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     cplxview(1)       Geometry Center (Oct 29 1993)	   cplxview(1)

     NAME
	  cplxview - module to visualize the graphs of complex
	  functions.

     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
	  coordinates.	Since the graphs of complex functions live in
	  C^2, this viewer makes use of the n-dimensional viewing
	  capabilities of geomview (see ndview).

	  What you see at start-up: the graph of the complex
	  exponential 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 dimension 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")
	  function, 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
	  control than that afforded in this system, you might
	  incorporate 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

     Page 1					    (printed 12/22/98)

     cplxview(1)       Geometry Center (Oct 29 1993)	   cplxview(1)

	  dimensional) graph of the real part of the function, the
	  (three dimensional) graph of the imaginary part of the
	  function, 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
	  coordinates 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 symbols 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 system 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
	  information can be found in the manual pages, and comments
	  are appreciated.

     AUTHORS
	  Olaf Holt and Nils McCarthy

     Page 2					    (printed 12/22/98)

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