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 



Frequently Used Commands
Topic

Example

Command


Compute a determinant

Compute

determinant(matrix([4,3], [2,1]));

Compute a limit

Calculate

limit((x^2+x6)/(x^2+2*x8),x,2);

Compute a power series

Compute the power series of degree 5 for about x=0

taylor(sin(x),x,0,5);

Compute the partial fraction decomposition of an expression

Find the partial fraction decomposition of

partfrac(x/(x^23*x4),x);

Define a function

Define

f(x):=x^2/(x^2+1);

Define a matrix

Define A=

a:matrix([4,3], [5,0]);

Differentiate an expression

Compute

diff(sin(x),x);

Display an expression as a single fraction

Write as a single fraction

ratsimp(1+1/x);

Factor a polynomial

Factor

factor(5*x^28*x4);

Find the eigenvalues and corresponding eigenvectors of a matrix

Find the eigenvalues and corresponding eigenvectors of

eigenvectors(matrix([17, 15], [20, 18]));

Find the inverse of a matrix

Calculate

invert(matrix([4,3], [4, 4]));

Generate a random number

Generate a random integer between 0 and 10

random(11);

Graph a function

Graph on the interval [6, 6]

plot2d(x/(x^2+1), [x,6, 6], WEB_IMAGE)$

Graph a function of two variables in three dimensions

Graph on
and

plot3d(sin(x)*cos(y), [x,0, 4*%pi], [y, 0, 2*%pi], [grid, 60, 60], WEB_IMAGE)$

Graph parametric equations

Graph
for

plot2d([parametric, cos(t), 4*sin(t), [t,0, 2*%pi], [nticks, 200]], WEB_IMAGE)$

Graph several functions

Graph and
on the interval

plot2d([sin(x^2), sin(x)^2], [x, 0, 2*%pi], WEB_IMAGE)$

Integrate an expression

Compute

integrate(sin(x),x);

Multiply an algebraic expression

Compute

expand((5*x+2)*(x2));

Multiply together two matrices

Compute AB if
A=
B=

a:matrix([4,2], [7,4])$
b:matrix([1,9], [6, 6])$
a.b;

Reduce a fraction to lowest terms

Reduce
to lowest terms

ratsimp((x1)/(x^21));

Solve a differential equation

Solve

ode2('diff(y,x)=1+y,y,x);

Solve a system of equations

Solve

solve([2*xy=7, 4*x+2*y=2], [x,y]);

Solve an equation

Solve

solve(x^24*x5=0,x);



