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

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 DIS-
       CGRP, 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 conven-
       tion 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 char-
       acter 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)