Plotting in Maxima

1. Plotting in Maxima

2. There are two packages currently used for plotting in Maxima • gnuplot • xMaxima • There may be some problems plotting if Maxima is not completely and correctly installed. • We will use gnuplot most of the time.

3. There are many ways to plot in Maxima • Recall the function f(x) defined as SIN(x) * SQRT(1 + X^3) that we used in our spreadsheet example using Excel. We can plot this in Maxima, also.

6. One way to plot in Maxima: • Example: plot2d(sin(x)*sqrt(1 + x^3), [x, 1, 20]);

8. The Maxima system has an interface to the external gnuplot plotting software. • What’s gnu? • An effort of the free software foundation • The creator of the GNU General Public License

9. The GPL • The GNU Public license says, basically • You can use the software • You can copy it • You can bundle it commercially • You can sell it • You can sell services (installation, maintenance, etc.) • You can modify it, but …

10. The GPL • The GNU Public license says, basically • You can use the software • You can copy it • You can bundle it commercially • You can sell it • You can sell services (installation, maintenance, etc.) • You can modify it, but • You have to make the code available to anyone

11. We will use the GNU plotting routines almost exclusively • The next example, do the plot, but save it to a file. • What type of file? • jpg

12. We did plot2d(sin(x)*sqrt(1 + x^3), [x, 1, 20]; before – now save graph to a file. load(draw); plot2d(sin(x)*sqrt(1 + x^3), [x, 1, 20], [gnuplot_term, png], [gnuplot_out_file, "F:\sin-sqrt-graph.jpg"]);

13. Something is created

14. How can we open it? • This can now be shared with any other application that can read jpg files. • A standard for scientific description of data.

15. How can we open it? A browser

16. Other applications can open file

17. Lets’ go over the syntax plot2d(sin(x)*sqrt(1 + x^3), [x, 1, 20], [gnuplot_term, png], [gnuplot_out_file, "F:\sin-sqrt-graph.jpg"]); • Code to print to a file is in teal color • Notice that everything inside the closing right parenthesis is delimited by square brackets [ and ]

18. What is delimited by [ and ] ? • Lists • Arrays • The Maxima evaluation software uses lists to indicate optional arguments

19. [gnuplot_term, png], [gnuplot_out_file, "F:\sin-sqrt-graph.jpg"]); • First term of the list is in red • It sets the value of the optional argument of gnuplot_term to png, for sending data

20. [gnuplot_term, png], [gnuplot_out_file, "F:\sin-sqrt-graph.jpg"]); • First term of the list is in red • It sets the value of the optional argument of gnuplot_term to png, for sending data • Second term of the list is in teal color • It sets the optional argument – the name of the output file, gnuplot_out_file, to"F:\sin-sqrt-graph.jpg"

21. gnuplot • Extremely powerful • Many options, probably too many to master completely • Use the examples here as a prototype for your work

22. Plotting discrete points in Maxima

23. Another graphing example • Plotting a discrete set of points

24. In Maxima: A : array(flonum, 20, 2); for i: 0 step 1 thru 19 do A[i,0]: i; for i : 0 step 1 thru 19 do A[i,1] :sin(i)* sqrt(1 + i ^3); We need flonum to provide floating point numbers to the graphics routine

25. Can do the two loops together as for i: 0 step 1 thru 19 do { A[i,0]: i , A[i,1] :sin(i)* sqrt(1 + i ^3) };

26. Now draw the points load(draw); C:/PROGRA~1/MAXIMA~1.1/share/maxima/5.18.1/share/draw/draw.lisp draw2d(points(A));

27. Note the cursor position in bottom left

28. Note the cursor position in bottom left

29. Maxima does calculus

30. Let’s try some calculus f(x):= sin(x)*sqrt(1 +x^3)$ Now differentiate with respect to x g(x):=diff(f(x),x)$ Plot them both plot2d([f(x),g(x)] , [x,1,20]); Note the use of a list for f(x), g(x)

32. Where are the maxima and minima? • We can use Maxima to find the maxima (and minima) • Find the critical points – where the derivative is 0 • Remember – gnuplot tracks cursor position • Move the cursor to where the derivative appears to be 0 – these are the critical points (approximately)

38. Let’s solve g(x) = 0

39. Maxima can’t “solve” g(x) = 0 for x

40. Maxima can’t do everything • It can’t solve such general equations • Equation solving usually requires equations with algebraic functions only.