From Wiki

I'm using certain standard terms a little differently than you might see on other sites or "in the literature". I'm starting to come up with some solid thoughts on calculator evolution, and maybe someday they'll be both solid and coherent.

Mostly, these notes are to describe various operations modes. Below, we'll provide keying examples for a single mathematical expression, um, let's say 2.5114 * (1 + tan(34 degrees) / sqrt(2)). We'll assume the calculator is cleared and ready for action, and the angle mode is degrees. (The result is 3.709, if you're curious.)

[edit] RPN

Meaning "Reverse Polish Notation". This is not pejorative, regardless of what diehard TI fans might think. This was actually developed by a Pole. RPN is a stack-based postfix operating method. It is up to the user to put the correct values on the stack (making use of the [ENTER] key where necessary) and then combining or altering these values using mathematical operations keys.

• Keying example: [2] [.] [5] [1] [1] [4] [ENTER] [1] [ENTER] [3] [4] [tan] [2] [2nd] [sqrt] [/] [+] [*]
  • 18 keystrokes. You can stop and write down the values of tan(34), sqrt(2), tan(34)/sqrt(2), 1 + tan(34)/sqrt(2), and the final result. Test calculator: Hewlett Packard HP-28S

[edit] Semi-Algebraic

TI used to call this "AOS" for "Algebraic Operating System", but that's a trade mark, so I am calling it "semi-algebraic". We were told in the sales brochures that this method let us enter our formulas just as they were written on the page. Well, they were close. Semi-algebraic calculators provide parenthesis keys, so when faced with 15 * ((3 + 4) * (7 + 8)), we can indeed key as written. But the unary functions and operators were pressed after their corresponding argument, for instance "30 [sin]" rather than "sin(30)"

• Keying example: [2] [.] [5] [1] [1] [4] [*] [(] [1] [+] [3] [4] [tan] [/] [2] [sqrt] [)] [=]
  • 18 keystrokes. You can stop and write down the values of tan(34), sqrt(2), 1 + tan(34)/sqrt(2) and the final result. Test calculator: Texas Instruments TI-30/TI-30 (1976).

[edit] Algebraic

This time, we really are going to key it in like it's written on the page. Some calculators include a "textbook" mode, an equation editor that actually typesets your input to look like it does in the mathbook. Others end up looking much like the way I typed the formula above. Some calculators will combine this into a symbolic result, rather than a numeric value, on the theory that "sqrt(2)" is exactly the square root of two, while 1.4142 is merely an "approximation".

• Keying example: [2] [.] [5] [1] [1] [4] [*] [(] [1] [+] [tan(] [3] [4] [)] [/] [2nd] [sqrt(] [2] [)] [)] [ENTER]
  • 21 keystrokes. You don't see any intermediate results, just the final answer. Test calculator: Texas Instruments TI-30/TI-30XIIB (2004) (On the TI-82, I had to provide opening parentheses as well as closing for the tangent and square root functions, adding two keystrokes)

Personally, I'm a little taken aback by the new TI symbolic calculators. For me, intermediate results provide an ongoing sanity check while I'm working out a formula. The symbolic units make it a little too easy to plug-n-chug (a complaint uttered by my teachers regarding the original TI-30, by the way). Imagine adding a column of figures on a symbolic calculator. You'd see this long string of addends (hopefully not overflowing the input buffer), and then you see the result. Makes me nervous, it does. Now I actually think the symbolic calculators are wonderful things -- as long as you aren't making numeric calculations. Otherwise they'll drive you insane. The Hewlett Packard HP-49g Plus is both a symbolic calculator and an RPN calculator; you can use it if you're just poking through some figures, and you can use it to work out the value of that rotation integral you just derived. With the TI models, you nearly need two calculators. Darn it, if I just want to see what the square root of the number on the screen is, I should just have to hit the square root key. I don't want to tell the calculator "Please evaluate sqrt(Ans)".