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

       discrete	group file formats

       An ascii	file representation of a discrete geometric group.

       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  val-
       ues.  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	  default
		   conformalball  [not currently implemented]
	      display These values set characteristics of the the display of the discrete
		   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-insensi-

       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	geome-
       try.  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  ma-
       trices 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  charac-
       ter  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  ele-
       ments,  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  fol-
	      (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 )
			   1		 0	       0	     0
			   0		 1	       0	     0
			   0		 0	       1	     0
			   1		 0	    -0.1	     1

			   1		 0	       0	     0
			   0		 1	       0	     0
			   0		 0	       1	     0
			 0.1		 1	       0	     1

			   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 )
	      {	= 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

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

       Charlie Gunn.

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

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


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