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
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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
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