Wolfram Language Cheat Sheet
Learn Wolfram Language from the basics →
Basics
Shift + Enter- Evaluate the current notebook cell
f[x, y]- Function call — square brackets, capitalized built-ins
x = 5 / f[x_] := x^2- Immediate assignment / delayed definition
expr;- Semicolon suppresses the output
% / Clear[x]- Last result / remove a value
(* comment *)- Comment (can be nested)
?Plot- Quick help for a function
Numbers
1/3 + 1/6- Exact arithmetic: 1/2
N[Pi, 30]- Numeric value to 30 digits
10/4.- A decimal point makes it approximate: 2.5
Quotient[17, 5] / Mod[17, 5]- Integer division and remainder
Round / Floor / Ceiling- Rounding
Prime[10] / PrimeQ[n] / FactorInteger[n]- Number theory
Lists
{1, 2, 3} / Range[10] / Table[i^2, {i, 5}]- Create lists
list[[1]] / list[[-1]] / list[[2 ;; 4]]- Parts: first, last, span
Length / Total / Mean / Sort / Reverse- Common list functions
{1, 2, 3} + 10- Arithmetic works element-wise: {11, 12, 13}
Select[list, EvenQ]- Keep elements that pass a test
Append / Join / Flatten / Partition- Build and reshape
Functional Programming
#^2 & / x |-> x^2- Pure (anonymous) functions
f /@ {a, b}- Map: {f[a], f[b]}
f @@ {a, b}- Apply: f[a, b]
f @@@ {{a, b}, {c, d}}- Apply at level 1: {f[a, b], f[c, d]}
f @ x / x // f- Prefix and postfix call
Fold[f, x, list] / Nest[f, x, n]- Accumulate / repeat a function
Patterns & Rules
x_ / x_Integer / x__ / x___- Any expression / of a head / 1+ / 0+ items
x_ /; x > 0 / x_?EvenQ- Conditions on patterns
expr /. x -> 3- Replace all: substitute a value
f[n_] :> n^2- Delayed rule (right side evaluated per match)
Cases[list, _Integer]- Elements matching a pattern
MatchQ[expr, pattern]- Test a match
Symbolic Math
Expand / Factor / Simplify / Together / Apart- Rewrite expressions
Solve[x^2 == 4, x]- Exact solutions as rules
NSolve / FindRoot[Cos[x] == x, {x, 1}]- Numeric solutions
D[f, x] / Integrate[f, x]- Derivative / integral
Integrate[f, {x, 0, 1}] / NIntegrate- Definite integral, exact or numeric
Limit / Series / Sum / DSolve- Limits, series, sums, differential equations
Associations & Data
a = <|"x" -> 1, "y" -> 2|>- Association (key-value map)
a["x"] / Lookup[a, "z", 0]- Look up a key, with a default
Keys / Values / KeySort / KeyValueMap- Work with keys and values
Counts[list] / GroupBy[list, f]- Count or group into associations
Import["data.csv", "Dataset", HeaderLines -> 1]- Load a CSV as a Dataset
ds[Select[#age > 30 &], "name"]- Query a Dataset
Plotting & Deployment
Plot[Sin[x], {x, 0, 2 Pi}]- Plot a function
ListPlot / BarChart / Histogram- Plot data
Manipulate[Plot[Sin[a x], {x, 0, 6}], {a, 1, 5}]- Interactive controls
Export["plot.png", graphic]- Save a graphic or data to a file
CloudDeploy[APIFunction[{"n" -> "Integer"}, #n^2 &]]- Deploy a web API
wolframscript -file script.wls- Run a script from the terminal