I’m often surprised by maths teachers complaining, in blogs or online postings, of the lack of a good freeware general purpose computer algebra system. In fact there are several. The topic of this posting is Maxima.
Maxima can do most things, and there is a small army of developers and users constantly extending and upgrading it. As a tiny introduction, here is Newton’s method, done interactively. Maxima uses a singe colon for assigning a variable, and colon-equals for defining a function. First, the function:
Next, Newton’s method applied to this function:
Now, with a starting value of 0.7, we can start the iterations (as with Maple, Maxima uses the percentage sign to refer to the results of the previous command):
(%i3) nr(0.7); (%o3) 0.8314862526437223 (%i4) nr(%); (%o4) 0.8095730086415593 (%i5) nr(%); (%o5) 0.8087317874228543 (%i6) nr(%); (%o6) 0.8087306004817508 (%i7) nr(%); (%o7) 0.808730600479392 (%i8) nr(%); (%o8) 0.808730600479392