Maxima was inspired by the first successful computer algebra system, Macsyma developed at MIT. It is able to perform symbolic integration, differentiation, expansions, and simplifications of expressions.
There are several available interfaces for maxima. The basic program can be run from the command line. But a better way to use Maxima is via wxMaxima and xMaxima. Between the two, I gravitate towards wxMaxima. Here are some capabilities of Maxima.
Here are some simple outputs from Maxima just to get started.
(%i1) diff(x^3, x);
(%o1) 3*x^2
(%i2) expand((x+y)^3);
(%o2) y^3+3*x*y^2+3*x^2*y+x^3
(%i3) integrate(x^3,x);
(%o3) x^4/4
(%i4) factor(x^2 + 2 *x + 1);
(%o4) (x+1)^2
(%i5) 15!
(%o5) 1307674368000
In the above example, after entering ; we press shift enter, not just the enter key to see the results. The outputs are actually pretty printed.
We will add more entries to using Maxima in the future! Stay tuned.
I'm happy to see wxMaxima on your site -- it's a great open-source alternative to the commercial big dogs (Maple, Mathematica and Matlab) for lower division math, engineering and science students. I recently wrote two CC-BY-NC-SA open textbooks for wxMaxima here: http://wxmaximafor.wordpress.com/ . These books can be used by calculus instructors who want to assign extra CAS homework problems or run a complete 1-unit calculus lab, but they are also a great reference for students who want to learn computer algebra independently and by-example. Thanks, Zak.
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