cplxview(1)                 General Commands Manual                cplxview(1)

       cplxview - module to visualize the graphs of complex functions.

       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 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.

       Olaf Holt and Nils McCarthy

Geometry Center                   Oct 29 1993                      cplxview(1)