Computer Algebra Recipes

INTRODUCTORY RECIPE 7
plotting options available can be found by clicking on the underlined hyperlink
plot/details that appears on the help page, and then on plot[options]. Try
including some other options in the plot command. For example, change the
color of the ball's trajectory from the default red to, say, blue.
The ¯nal part of the problem is to animate the trajectory of the ball with
the vertical fence included. The fence is now plotted, but not displayed, being
assigned the name fence. The coordinates of the bottom and the top of the
fence are entered as Maple lists and then formed into another list, i.e., one has
a \list of lists." The fence will be plotted as a vertical (default red) line.
> fence:=plot([[xf,0],[xf,yf]]):
To produce specialized plots, such as an animated one, we must access the plots
library package. This is done by entering the command with(plots). The
preface with always indicates a Maple library package is being \loaded" into
the worksheet. Library packages are extremely important, since they contain
approximately 90% of Maple's mathematical knowledge. Normally, we would
end the command with a colon, but here a semicolon is used to see what plot
commands are contained in the plots library. 5
> with(plots);
Warning, the name changecoords has been redefined
[Interactive; animate; animate3d; animatecurve; arrow; changecoords;:::]
The animate command, appearing in the above list, will be used to animate the
motion of the ball. The syntax is animate(plot command,[plot arguments],
time range,options). Thepointplot command will plot the ball as a point.
The plot arguments symbol=circle and symbolsize=14 instruct Maple to plot
the point as a size-14 circle. 6 Included in the plot arguments list are the ball's
x- andy-coordinates given as a list of lists. The time range is t =0toT2 .In
the options, the number7 of frames is taken to be 200, the frames being equally
spaced in time. The option background=fence causes the fence to appear as
background in each time frame. Finally, the scaling is constrained.
> animate(pointplot,[[[x,y]],symbol=circle,symbolsize=14],
t=0..T2,frames=200,background=fence,scaling=constrained);
When the animate command line is executed on the computer, the initial frame
of the animation will appear on the screen. Clicking on the picture with the left
mouse button places the picture in a viewing box and opens up an animation bar
at the top of the screen. The animation is started by clicking on the arrowhead
( ¤ ) and stopped by clicking on the square ( 2 ).
5 Only a partial list of plot commands is shown here in the text, as indicated by the dots.
Note that a warning message is also produced that informs us that the name changecoords
has been rede¯ned in the current release of Maple. If desired, warnings can be removed by
inserting the command interface(warnlevel=0) prior to loading the library package. From
now on, all such warnings will generally be arti¯cially removed in the text.
6 The default symbol is a diamond and the default size is 10.
7 The default number is 25 frames. 200 frames produces a smoother animation.