I have been considering a port, but I definitely want to get it working once before even attempting to port it anywhere.

Try reading Algorithms for Computer Algebra. It's an excellent resource for that kind of stuff. As for the Risch algorithm...

It's great at solving monstrous integrals that would fry your brain, but it's very bad at producing pretty answers. For example, the integral of Sin(X) produces a nasty little equation involving imaginary exponentials that's equivalent to -Cos(x).

Looks kind of nice. I am happy that IE will be faster, because on computers that you are not allowed to install stuff on (school...), not having firefox/chrome drives me mad.

IE10 is a lot faster, if a bit buggy ATM. However, what I really like about Windows 8 is that you really aren't forced to do anything you don't want to. For example, I have the latest stable build of Firefox on my computer as well as a bunch of other Windows 7 applications that work perfectly. You also aren't really forced to interact with the Mosaic or use only web apps too much if you don't want to. It takes some getting used to, but once you get past the oddities, it's quite a nice OS.

There was an option that might have said something about saving files, but it was very ambiguous about what was intended and there was no warning of data loss. It's my fault for installing the OS in the first place though

I finally got a chance to try out Windows 8 and I must say that it's a lot better than I thought it would be.

Good things:

• The new IE is blazing fast. It'll be a serious competitor in the browser market again if they can keep it that way.
• You can use your desktop. The full desktop from Windows 7 appears to exist relatively unaltered in Windows 8. The only difference I've found is a smaller selection of backgrounds* and the windows themselves are more angular/ugly.
• The built-in apps are interesting. While I can't say I'll use most of them, I know quite a few people who would definitely find them useful. The selection is reminiscent of Linux Mint
• The learning curve isn't too steep. Users of previous versions of windows shouldn't have to spend a lot of time learning the new OS
• It's great on a tablet. While I can't say I've actually tested it on a Tablet, the configuration of the GUI leads me to believe that a Tablet running Win8 would be delightful to use.
• Task manager has gotten a well-deserved upgrade.

The Downside

• Textual input seems to be bit buggy. The cursor will occasionally jump five characters ahead of where it should be, leading to a huge whitespace gap while typing.
• Some of the default drivers don't appear to be as good as those in previous versions of Windows. My touchpad has always been odd, but it's very sensitive in the new OS. Accidentally brushing it will send it flying across the screen. I've had the same problem with Linux drivers.
• JavaScript doesn't appear to be fully compatible in the new IE. I've seen several applications, including Omnom, break as in the new browser.
• Some of the interfaces aren't exactly intuitive for PC users. For example, in tile mode, IE requires the right mouse button to be clicked before it will show the menu bars and there's no apparent way to shut the browser down short of closing every tab individually.
• Integration between the Mosaic and Desktop portions of the OS is virtually non-existent. A process opened in the Mosaic will often not show up in the Desktop and vice versa. It's slightly annoying as it means that one must switch between the modes to use applications in both*
• The Mosaic panel is awkward to navigate through using a mouse/touchpad. You're required to move the mouse through the entire length of the screen to hit a narrow scroll bar at the bottom of the screen. It'd be much easier if one could "grab" the background with the mouse and use that instead.

*It's still in pre-beta, so that's hardly surprising.

All I know is that my papers use the AMS math fonts

The TI-BASIC available on the 83+ series can be translated into Casio-BASIC almost line for line. The Prizm and the TI have incredibly similar forms of BASIC and are pretty much equivalent in power. If anything, Casio-BASIC is more powerful because it has a few more commands available than TI-83+ BASIC.