mathematica

Bracketing

Command	Meaning
2 + 8 I	complex
"text"	string

Command	Meaning
{a, b, c}	vector, list
{{a, b}, {c, d}}	2 × 2 matrix
n.m	matrix multiply
Inverse[m]	inverse of matrix
Transpose[m]	transpose
Det[m]	determinant
MatrixPower[m, n]	m^n
MatrixExp[m]	e^m
LinearSolve[m, b]	solve mx = b
Eigenvalues[m]	eigenvalues
Eigenvectors[m]	eigenvectors
Eigensystem[m]	eigenvalues and eigenvectors

Command	Meaning
Solve[lhs==rhs, x]	solve algebraic equation for x
DSolve[eqn, y[x], x]	solve differential equation
Reduce[eqn, x]	reduce equations
Eliminate[eqn, x]	eliminate variable x

Command	Meaning
<<file	read expressions from `file`, return last expression.
expression>>file	write `expression` to `file`.
expression>>>file	append `expression` to `file`.
!!file	display the content of `file`.
Save["file", x]	save the definition of `x` to `file`.
!command	issue a UNIX command.

Table[expression, {i, max}]: make a list of values of expression with i from 1 to max.
Module[{a, b, c}, expression1; expression2;…]: a procedure with local variables a, b, c return value of last expression.
Do[expression, {i, min, max, di}]: evaluate expression with i run from min to max in steps of di.
While[test, body]: evaluate body repeatedly, so long as test is True.
For[star,test,inc,body]: evaluate start, then repeatedly evaluate body and inc, until test fails.
If[test, then, else]: evaluate then if test is True, and else if it is False.
Which[test1,value1,test2,value2,…]: give the value associated with the first test that is True.
Switch[expression, form1, value1, form2, value2, …]: give the value associated with first form matching expression.
Function[x, body]: specify a pure function.
Nest[f, x, n]: apply the function f nested n times to x.
Apply[f, {a, b, c}]: f(a, b, c).
Map[f, {a, b, c}]: apply f to each elements, {f(a), f(b), f(c)}.