they are considered to act on column vectors as in: M.v = v'.  This
       is the usual mathematical convention convention. So, if you  use  this  convention  you  must  mark  your
       matrices as being transposed.

       Group  elements are specified by an optional character string followed by a list of 16 real numbers.  For
       the case of generators, the character string represents the name of that generator. Its main use is  with
       the  automatic group software: the name used here should match that of the generator in the word acceptor
       file.  It should, for example, be a single character for the software to  work  reliably.  For  composite
       elements, the string is the word in the generators which describes this group element.

       OOGL libraries expect discrete group files to use the '.dgp' suffix.

       A file which describes the group of the three dimensional torus follows:
              DISCGRP
              (group 3torus )
              (comment "  This is a test of the new discrete group library.  " )
              (attribute Euclidean )
              (display centercam )
              (enumdepth 3 )      # look at all words of length 3 or less in generators
              (enumdist 10.0 )    # and which don't move the origin more than 10.0
              (dimn 3 )
              (ngens 3 )
              (gens
              a
                           1             0             0             0
                           0             1             0             0
                           0             0             1             0
                           1             0          -0.1             1

              b
                           1             0             0             0
                           0             1             0             0
                           0             0             1             0
                         0.1             1             0             1

              c
                           1             0             0             0
                           0             1             0             0
                           0             0             1             0
                           0           0.2             1             1

              )
              (cpoint 0.000000 0.000000 0.000000 1.000000 )
              (camgeom
              { = OFF
              5 2 5

              0 0 0
              -0.1 0 0.5
              0.1 0 0.5
              0 -0.1 0.5
              0 0.1 0.5

              3     0 1 2    200 200 0 .8
              3     0 3 4    0 200 200 .8
              }
              )

FILES

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

AUTHORS

       Charlie Gunn.

BUGS

       For dimension 2, the code should read and write 3 x 3 matrices.

                                                 Date: 92/08/26                                     discgrp(5gv)