Computer algebra

I've been looking into computer algebra systems for some mathematical noodling that I'm doing.  I'm rusty enough at calculus that they are a useful crutch, but if I get handy enough with them they could be useful in ways beyond my current problem.  I'm interested mostly in doing symbolic manipulation and I've found that Maxima seems to be the free gold standard for what I'm interested in.  However, I've ended up using a program called SpaceTime, because it seemed to have a lower threshold to get to useful results and because it has versions that run on my PC and on my iPhone.  The PC version is free and the iPhone version is $20, which I haven't yet decided to pay, but isn't it wonderful that I can try it out for free?

There is an interesting anecdote or two here, illustrating why one might want to do computer algebra.

Spam :(

I use Hotmail for a main email account. They generally have good spam filtering on the incoming email. Unfortunately they don't do so well on outgoing.

"I" ended up sending spam. Out to my whole email list. I don't know how it happened, since I am quite careful and well aware of various net pitfalls.

I suspect that my son browsed to an unsafe site while I had an open Hotmail window. I was using Internet Explorer of course. Thank you, Bill Gates!

I ran a virus check (definitions were only 24H out of date on my previous scan less than 12 hours before), nonetheless I had to check. No virus found. Also changed my Hotmail password from a wired computer in case of wireless intercept. I use 128bit WEP, have IP-selective service, and my nearby neighbors are idiots by all indications, so a wireless intercept is unlikely. Still, you can't be too cautious.

I had used IE because certain people in my house don't seem to get Firefox with Noscript. Now they will have to learn to love it.