## 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 determinant(matrix([4,-3], [2,1]));
Compute a limit Calculate limit((x^2+x-6)/(x^2+2*x-8),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^2-3*x-4),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^2-8*x-4);
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_PLOT)$Graph a function of two variables in three dimensions Graph on and plot3d(sin(x)*cos(y), [x,0, 4*%pi], [y, 0, 2*%pi], [grid, 60, 60], WEB_PLOT)$
Graph parametric equations Graph for plot2d([parametric, cos(t), 4*sin(t), [t,0, 2*%pi], [nticks, 200]], WEB_PLOT)$Graph several functions Graph and on the interval plot2d([sin(x^2), sin(x)^2], [x, 0, 2*%pi], WEB_PLOT)$
Integrate an expression Compute integrate(sin(x),x);
Multiply an algebraic expression Compute expand((5*x+2)*(x-2));
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((x-1)/(x^2-1));
Solve a differential equation Solve ode2('diff(y,x)=1+y,y,x);
Solve a system of equations Solve solve([2*x-y=7, 4*x+2*y=2], [x,y]);
Solve an equation Solve solve(x^2-4*x-5=0,x);