Quick Reference

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);