The math syntax

On the page, math is drawn: fractions stacked, roots with their sign, subscripts lowered. Underneath, every statement is a line of plain text, the linear syntax. It is what a .bbm file holds, what the command line prints, what AI assistants read and write, and what Ctrl+C copies.

M_max := q*L^2/8 = ? kN*m

is drawn as M_max := q·L²/8 = 54 kN·m. You never need to type the text form in the app (the keys build the math), but it is good to read.

Statements

Write	Means	Key in the app
x := 3 m	Define x	:
g ::= 9.81 m/s^2	A global definition (≡), defined before everything else	~
x = ?	Show x’s value	=
x = ? mm	Show it in mm	=, then the unit
M := q*L^2/8 = ? kN*m	Define and show	= at the end of a definition
diff(x^3, x) -> ?	Evaluate symbolically (→)	Ctrl+.
x^2 - 4 -> solve(x) -> ?	Symbolic, with a keyword	Ctrl+Shift+.

? is an empty slot. After = or -> it is where the result goes; anywhere else it is a placeholder still to fill, drawn as ■. In a file, a result is kept after the statement, as #= 54 kN*m (or #! message for an error); see the file format.

Numbers and text

Write	Is
3, 3.5, .5, 1.2e-3	Numbers
2i, 3 + 4i	Complex numbers (the imaginary unit is 1i; a plain i is a name)
0x1F, 0o17, 0b101	Hexadecimal, octal, binary (0x1F + 0b101 is 36)
"hello"	Text (a string)
[1, 2; 3, 4]	A matrix: , between columns, ; between rows
[1; 2; 3]	A column vector

Names

• Letters, digits, _ and ', starting with a letter: x, F2, f'. Case matters: F and f are different.
• Greek letters are themselves: α, Δ. In plain ASCII, \alpha and \Delta are read as α and Δ.
• Subscripts: everything after the first _ is a subscript, drawn lowered: M_max. Typed with . in the app. x_1 is a name, not an index.
• Units are names too, so m, kN and s are built-in names. Defining your own m hides the metre below it.
• ∇, ∂ and ° count as letters: ∇H, Δ°C.
• Any other character needs the name in backticks: `θ*`, `x%`. In the app, Ctrl+Shift+K types such a name; the backticks are never drawn.
• x_ (an empty subscript, typed x.) is a different name from x that looks the same.

Name styles

A name can be plain (drawn italic), bold or upright, and each style is a different variable: F, \bf F and \rm F can hold three values. Ctrl+B makes a name bold; Ctrl+I turns a plain name upright and back.

• Built-in units, functions and constants are plain, except the gram, which is the upright \rm g (plain g is gravity).
• \it marks a plain name, for a variable named like a keyword: \it if := 4.

Operators

From loosest to tightest:

Write	Is
try a on error b	a, or b if a fails
a or b, a xor b	Logical or, exclusive or
a and b	Logical and
not a	Logical not
==, !=, <, <=, >, >=	Comparisons, giving 1 (true) or 0 (false). == is the bold equals (Ctrl+=). Chains: 0 < x < 1
a..b, a, b..c	A range (only as a definition’s whole value, or in a for)
+, -	Add, subtract
*, /, ÷, ×	Multiply, divide, cross product
-a	Negative
a^b	Power (-x^2 is −(x²))
a!, M^T, M^<j>	Factorial, transpose, column j
v[i], M[i, j], f(x)	Element, call

• Multiplying by a name needs no *: 12 kN/m is 12·kN/m, and q L^2 (with a space) is q·L², drawn with a thin space instead of a dot.
• A division / is drawn stacked. ÷ and ∕ divide on the line, drawn ÷ or /; right-click a division to change it.
• A multiplication * is drawn as the sheet says (a dot by default; Format → Multiplication); · is always a dot. Right-click one to change it.
• |x| is the absolute value, a vector’s length, or a matrix’s determinant.

Functions

As text

f(x) := x^2 + 1
g(x, y) := sqrt(x^2 + y^2)
h := f

Open this example · Download .bbm

Some built-ins are drawn as math:

Write	Drawn as
sqrt(x), nthroot(x, n)	√x, ⁿ√x
sum(e, i), sum(e, k, a, b)	Σ over a range variable, or from a to b
prod(e, i), prod(e, k, a, b)	Π
int(e, x, a, b)	∫ from a to b … dx
diff(e, x), diff(e, x, n)	d/dx, dⁿ/dxⁿ
lim(e, x, a)	lim as x → a
vec(e)	an arrow over e: element by element

The functions reference has every one. Functions from a Python file are reached with a dot: bt := use "beam_tools.py", then bt.moment(q, L) (Python).

Ranges and indices

i := 0..10           whole numbers 0 to 10
x := 0, 0.1..1       0, 0.1, 0.2 … 1
v[i] := i^2          one element per value of i
M[1, 2]              an element
M^<2>                column 2

Indices count from ORIGIN, 0 unless the sheet sets it (ORIGIN := 1, or origin: 1 in the settings).

Programs

A definition ending in := takes the indented lines below it as a program, two spaces per level:

As text

f(x) :=
  if x < 0
    return -x
  otherwise
    x

Open this example · Download .bbm

Write	Is
a <- expr	A local variable (drawn ←)
if cond + lines, otherwise + lines	Conditions
x if cond, x otherwise	The same on one line
for k in 1..n, for x in v	A loop over a range or a vector
while cond	A loop while cond holds
return x, break, continue	Leave the program, the loop, or this turn of it

A program’s value is that of the last line it runs. No blank lines inside a program, and indent with spaces, not tabs. Where a program is only part of a value, the word program stands in its place, with its lines below:

As text

r := program*2 = ?
  a <- 3
  a + 1

Open this example · Download .bbm

gives 8.

Solve blocks

As text

x := 1
y := 1
given
x^2 + y^2 == 4
x - y == 1
s := find(x, y) = ?

Open this example · Download .bbm

See Solve equations.

Symbolic

(x + 1)^2 -> expand -> ?
x^2 - 4 -> solve(x) -> ?

Keywords chain from left to right, each followed by ->; the statement ends with -> ?. See Symbolic algebra.

No comments

Math has no comments: notes go in text regions beside it. In a file, #= and #! at the end of a line hold results and errors.