Intro to WolframLang Mathematica Notation

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}[[1]] 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.

Misc

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