cplxview(1) General Commands Manual 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 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 Geometry Center Oct 29 1993 cplxview(1)