Quick Reference

Frequently Used Abbreviations

+	addition
-	subtraction
*	multiplication
.	matrix noncommutative multiplication
/	division
^	exponentiation
!	factorial
:	variable assignment
:=	function assignment

=	equal
#	not equal
>	greater than
>=	greater than or equal to
<	less than
<=	less than or equal to
$	output suppressor
%	latest expression
;	block/line terminator

Five Basic Rules

Multiplication is represented by asterisk (*), for example: 2*x.
A semicolon (;) or dollar sign ($) must be included at the end of each command.
To submit your query, press button marked 'Execute'.
The arguments of functions are given in parenthesses (...).
To multiply matrices, use period (.), for example, m1.m2.

Frequently Used Commands

Topic	Example	Command
Compute a determinant	Compute $\left\|\begin{array}{cc}4&-3\\2&1 \end{array}\right\|$	determinant(matrix([4,-3], [2,1]));
Compute a limit	Calculate $\lim_{x \to 2}{{x^2+x-6}\over{x^2+2\,x-8}}$	limit((x^2+x-6)/(x^2+2*x-8),x,2);
Compute a power series	Compute the power series of degree 5 for $sin(x)$ about x=0	taylor(sin(x),x,0,5);
Compute the partial fraction decomposition of an expression	Find the partial fraction decomposition of ${{x}\over{x^2-3\,x-4}}$	partfrac(x/(x^2-3*x-4),x);
Define a function	Define $f(x)={{x^2}\over{x^2+1}}$	f(x):=x^2/(x^2+1);
Define a matrix	Define A= $\left(\begin{array}{rr} 4 & 3 \\ 5 & 0 \end{array}\right)$	a:matrix([4,3], [5,0]);
Differentiate an expression	Compute ${{d}\over{dx}}sin(x)$	diff(sin(x),x);
Display an expression as a single fraction	Write $1+{{1}\over{x}}$ as a single fraction	ratsimp(1+1/x);
Factor a polynomial	Factor $5\,x^2-8\,x-4$	factor(5x^2-8x-4);
Find the eigenvalues and corresponding eigenvectors of a matrix	Find the eigenvalues and corresponding eigenvectors of $\left(\begin{array}{rr} -17 & -15 \\ 20 & 18 \end{array}\right)$	eigenvectors(matrix([-17, -15], [20, 18]));
Find the inverse of a matrix	Calculate ${\left(\begin{array}{rr} -4 & 3 \\ 4 & -4 \end{array}\right)}^{-1}$	invert(matrix([-4,3], [4, -4]));
Generate a random number	Generate a random integer between 0 and 10	random(11);
Graph a function	Graph ${{x}\over{x^2+1}}$ on the interval [-6, 6]	plot2d(x/(x^2+1), [x,-6, 6], WEB_PLOT)$
Graph a function of two variables in three dimensions	Graph $sin(x)\,cos(y)$ on $0\leq x \leq 4\,\pi$ and $0\leq y \leq 2\,\pi$	plot3d(sin(x)cos(y), [x,0, 4%pi], [y, 0, 2*%pi], [grid, 60, 60], WEB_PLOT)$
Graph parametric equations	Graph $x=cos(t)$ $y=4\,sin(x)$ for $0\leq t \leq 2\,\pi$	plot2d([parametric, cos(t), 4sin(t), [t,0, 2%pi], [nticks, 200]], WEB_PLOT)$
Graph several functions	Graph ${sin(x)}^2$ and $sin(x^2)$ on the interval $[0, 2\,\pi]$	plot2d([sin(x^2), sin(x)^2], [x, 0, 2*%pi], WEB_PLOT)$
Integrate an expression	Compute $\int{sin(x)}\;dx$	integrate(sin(x),x);
Multiply an algebraic expression	Compute $(5\,x+2)(x-2)$	expand((5x+2)(x-2));
Multiply together two matrices	Compute AB if A= $\left(\begin{array}{rr} 4 & 2 \\ 7 & 4 \end{array}\right)$ B= $\left(\begin{array}{rr} 1 & 9 \\ 6 & 6 \end{array}\right)$	a:matrix([4,2], [7,4])$ b:matrix([1,9], [6, 6])$ a.b;
Reduce a fraction to lowest terms	Reduce ${{x-1}\over{x^2-1}}$ to lowest terms	ratsimp((x-1)/(x^2-1));
Solve a differential equation	Solve ${dy \over {dx}}=y+1$	ode2('diff(y,x)=1+y,y,x);
Solve a system of equations	Solve $\begin{cases} 2x - y = 7 \\ 4x + 2y = 2 \end{cases}$	solve([2x-y=7, 4x+2*y=2], [x,y]);
Solve an equation	Solve $x^2-4\,x-5=0$	solve(x^2-4*x-5=0,x);