Sympy is pretty awesome. I use live.sympy.org a lot with my students because you can bookmark an entire interactive session as a (long) URL. For example, suppos

Sympy is pretty awesome. I use live.sympy.org a lot with my students because you can bookmark an entire interactive session as a (long) URL. For example, suppose you had to answer the following question. Find the position of the object at t=3 seconds, if it starts from x_i=20[m], with v_i=10[m/s] and undergoes a constant acceleration of a=5[m/s^2]. Ans: 72.5[m]. Sol.: http://bit.ly/1hJS9P3 http://bit.ly/1hJS9P3 Below are some more examples of cool stuff sympy can do. Expand, factor, and solve polynomials: >>> P = (x-1)*(x-2)*(x-3) >>> P.expand() x**3 - 6*x**2 + 11*x - 6 >>> P.factor() (x - 1)*(x - 2)*(x - 3) >>> roots = solve(P,x) >>> roots [1, 2, 3] Derive the solutions of a quadratic equation: >>> solve( a*x**2 + b*x + c, x) [(-b + sqrt(-4*a*c + b**2))/(2*a), -(b + sqrt(-4*a*c + b**2))/(2*a)] Compute symbolic outputs of trig functions: >>> sin(pi/6) 1/2 >>> cos(pi/6) sqrt(3)/2 Sympy knows about trig identities: >>> sin(x) == cos(x - pi/2) True >>> simplify( sin(x)*cos(y)+cos(x)*sin(y) ) sin(x + y) >>> e = sin(x)**2 + cos(x)**2 >>> trigsimp(e) 1 Find the solution to the simple harmonic oscillator differential equation (x''(t)+w^2x(t)=0): >>> sol = dsolve( diff(x(t),t,t) + w**2*x(t), x(t) ) >>> sol x(t) == C1*sin(w*t) + C2*cos(w*t) For v4.1 of my math book, I'm going to add a short sympy tutorial. I'll post a printable version of it to HN when I release, so stay tuned ;)