Cheatsheet

One page covering everything, for scanning or bookmarking. Each area has its own page with the full detail.

Every example below is executed against the engine when the documentation is built, so if one of them is wrong the build fails rather than the page quietly going stale.

Arithmetic

2 + 2 * 10 // 22
(2 + 3) * 4 // 20
2^10 // 1,024
17 mod 5 // 2
2.5k // 2,500
3M // 3,000,000

Note that % means percent, not modulo. Use mod or modulo for remainder. Writing 17 % 5 is a parse error rather than 2, because 17 % is already a complete expression.

Percentages

10% of 250 // 25
increase 100 by 10% // 110.00
100 to 150 // 50.00%
5% of what is 6 // 120

Units

100cm + 2m // 300.00 cm
1 km + 500 m // 1.50 km
5 km to miles // 3.11 miles
1 hour to minutes // 60 minutes
72F to C // 22.22 C
20C in F // 68.00 F

Functions

sqrt(16) // 4
max(3, 7) // 7
round(3.7) // 4
gcd(12, 18) // 6
hex(255) // 0xFF
bin(5) // 0b101

Statistics and phrasing

average of 10, 20, 30 // 20
median of 1, 5, 3 // 3
larger of 10 and 4 // 10
half of 50 // 25
clamp 15 between 1 and 10 // 10

Conversions

255 as hex // 0xFF
255 as binary // 0b11111111
0.5 as % // 50.00%
0.75 as fraction // 3/4

Programmer math

0xFF // 255
0b1010 // 10
0o17 // 15
1 << 8 // 256
0xFF & 0x0F // 15
0xF0 | 0x0F // 255
12 xor 10 // 6
1 KiB in bytes // 1024.00 bytes

Conditionals

5 > 3 // true
10 == 10 // true
true and false // false
if 5 > 3 then 100 else 200 // 100

Variables and functions

Colon-prefixed names are explicit. A bare name works too.

:a = 10
:b = 20
:a + :b // 30

f(x) = 2*x + 1
f(5) // 11

Matrices and vectors

[1,2;3,4] // [1, 2; 3, 4]
[1,2,3] * 10 // [10, 20, 30]
[1,2,3] + [10,20,30] // [11, 22, 33]
[1,2,3][0] // 1
[1,2;3,4]^T // [1, 3; 2, 4]
det([1,2;3,4]) // -2

Ranges, map and reduce

A range is written start:end. It is only recognised inside brackets or a function call, because a bare 0:3 is a clock time. See map, reduce and aggregates.

map(10*x, 0:3) // [0, 10, 20, 30]
sum(x, 0:4) // 10
sum(x, [10, 20, 30]) // 60
reduce(acc+x, [1,2,3]) // 6
prod(x, [2,3,4]) // 24

Symbolic

An unknown stays an unknown rather than becoming an error.

1+2+b+3+b => // 2b+6
x^2+3x+2 => // x^2+3x+2

Algebra

expand((x+1)*(x+2)) // x^2+3x+2
factor(x^2-4) // (x-2)*(x+2)
solve(x^2-4=0, x) // [-2, 2]
solve(2x+6=0, x) // -3
cancel((x^2-1)/(x-1)) // x+1
apart((3x+5)/(x^2-1)) // 4/(x-1)-1/(x+1)

An equation with one unknown can also be written on its own line.

x^2-4 = 0
x => // [-2, 2]

Complex numbers

3i // 3i
1i*1i // -1
sqrt(-4) // 2i
conj(2+3i) // 2-3i
solve(x^2+1=0, x) // [-i, i]

Calculus

der(x^3, x) // 3x^2
integral(x^2, x) // 1/3x^3
taylor(sin(x), x=0, 5) // 1/120x^5-1/6x^3+x
jacobian(x*y, x+y) // [y, x; 1, 1]

Money

$100 + $50 // $150.00
10 dollars // $10.00
tax on 100 at 20% // 20

Currency conversion such as 10 USD to GBP reaches the network, so it resolves asynchronously rather than returning a value immediately. See async and live data.

Dates and times

Results depend on the current date, so these are shown rather than asserted.

Expression	Result
25/12/2023 + 20 days	Sunday, January 14, 2024
next friday	the date of the coming Friday
days until 25/12/2026	the number of days, as a duration
9:00am + 3 hours	12:00:00 PM on the current day
7:30 to 20:45	795 minutes

Bigger integers

123n * 2 // 246

Comments and headings

A line starting with # is a heading and evaluates to nothing. Text after // is a comment.

2 + 2 // comment // 4

A label followed by a colon is kept, and the expression after it is evaluated.

total: 5 + 3 // 8