The language

An Axis file is a list of statements. Each one becomes one item in the graph, whether an expression, a note, a folder or a table, in the order it is written - so the file reads top to bottom the way the expression list does.

// A comment runs to the end of the line, and never reaches the graph.
"A note is a string on its own."

f(x) = x ^ 2 - 4x + 3
c = 3
y = c * x - 4

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Statements end at a newline

A statement ends at the newline after it, or at a ;, so two short ones may share a line. That holds at the top level and inside every block: a folder, a table, a config, a style or an @{ … } block.

a = 1; b = 2
y = a x + b

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A comma never separates statements - commas belong to expressions: points, lists, calls, action runs, and the bindings of with and for. Inside an open bracket a newline ends nothing, so a long list or piecewise may spread over as many lines as it likes:

P = [
    (-2, 4),
    (0, 0),
    (2, 4),
] @ color: GREEN, pointSize: 14

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Comments are // to the end of the line. There are no block comments.

Definitions and equations

What = means depends on its left-hand side:

• f(x) = …, a call on fresh names, defines a function.
• a = …, where a is a name other than x or y (or r and theta in a polar equation), defines a variable.
• Anything else is an equation, and is graphed.

f(x) = x ^ 2 - 4x + 3
g(x) = f(2x - 1)
k = 0.5
y = k * g(x)
x ^ 2 + y ^ 2 = 9
y < x - 2

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A function definition graphs as well as defining the function, and an inequality shades the region where it holds. A statement need not have an = at all: a point, a list of points, or polygon(…) on its own is drawn.

Notes

A string on its own line is a note - the text card in Desmos’ expression list. It is how a graph explains itself to whoever opens it next, where a comment explains the file to whoever reads it.

"Drag the slider to change the slope."
m = 1 @ slider: -3..3 step 0.1
y = m x

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Metadata

Anything after an @ is metadata: how the statement it trails looks and behaves. Properties are separated by commas, and when there are too many to sit comfortably on the line, @{ … } gives them one line each.

y = x ^ 2 @ color: RED, lineWidth: 4
y = x ^ 3 @{
    color: BLUE
    lineStyle: DASHED
    label: "cubic"
}
k = 10 @ hidden

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A property that is true or false may be written bare, as hidden is above, and means true. Styling covers the properties that change how a statement looks, and the property reference lists every one and where it may be written.

Folders

folder "Title" { … } groups the statements inside it. Desmos has one level of folders, so a folder inside a folder is an error. The title is optional, and metadata written immediately after the { belongs to the folder itself:

folder "Working values" { @ collapsed
    amp = 2 @ slider: 0..5 step 0.1
    freq = 3 @ slider: 1..8 step 1
}

y = amp * sin(freq * x)

folder { y = amp * cos(freq * x); y = amp }

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A folder takes collapsed, hidden and secret. Metadata on a line of its own anywhere else trails nothing, and is an error.

Tables

table { … } is a Desmos table, one column per entry. x = [1, 2, 3] is a column with a header and its values; the first column is what the others are plotted against.

table {
    x = [1, 2, 3, 4, 5]
    y = [2, 4, 8, 16, 32] @ color: RED
}

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Tables and lists has the rest of it: computed columns, styling a whole table, and when a list is the better tool.

Config

config { … } sets up the calculator itself rather than any one expression: the grid and axes, the viewport, the theme, and which parts of the Desmos interface appear. A file has at most one, at the top level.

config {
    showGrid: true
    xmin: -2
    xmax: 8
    xAxisLabel: "time (s)"
}

h(t) = 20t - 4.9t ^ 2

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A compiled file is meant to be a finished graph rather than an editor, so Axis leaves off the chrome desmos.com wraps around one: the settings menu, the zoom buttons and the border are off, and the expression list starts collapsed. config asks for any of them back - zoomButtons: true, expressionsCollapsed: false, and so on. The settings reference lists every entry.

calculator picks which Desmos calculator draws the graph: GRAPHING, the default, GEOMETRY or GRAPHING_3D.

config { calculator: GEOMETRY }

A = (0, 0)
B = (4, 1)
polygon(A, B, (1, 3))

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The geometry and 3D calculators draw the same expressions the graphing one does. What only they have - geometric constructions, a z axis - is not in Axis yet.

The other statements

Four statements have pages of their own:

• style names a set of properties to reuse, and macro names an expression (Macros and styles).
• import brings another file in as a folder, and image places a picture (Imports and images).
• ticker runs an action over and over for as long as the graph is open (Sliders and animation).

config, style, macro and ticker belong at the top level; written inside a folder, each is an error.