Maxima’s plotting interface, primarily through plot2d and plot3d, supports publication-oriented visualization when used with explicit labels, legends, grids, and carefully chosen plot ranges. The following patterns emphasize scientifically legible annotation and reproducible plotting sessions.

Core 2D Plotting Patterns

A single function is plotted as plot2d(expr, [x, xmin, xmax]), while multiple curves are plotted by passing a list of expressions. For scientific readability, it is standard to attach axis labels, a legend, and a descriptive title.

  • plot2d(expr, [x, xmin, xmax]); plots one function.
  • plot2d([expr1, expr2, …], [x, xmin, xmax]); plots multiple functions.
plot2d(sin(x), [x, -%pi, %pi]);
plot2d([sin(x), cos(x)], [x, -%pi, %pi]);

plot2d(
    [sin(x), cos(x)],
    [x, -2*%pi, 2*%pi],
    [xlabel, "x"],
    [ylabel, "Function value"],
    [legend, "sin(x)", "cos(x)"],
    [title, "Trigonometric Functions"],
    [gnuplot_preamble, "set grid"]
);

Labelling, Ranges, and Styles for Scientific Presentation

Scientific plots typically specify the displayed domain and, when necessary, the ordinate range. The option [y, ymin, ymax] constrains the y-axis, which is useful for decaying functions or bounded probability densities. A minimal style control is available through [style, …], and enhanced text handling can be requested from the backend through a gnuplot preamble.

  • [xlabel, “text”] sets the x-axis label.
  • [ylabel, “text”] sets the y-axis label.
  • [legend, “f(x)”, “g(x)”, …] labels curves.
  • [grid, true] toggles grid lines.
  • [title, “text”] sets a plot title.
  • [y, ymin, ymax] sets the y-range.
  • [style, [lines,1], [points,2]] controls line/point styling.
  • [gnuplot_preamble, “set termoption enhanced”] enables enhanced text formatting in the backend.
plot2d(
    exp(-x^2),
    [x, -3, 3],
    [y, 0, 1.2],
    [xlabel, "x"],
    [ylabel, "exp(-x^2)"],
    [title, "Gaussian Curve"]
);

plot2d(
    [sin(x), cos(x)],
    [x, -2*%pi, 2*%pi],
    [xlabel, "x"],
    [ylabel, "Function value"],
    [legend, "sin(x)", "cos(x)"],
    [title, "Trigonometric Functions"],
    [gnuplot_preamble, "set grid"]
);

Parametric and Discrete Data Plots

Parametric curves are specified by the [parametric, xexpr, yexpr, [t, tmin, tmax]] form. Discrete datasets are plotted by supplying a list of points via [discrete, list], which is appropriate for sampled measurements, numerical outputs, or tabulated results.

  • [parametric, xexpr, yexpr, [t, tmin, tmax]] plots a parametric curve.
  • [discrete, list] plots discrete data points.
plot2d(
    [parametric, cos(t), sin(t), [t, 0, 2*%pi]],
    [xlabel, "x"],
    [ylabel, "y"],
    [title, "Unit Circle"],
    [grid, true]
);

pts : [[0,0], [1,1], [2,4], [3,9], [4,16]]$
plot2d(
    [discrete, pts],
    [xlabel, "x"],
    [ylabel, "y"],
    [title, "Discrete Data"]
);

3D Surfaces and Physics-Oriented Examples

Three-dimensional plots are produced with plot3d(expr, [x, xmin, xmax], [y, ymin, ymax]) and can be annotated analogously with axis labels and a title. In physics-oriented visualization, it is common to plot families of “wavefunction-like” expressions with shared weight functions and polynomial factors, and to label each curve by an index such as $n$.

  • plot3d(expr, [x, xmin, xmax], [y, ymin, ymax]); plots a surface over a rectangular domain.
plot3d(
    sin(x^2 + y^2)/(x^2 + y^2 + 1),
    [x, -3, 3],
    [y, -3, 3],
    [xlabel, "x"],
    [ylabel, "y"],
    [title, "3D Surface Plot"]
);

plot2d(
    [exp(-x^2), x*exp(-x^2), (2*x^2-1)*exp(-x^2)],
    [x, -3, 3],
    [xlabel, "x"],
    [ylabel, "Wavefunction-like forms"],
    [legend, "n=0", "n=1", "n=2"],
    [title, "Gaussian-weighted Polynomial Functions"],
    [gnuplot_preamble, "set grid"]
);

kill(all)$

plot2d(
    [sin(x), cos(x)],
    [x, -2*%pi, 2*%pi],
    [xlabel, "x"],
    [ylabel, "f(x)"],
    [legend, "sin(x)", "cos(x)"],
    [title, "Scientific Plot Example"],
    [grid, true]
)$