Maxima - a sophisticated computer algebra system

### Examples of the new Maxima Gnuplot interface

#### Basic usage

The Maxima-Gnuplot interface offers three terminal choices: default, ps and dumb.

    Maxima 5.9.0.1cvs http://maxima.sourceforge.net
    Using Lisp CMU Common Lisp 18e fedora release 0.fdr.2.e.1
    Distributed under the GNU Public License. See the file COPYING.
    Dedicated to the memory of William Schelter.
    This is a development version of Maxima. The function bug_report()
    provides bug reporting information.
    (C1) plot2d(sin(x),[x,0,2*%pi]);

    (D1)

    (C2) plot2d(sin(x),[x,0,2*%pi],[gnuplot_term,ps],[gnuplot_out_file,"sin.eps"]);
    output file "sin.eps".
    (D2)

Click on the above image to see the actual postscript file

    (C3) plot2d(sin(x),[x,0,2*%pi],[gnuplot_term,dumb]);

        1 ++--------+--$$$$$$$+---------+---------+---------+---------+--------++
          +         $$$      $$$        +         +         +     SIN(x) $$$$$$ +
          |       $$$           $$                                              |
          |      $$              $$$                                            |
      0.5 ++   $$                  $$                                          ++
          |   $$                    $$                                          |
          |  $$                      $$                                         |
          | $$                         $$                                       |
          |$$                           $$                                      |
        0 $+                             $$                             $$     ++
          |                               $$                           $$       |
          |                                $$                         $$        |
          |                                 $$                       $$         |
     -0.5 ++                                  $$                    $$         ++
          |                                    $$                  $            |
          |                                     $$               $$             |
          |                                       $$           $$$              |
          +         +         +         +         +$$$$     +$$$      +         +
       -1 ++--------+---------+---------+---------+---$$$$$$$---------+--------++
          0         1         2         3         4         5         6         7

    (D3)

Those of us who remember when "vt100" was not just a menu item in a terminal editor, but an actual thing that would hurt to drop on your foot, should find the following picture nostalgic.

#### More advanced usage

The new adaptive plotting routines (based on an algorithm from yacas) allow plotting of functions with singularities.

    (C4) plot2d([gamma(x),1/gamma(x)],[x,-4.5,5],[y,-10,10],
    [gnuplot_preamble,"set key bottom"]);

    (D4)

It is now possible to take advantage of the advanced features of Gnuplot. Note the tick labels on the horizontal axis in the following figure.

    (C5) plot2d([cos(x),sin(x),tan(x),cot(x)],[x,-2*%pi,2*%pi],[y,-2,2],
    [gnuplot_preamble,"set xzeroaxis; set xtics ('-2pi' -6.283, '-3pi/2' -4.712,
    '-pi' -3.1415, '-pi/2' -1.5708,  '0' 0,'pi/2' 1.5708, 'pi' 3.1415,'3pi/2' 4.712,
    '2pi' 6.283)"]);

    (D5)

The postscript version of the previous figure can take advantage of Gnuplot's enhanced postscript terminal.

    (C6)
    plot2d([cos(x),sin(x),tan(x)],[x,-2*%pi,2*%pi],[y,-2,2],[gnuplot_preamble,"set
    xzeroaxis; set xtics ('-2{/Symbol p}' -6.283, '-3{/Symbol p}/2' -4.712,
    '-{/Symbol p}' -3.1415, '-{/Symbol p}/2' -1.5708,  '0' 0,'{/Symbol p}/2' 1.5708,
    '{/Symbol p}' 3.1415,'3{/Symbol p}/2' 4.712, '2{/Symbol p}'
    6.283)"],[gnuplot_term,ps],[gnuplot_out_file,"trig.eps"]);

    output file "trig.eps"
    (D6)

Click on the above image to see the actual postscript file

#### 3D plotting and pm3d

##### Plotting without pm3d

The default three-dimensional plotting generates a mesh. It works with all versions of Gnuplot.

    (C7) plot3d(atan(-x^2+y^3/4),[x,-4,4],[y,-4,4],[grid,50,50]);

    (D7)

##### Plotting with pm3d

Gnuplot 4.0 includes pm3d, which provides many advanced options for three- and four-dimensional plotting. Use of pm3d is turned off by default because Gnuplot 4.0 is not yet commonly installed. (Indeed, as of this writing, April 15, 2004, Gnuplot 4.0 has not yet been officially released.) If Gnuplot 4.0 (or one of the many earlier cvs/beta releases) is installed, Maxima can take advantage of the features in pm3d.
The default plot with pm3d includes a mesh and a colored surface.

    (C8)
    plot3d(atan(-x^2+y^3/4),[x,-4,4],[y,-4,4],[grid,50,50],[gnuplot_pm3d,true]);
    (D8)

Several variations are possible. Here is one with no mesh and contours on at the base.

    (C9)
    plot3d(atan(-x^2+y^3/4),[x,-4,4],[y,-4,4],[grid,50,50],[gnuplot_pm3d,true],[gnup
    lot_preamble,"set pm3d at s;unset surface;set contour;set cntrparam levels
    20;unset key"]);

    (D9)

The following variation includes the mesh and puts the colors on the base.

    (C10) surface-pm3d-2:
    plot3d(atan(-x^2+y^3/4),[x,-4,4],[y,-4,4],[grid,50,50],[gnuplot_pm3d,true],[gnup
    lot_preamble,"set pm3d at b"]);

    (D10)

Some functions are too complicated to be practically visualized with a mesh.

    (C11) plot3d(cos(-x^2+y^3/4),[x,-4,4],[y,-4,4],[grid,150,150]);

    (D11)

However, the above function can be effectively visualized using pm3d's "map view."

    (C12) plot3d(cos(-x^2+y^3/4),[x,-4,4],[y,-4,4],[gnuplot_preamble,"set view map;
    unset surface"],[gnuplot_pm3d,true],[grid,150,150]);

    (D12)