Frequently Used Abbreviations

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_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)*(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); 