# Intro to Mathematica/WolframLang Notation

By Xah Lee. Date: . Last updated: .

Here's a very brief intro to WolframLang syntax, showing just the most commonly used syntax that is not obvious.

## Arithmetic Operator

• `x ^ y` means x raised to power of y.

## Brackets

• Square brackets means function argument. e.g. `Sin[x]`
• Parenthesis means order of operation. e.g. `(3 + 5) * 2`
• Curly braces means list. e.g. `{a,b,c}`, also for vector. Nested list represent a matrx or tree.
• Double Square brackets means getting an element from a list. e.g. `{x,y,z}[]` returns `x`.

## Vector and Matrix

• `{a,b}` is a 2D vector. `{a,b,c}` is 3D vector.
• nested list `{{a,b},{c,d}}` is a matrix, with 1st row `{a,b}`, second row `{c,d}`.
• `{a,b} . {x,y}` means dot product.
• `{a,b} + {x,y}` means `{a + x, b + y}`.
• `c * {x,y}` means `{c * x, c * y}`.
• `{x,y} / c` means `{x/z, y/z}`.

## Function

• `f[x,y]` is a function.
• `f @ x` is the prefix notation for `f[x]`. e.g. `Cos @ x` means `Cos[x]`, `Cos @ Norm @ {x,y}` means `Cos[Norm[{x,y}]]`.
• `x // f` is the postfix notation for `f[x]`. e.g. `x // Cos` means `Cos[x]`.
• `#` the hash sign stand for parameter of a function. `#` or `#1` is first parameter, `#2` second, etc.
• `&` (ampersand) means the expression before is a function, with hash sign `#` meaning its parameters. e.g. `(#1 + #2 &)` is the same as `Function[ {x, y}, x + y ]`

## Complex Number

• `I` (Capital letter I) is the imaginary number.
• `Pi` is π.

## Misc

• space is implicit multiplication. e.g. `a b` means `a * b`.