Introduction to ax-plots

Interactive Plotly.js plotting for Maxima via Aximar. Provides functions that reuse Maxima’s draw package object syntax (explicit, parametric, points, implicit) and add new objects (lines) for data plotting. Renders with Plotly instead of gnuplot. Lists and ndarrays (from the numerics package) are accepted transparently.

To use the package:

load("ax-plots");

2D Plotting

ax_plot2d (y1, x1, y2, x2, …, options) — Function

Plot expressions and/or data as interactive Plotly.js line charts. Arguments are consumed as (y, x) pairs, where y is what to plot and x is the domain.

Each pair can be:

• Expression + range: y is an expression (or list of expressions), x is [var, min, max]
• Data + data: y is a list or ndarray of values, x is a list or ndarray of coordinates

Calling forms:

• ax_plot2d(expr, [var, min, max]) — single expression
• ax_plot2d([expr_1, ..., expr_n], [var, min, max]) — multiple expressions sharing a range
• ax_plot2d(ys, xs) — data pair (lists or ndarrays), plotted as lines
• ax_plot2d([ys_1, ..., ys_n], xs) — multiple y series sharing one x
• ax_plot2d(expr, [var, lo, hi], ys, xs, ...) — mixed expressions and data

Examples

/* Single expression */
ax_plot2d(sin(x), [x, -%pi, %pi])$

/* Multiple expressions */
ax_plot2d([sin(x), cos(x)], [x, -5, 5])$

/* Data from lists */
ax_plot2d([1,4,9,16], [1,2,3,4])$

/* Data from ndarrays (requires numerics package) */
xs : np_linspace(-3, 3, 50)$
ax_plot2d(np_mul(xs, xs), xs)$

/* Apply a custom function with np_map */
f(x) := x^3 - x$
ax_plot2d(np_map(f, xs), xs)$

/* Or use a lambda for quick one-off transforms */
ax_plot2d(np_map(lambda([x], x^3 - x), xs), xs)$

/* Multiple y series sharing x */
ax_plot2d([np_pow(xs, 2), np_sin(xs)], xs)$

/* Mixed expressions and data */
ax_plot2d(sin(x), [x, -3, 3], np_pow(xs, 2), xs, title="Mixed")$

/* With options */
ax_plot2d(x^2, [x, -3, 3], title="Parabola", color="red")$

Style Options

Style options apply to subsequent traces until overridden:

Layout Options

See also: ax_draw2d, ax_draw3d, ax_polar, plot2d

ax_draw2d ([args]) — Function

Draw 2D interactive plots using Plotly.js. Accepts Maxima draw package objects and Aximar-specific objects, rendering them as interactive charts with pan, zoom, and hover.

Supported Objects

Draw package objects:

Aximar objects:

Examples

/* Explicit curves with styling */
ax_draw2d(
  color="red", explicit(x^2, x, -3, 3),
  color="blue", explicit(x^3, x, -2, 2)
)$

/* Filled contour */
ax_draw2d(
  ax_contour(sin(x)*cos(y), x, -%pi, %pi, y, -%pi, %pi),
  colorscale="Viridis", title="Contour Plot"
)$

/* Bar chart */
ax_draw2d(
  ax_bar(["Q1","Q2","Q3","Q4"], [100,150,120,180]),
  title="Quarterly Sales"
)$

/* Histogram */
ax_draw2d(
  ax_histogram(makelist(random(100)/10.0, i, 1, 500)),
  nbins=20, title="Distribution"
)$

/* Line plot from data */
ax_draw2d(lines([1,2,3,4,5], [1,4,9,16,25]))$

/* Scatter with separate x/y lists */
ax_draw2d(points([1,2,3,4,5], [1,4,9,16,25]))$

/* Lines and points accept ndarrays (requires numerics package) */
xs : np_linspace(-3, 3, 50)$
ax_draw2d(
  lines(xs, np_mul(xs, xs)),
  points(xs, np_sin(xs))
)$

/* Use np_map with a lambda for custom transforms */
ax_draw2d(lines(xs, np_map(lambda([x], x^3 - x), xs)))$

/* Phase portrait: vector field + streamlines */
ax_draw2d(
  color="#cccccc", ax_vector_field(-y, x, x, -3, 3, y, -3, 3),
  color="red", ax_streamline(-y, x, x, -3, 3, y, -3, 3),
  aspect_ratio=true, title="Phase Portrait"
)$

/* Streamlines with custom initial conditions */
ax_draw2d(
  initial_points=[[1,0],[0,1],[-1,0],[0,-1]],
  t_range=[0,8],
  ax_streamline(-y, x, x, -3, 3, y, -3, 3),
  aspect_ratio=true
)$

Style Options

Options use Plotly-native naming and apply to subsequent objects until overridden:

Layout Options

See also: ax_plot2d, ax_draw3d, ax_polar, draw2d

ax_polar (expr, [var, min, max]) — Function

Plot r(θ) curves in polar coordinates as interactive Plotly.js charts. Standalone function (like ax_plot2d).

Calling forms:

• ax_polar(expr, [θ, min, max], options) — single expression
• ax_polar([expr_1, ..., expr_n], [θ, min, max], options) — multiple expressions

Examples

/* Cardioid */
ax_polar(1 + cos(θ), [θ, 0, 2*%pi])$

/* Rose curve */
ax_polar(sin(3*θ), [θ, 0, 2*%pi], color="red", title="Rose Curve")$

/* Multiple curves */
ax_polar(
  [1 + cos(θ), 1 - cos(θ)],
  [θ, 0, 2*%pi],
  title="Cardioids"
)$

/* Spiral */
ax_polar(θ/10, [θ, 0, 6*%pi], title="Archimedean Spiral")$

Style Options

Layout Options

See also: ax_plot2d, ax_draw2d

3D Plotting

ax_draw3d ([args]) — Function

Draw 3D interactive plots using Plotly.js with WebGL rendering. Produces rotatable, zoomable 3D charts.

Supported Draw Objects

Examples

/* 3D surface */
ax_draw3d(explicit(sin(x)*cos(y), x, -%pi, %pi, y, -%pi, %pi))$

/* 3D scatter */
ax_draw3d(points([[1,1,1],[2,2,4],[3,3,9]]), marker_size=5)$

/* 3D scatter with separate coordinate arrays */
ax_draw3d(points([1,2,3], [4,5,6], [7,8,9]))$

/* 3D line plot from data */
ax_draw3d(lines([[0,0,0],[1,1,1],[2,0,2]]))$

/* 3D line from separate arrays (e.g. ndarrays) */
t : np_linspace(0, 6.28, 200)$
ax_draw3d(lines(np_cos(t), np_sin(t), np_scale(0.1, t)))$

/* With options */
ax_draw3d(
  explicit(x^2 - y^2, x, -2, 2, y, -2, 2),
  title="Saddle Surface",
  colorscale="Viridis"
)$

Style Options

Layout Options

See also: ax_plot2d, ax_draw2d, ax_polar, draw3d

Statistical Charts

ax_bar (categories, values) — Function

Bar chart for labeled or numeric data. Use inside ax_draw2d.

Calling forms:

• ax_bar(categories, values) — string category list + numeric value list
• ax_bar(values) — just values (auto-numbered 1, 2, 3, …)

For multiple series, use different name options and bar_mode layout option.

Examples

/* Basic bar chart */
ax_draw2d(
  ax_bar(["Q1","Q2","Q3","Q4"], [100,150,120,180]),
  title="Quarterly Sales"
)$

/* Colored bars */
ax_draw2d(
  color="steelblue", ax_bar(["A","B","C"], [10,20,30]),
  title="Categories"
)$

/* Grouped bars (multiple series) */
ax_draw2d(
  name="2024", ax_bar(["Q1","Q2","Q3"], [100,150,120]),
  name="2025", ax_bar(["Q1","Q2","Q3"], [110,160,140]),
  bar_mode="group", title="Year Comparison"
)$

/* Stacked bars */
ax_draw2d(
  name="Product A", ax_bar(["Jan","Feb","Mar"], [30,40,35]),
  name="Product B", ax_bar(["Jan","Feb","Mar"], [20,25,30]),
  bar_mode="stack"
)$

Relevant Options

Layout Options

See also: ax_draw2d, ax_histogram

ax_histogram (data) — Function

Histogram of numeric data. Use inside ax_draw2d. Takes a flat list of numbers; Plotly handles binning automatically.

Examples

/* Basic histogram */
data: makelist(random(100)/10.0, i, 1, 500)$
ax_draw2d(ax_histogram(data), title="Distribution")$

/* Control bin count */
ax_draw2d(ax_histogram(data), nbins=30)$

/* Overlaid histograms */
data1: makelist(random_normal(0, 1), i, 1, 500)$
data2: makelist(random_normal(2, 1.5), i, 1, 500)$
ax_draw2d(
  color="blue", opacity=0.5, name="Group A", ax_histogram(data1),
  color="red", opacity=0.5, name="Group B", ax_histogram(data2),
  bar_mode="overlay", title="Comparing Distributions"
)$

Relevant Options

Layout Options

See also: ax_draw2d, ax_bar

ax_heatmap (z_matrix) — Function

Heatmap visualization. Use inside ax_draw2d.

Calling forms:

• ax_heatmap(z_matrix) — pass a Maxima matrix(...) directly
• ax_heatmap(z_matrix, x_labels, y_labels) — matrix with string lists for axis labels
• ax_heatmap(expr, xvar, xlo, xhi, yvar, ylo, yhi) — symbolic expression sampled on a grid

Examples

/* From a matrix */
ax_draw2d(ax_heatmap(matrix([1,2,3],[4,5,6],[7,8,9])))$

/* With axis labels */
M: matrix([85,90,78],[92,88,95])$
ax_draw2d(
  ax_heatmap(M, ["Math","Science","English"], ["Alice","Bob"]),
  colorscale="Blues", title="Scores"
)$

/* From an expression */
ax_draw2d(
  ax_heatmap(sin(x)*cos(y), x, -%pi, %pi, y, -%pi, %pi),
  colorscale="Hot"
)$

Relevant Options

See also: ax_draw2d, ax_contour

Field Plots

ax_contour (expr, xvar, xlo, xhi, yvar, ylo, yhi) — Function

Filled contour plot of a 2D expression. Use inside ax_draw2d. Samples f(x,y) on a grid and renders as a Plotly contour chart with multiple filled levels.

Distinct from implicit() which renders a single contour line at f(x,y)=0.

Examples

/* Basic contour plot */
ax_draw2d(ax_contour(x^2 + y^2, x, -3, 3, y, -3, 3))$

/* With colorscale and contour count */
ax_draw2d(
  ax_contour(sin(x)*cos(y), x, -%pi, %pi, y, -%pi, %pi),
  colorscale="Viridis", ncontours=20,
  title="sin(x)*cos(y)"
)$

/* Hide colorbar */
ax_draw2d(
  ax_contour(x*y, x, -2, 2, y, -2, 2),
  showscale=false
)$

Relevant Options

See also: ax_draw2d, ax_heatmap, implicit

ax_vector_field (Fx, Fy, xvar, xlo, xhi, yvar, ylo, yhi) — Function

2D vector field (quiver) plot. Use inside ax_draw2d. Given a vector field F = (Fx(x,y), Fy(x,y)), samples on a grid and renders arrows showing the field direction and magnitude.

Examples

/* Rotation field */
ax_draw2d(ax_vector_field(-y, x, x, -3, 3, y, -3, 3))$

/* Source/sink */
ax_draw2d(
  ax_vector_field(x, y, x, -2, 2, y, -2, 2),
  title="Source"
)$

/* Direction-only (normalized arrows) */
ax_draw2d(
  ax_vector_field(-y, x, x, -3, 3, y, -3, 3),
  normalize=true, ngrid=25
)$

/* Phase portrait: vector field + streamlines */
ax_draw2d(
  color="#cccccc", ax_vector_field(-y, x, x, -3, 3, y, -3, 3),
  color="red", ax_streamline(-y, x, x, -3, 3, y, -3, 3),
  aspect_ratio=true, title="Phase Portrait"
)$

Relevant Options

See also: ax_draw2d, ax_streamline

ax_streamline (Fx, Fy, xvar, xlo, xhi, yvar, ylo, yhi) — Function

Streamline / phase portrait curves for a 2D ODE system dx/dt = Fx(x,y), dy/dt = Fy(x,y). Use inside ax_draw2d. Integrates trajectories from initial points using RK4.

Combine with ax_vector_field for a full phase portrait:

ax_draw2d(
  color="#cccccc", ax_vector_field(-y, x, x, -3, 3, y, -3, 3),
  color="red", ax_streamline(-y, x, x, -3, 3, y, -3, 3),
  aspect_ratio=true, title="Phase Portrait"
)$

Examples

/* Auto initial points */
ax_draw2d(ax_streamline(-y, x, x, -3, 3, y, -3, 3))$

/* Custom initial points and time range */
ax_draw2d(
  initial_points=[[0.5,0.5],[2,2],[3,1]],
  t_range=[0,20], dt=0.01,
  ax_streamline(x*(1-y), y*(x-1), x, 0, 4, y, 0, 4),
  title="Lotka-Volterra"
)$

Relevant Options

See also: ax_draw2d, ax_vector_field