[  Omega . A Computer Algebra System Explorer  ]
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## 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(5*x^2-8*x-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_IMAGE)$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_IMAGE)$
Graph parametric equations Graph $x=cos(t)$ $y=4\,sin(x)$ for $0\leq t \leq 2\,\pi$ plot2d([parametric, cos(t), 4*sin(t), [t,0, 2*%pi], [nticks, 200]], WEB_IMAGE)$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_IMAGE)$
Integrate an expression Compute $\int{sin(x)}\;dx$ integrate(sin(x),x);
Multiply an algebraic expression Compute $(5\,x+2)(x-2)$ expand((5*x+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([2*x-y=7, 4*x+2*y=2], [x,y]);
Solve an equation Solve $x^2-4\,x-5=0$ solve(x^2-4*x-5=0,x);