[ новости /+++ | форум | теги | ]

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 encoun-
     tered  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 con-
     tains 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  hyper-
     bolic,  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 con-
     vention 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 gen-
     erators, 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  gen-
     erator  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.

Партнёры:

Хостинг: