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NAME
     cplxview -	module to visualize the	graphs of  complex  func-
     tions.

DESCRIPTION
     Purpose:  to allow	the user to examine complex functions.

     Features:	functions  typed  into	the  function  panel  are
     interpreted via a fexpr, a	fast expression	evaluator written
     at	the Geometry Center.  The domain of the	function  may  be
     specified in a variety of ways, including user defined coor-
     dinates.  Since the graphs	of complex functions live in C^2,
     this viewer makes use of the n-dimensional	viewing	capabili-
     ties of geomview (see ndview).

     What you see at start-up: the graph of the	complex	 exponen-
     tial function, seen from four vantage points.  At the top of
     the windows, there	is a label similar  to	"cluster1:1_2_4".
     The  last three numbers correspond	to the directions visible
     in	the window.  In	this case, 1_2_4 corresponds to	the  real
     part  of  z, the imaginary	part of	z, and the imaginary part
     of	the function of	z.  The	color corresponds to  the  dimen-
     sion  that	 has been projected out, in this example the real
     part of the function of z.

     How-to-use-it:	  This section will describe the  meaning
     or	use of the buttons and inputs, organized by what is shown
     on	the main panel.

     Function:	please type the	function you would like	to  graph
     in	this input.  The parser	understands parenthesis, standard
     functions like sin	and log, and various constants,	namely i,
     e,	and pi.	 To get	exponentials, use the power ("pow") func-
     tion, as in "pow(2,z)".  When you are done	typing in the new
     function,	hit  return.   If the parser understands what you
     wrote,  you  will	see  a	message	 saying	  "new	 function
     installed"	in the message window.

     Domain:  this part	of the panel determined	the  domain  over
     which the function	is to be graphed.  The meaning of each of
     the four numbers is displayed to its left,	which changes  if
     you  change the coordinate	system.	 Use the arrows	to modify
     these numbers.  If	you would like more or less precise  con-
     trol  than	 that  afforded	 in this system, you might incor-
     porate your wishes	into the function you are graphing.   For
     example,  if  you	wish to	graph f(z) = log(z) very near the
     origin, you may instead wish  to  use  f(z)  =  log(z/1000).
     When  modifying  the domain, advanced users may wish to turn
     off normalization in geomview.

     Range: pressing this button will give you the  range  panel,
     on	 which	you  can  specify that you wish	to see the (three
     dimensional) graph	of the real part  of  the  function,  the
     (three dimensional) graph of the imaginary	part of	the func-
     tion,  or	the  actual  four-dimensional  graph,  as  viewer
     through the n-dimensional viewer.

     Meshsize:	you can	modify how fine	the mesh used to show the
     function  is.   Note  that	 this  is  a  regular mesh, which
     doesn't try to avoid  singularities.   Note  also	that  the
     fineness  of the mesh  (along with	the domain) is remembered
     as	you change coordinate systems.

     Coordtype:	 this button brings up the panel  for  specifying
     the  coordinate  system  you wish to use for determining the
     domain to be graphed.  There are three choices: rectangular,
     polar, and	user-defined coordinates.  The user-defined coor-
     dinates mean that z is defined in terms s and t,  which  are
     in	turn functions of u and	v.  The	same parsing mechanism is
     applied to	these functions	as to the function to be graphed.
     At	 the  right  on	the coordtype panel is the explanation of
     what z is assigned	to.  Advanced users may	use all	the  sym-
     bols  listed  there  (x,  y, r, theta, s, and t) in the main
     function window but are advised that there	may be unexpected
     consequences if they are used in the "wrong" coordinate sys-
     tem context.

     Sliders: users may	also make use of two  constants	 "a"  and
     "b" which are attached to sliders,	if they	so desire.  These
     constants can be inserted into a function just as one  might
     expect, for example, one could have a function "a*sin(z+b)",
     or	"pow(z,a+i*b)".	 The default setting of	the user  defined
     coordinates  uses	these  sliders to determine a rectangular
     domain whose size depends on the slider values.

     Help:  the	help button calls up this panel.   More	 informa-
     tion  can	be  found  in  the manual pages, and comments are
     appreciated.

AUTHORS
     Olaf Holt and Nils	McCarthy

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