 FunctionAdvisor/plot - Maple Programming Help

2-D and 3-D plots illustrating a mathematical function

Parameters

 plot - literal name;'plot' math_function - name of a known mathematical function; see FunctionAdvisor(known_functions)

Description

 • The FunctionAdvisor(plot math_function) command displays 2-D and 3-D plots illustrating math_function following, where possible, the NIST Digital Library of Mathematical Functions.
 • The 3-D plots displayed by FunctionAdvisor(plot math_function) involve three kinds of plot structures. First there are the standard 3-D plots you can construct using plot3d, used for instance for some functions of many arguments provided that the function is real for real values of its arguments. Second, there are 3-D plots constructed using plots:-complexplot3d, where the vertical axis represent the absolute value of the function and the two horizontal axes represent the Real and Imaginary parts of the main plotting complex variable. Finally, some plots are obtained using plots:-plotcompare with the option expression_plot, appropriate to illustrate branch cuts.
 • After displaying the plots on the screen, the actual value returned by FunctionAdvisor(plot math_function) is NULL. You can get the plots structures themselves in two different ways: right-click the plot, copy, then paste into an input region, or use MathematicalFunctions:-Get(plot, math_function) as shown in the last example.

Examples

2-D and 3-D plots illustrating the natural logarithm, respectively of a real and complex variable

 > $\mathrm{FunctionAdvisor}\left(\mathrm{plot},\mathrm{ln}\right)$  You can rotate the 3-D plots with the mouse. Also, you can change the way a plot (2-D or 3-D) is presented in different ways (Style, Color, Orientation, etc.) from the Context Panel for the plot or the Plot menu.

Note the similarity between the 2-D plots of ln and the exponential integral Ei function of a real variable; over the complex plane, however, these functions behave rather different

 > $\mathrm{FunctionAdvisor}\left(\mathrm{plot},\mathrm{Ei}\right)$     In most cases, when a function involves different number of arguments, plots for the different cases are presented, for example GAMMA represents both the Gamma function (case of one argument) and the incomplete gamma function (case of two arguments)

 > $\mathrm{FunctionAdvisor}\left(\mathrm{plot},\mathrm{\Gamma }\right)$      The 2-D plots of the JacobiSN (elliptic sin function) of a real variable resemble the plots for sin

 > $\mathrm{FunctionAdvisor}\left(\mathrm{plot},\mathrm{JacobiSN}\right)$        2-D and 3-D plots illustrating the important 2F1 case of the generalized hypergeometric function

 > $\mathrm{FunctionAdvisor}\left(\mathrm{plot},\mathrm{hypergeom}\right)$      To get the plot structure itself, for instance those for the hypergeometric function displayed above, use

 > $\mathrm{plots_hypergeom}≔\mathrm{MathematicalFunctions}:-\mathrm{Get}\left(\mathrm{plot},\mathrm{hypergeom}\right)$
 ${\mathrm{plots_hypergeom}}{≔}\left[\begin{array}{cccc}{\mathrm{PLOT}}{}\left({\mathrm{...}}\right)& {\mathrm{PLOT}}{}\left({\mathrm{...}}\right)& {\mathrm{PLOT}}{}\left({\mathrm{...}}\right)& {\mathrm{PLOT}}{}\left({\mathrm{...}}\right)\end{array}\right]{,}\left[\begin{array}{cc}{\mathrm{PLOT3D}}{}\left({\mathrm{...}}\right)& {\mathrm{PLOT3D}}{}\left({\mathrm{...}}\right)\end{array}\right]$ (1)

Having the plotting structures assigned to plots_hypergeom you can now manipulate each plot as desired, for example, consider the second 2-D plot:

 > $\mathrm{plots_hypergeom}\left[1\right]\left[2\right]$ Change the title, change the color, and make the plot be constrained (note the use of the keyword overrideoptions of plots:-display)

 > $\mathrm{plots}:-\mathrm{display}\left(\mathrm{plots_hypergeom}\left[1\right]\left[2\right],\mathrm{overrideoptions},\mathrm{color}="Blue",\mathrm{axes}=\mathrm{boxed},\mathrm{scaling}=\mathrm{constrained},\mathrm{title}="2F1 hypergeometric function"\right)$ > 

Compatibility

 • The FunctionAdvisor/plot command was introduced in Maple 2016.