Thanks allyn. That’s a good example how you’d enter it on a RPN calculator.
Well, aceplace57’s expression 2((8 + 9/3) * (40/8)) would most directly correspond to 2, 8, 9, 3, /, +, 40, 8, /, *, *.
What you’ve written corresponds instead directly to (2(8 + 9/3)) * (40/8).
Since multiplication is associative, the final answer is the same, but the expression-tree is different. The parentheses in the original expression indicate that the multiplication of 2 by everything else should be done last.
I’m getting: 2 8 9 3 / + * 40 8 / *
(Note that the operands appear, left to right, in the same order as in the in-fix original.)
Anybody agree? Disagree? This is just more-or-less off the top of my pointy head.
Grokking PN or RPN: It really helps if you had a WFF 'N PROOF game as a kid.
Something I noticed: Computer Science types, of course, are all just gaga about RPN. Like, they can’t imagine why anyone would write expressions any other way! (That includes myself, mostly.)
But I noticed, in talking to various math professors, that math professors mostly didn’t like, or didn’t understand, or didn’t appreciate Polish notation.
(And don’t even get started about Hungarian notation, which apparently got totally bastardized by Microsoft, even though it was invented there!)
Ah, so! I mis-read the parentheses also in my version. Indistinguishable has it right.
ETA: All the more argument for doing away with those damnable parentheseseses!
While that would work, aren’t you bringing that first * (to multiply by 2) in a bit too early to literally correspond to aceplace’s expression? That is, that final * should be by the initial two that you first entered on the stack.
So, I see:
2((8 + 9/3) * (40/8))
2 8 9 3 / + 40 8 / * *
ETA: While double checking my answer, it looks like I got ninja’ed by a few!
Yes, you’re right – I ignored a pair of brackets that I shouldn’t have.
COBOL has add, subtract, multiply, divide functions. Pretty much like you describe. I use them often. There’s also the compute statement that lets you enter a formula.
I’d use the compute here. compute x = 2((8 + 9/3) * (40/8)).
with effort I could break it up into multiple statements with the other functions.
Ok, aceplace57, if you can use add(x, y), mult(x, y), etc., you know how to use Forward Polish Notation. That’s all Forward Polish Notation amounts to; writing “add(x, y)” instead of “x add y” [putting the operation in front of its arguments, rather than between them].
Go ahead; actually give it a shot. How would you write 2((8 + 9/3) * (40/8)) in that setup?
[spoiler]2((8 + 9/3) * (40/8)) would become mult(2, mult(add(8, div(9, 3)), div(40, 8))).
Reverse Polish notation is just a slight change on that: since you evaluate the arguments before evaluating the result of the function they are passed to, you might argue that you should write the arguments before the function name, rather than the other way around.
If we did this, writing (x, y)add, (x, y)mult, etc., instead of add(x, y), mult(x, y), etc., then
2((8 + 9/3) * (40/8)) would become (2, ((8, (9, 3)div)add, (40, 8)div)mult)mult.
That’s reverse Polish notation, right there (but we can go ahead and remove all the parentheses, if we want to, since they don’t actually contribute any non-redundant information).
[/spoiler]
I got it. finally. It’s the same format as Excel formulas. Although it usually takes me a few tries to get the syntax right in Excel.
Thanks.
My HP 16C, purchased in 1982, works just as well now as it ever did. I am so used to RPN, I have trouble when I try to use a conventional calculator. Fortunately, it isn’t much of a problem, because, as noted upthread, I don’t use calculators much any more for anything beyond adding two or three numbers - anything more than that and I fire up a spreadsheet.
The 12c is available regularly, but the 15c was only released in a “limited edition” a couple of years ago. I bought it during the second round, for about a hundred bucks. Presumably the Amazon seller you linked to bought up a bunch of them but there’s only a limited supply.
I preferred the regular calculators because you could enter the formula directly off the page. I did have to enter the implied * to get windows calculator to do the final multiplication by 2 and of course press = But I finally got it to give the right answer. (I always miss-key trying to using Win calculator)
With RPN calculators you have to convert the operations in your head as you enter them. I recall watching friends in college using their HP RPN calculators. I never owned one.
2((8 + 9/3) * (40/8))
It’s funny - I’ve never been a “math person” and I’ve never done any programming. I’m even a little shaky doing formulas in Excel. But RPN, from the moment I first encountered it, has always made sense to me. I didn’t realize you could change the function on your computer or phone calculator to use it; I’ll have to look into that.
I wonder if Excel will take RPN notation?
I use Excel if I’m doing anything important. You can enter a equation and actually confirm there are no typos. No extra or missing parenthesis etc. I like seeing the whole equation I entered because then I can trust the result.
It took three tries before I got win calculator to give me the right answer. typos and bad mouse clicks did me in. You can’t even confirm the entire equation you entered. win calculator is frustrating for anything beyond simple arithmetic.
In what is possibly a demonstration of just how nerdy my crowd in college was, we actually had “races” (giving the same formula to two people) to determine which was faster: RPN calculators or algebraic notation calculators. For the record, RPN was faster.
I still have, and use at work, my HP 15C calculator. It’s got to be pushing 30 years old by now. My wife still uses her HP 11C.
All of the buttons on both of them still work as well as when they were new, which is kind of amazing when i think about it.
Just for the record, I would have done 2((8 + 9/3) * (40/8)) as
8 enter 9 enter 3 / + 40 * 8 / 2 *
Because I’m not fanatical about order of operations.
ETA: Or maybe even
8 enter 9 enter 3 / + 5 * 2 *
Scandalous!
I don’t know how (I went through a period of buying lots–literally lots–of old calculators), where (probably eBay), or when (sometime after 2000 'cuz that’s when they started making them) I got my HP 30S, but I got it running yesterday and found that, despite the ENTER key in the bottom corner, it uses algebraic entry. 
Have to find my Novus Scientific from about 1976 in one of these boxes if I want to use a calculator without equal, as old HP ads said. Its battery cover is less than a foot from my left knee and I have several 9v batteries to feed its lust for power.
The 15C calculator is beat all to hell, but is still kicking after 32 years. It’s pretty slow, but in most cases, it makes it easier to debug when I’m writing programs.
Once I figured out the RPN, I never could go back to old school. FWIW, I found I could enter more data for less keystrokes. I still have trouble when I have use conventional calculators, because I keep looking for the “ENTER” key.
I’ve had others: TI, Unisonic, Casio along with other long-extinct brands, and the calculator keys were always the first to go (no entry, double or triple entry, etc.). That was never (and still is) the case with the HP–never gave me a hiccup. It’s safe to say I’ve probably hit those keys at least a quarter million times while in college and continuing till this day.
Sad to say, when I excitedly tried out the new 15C Limited Edition, I found it to be a hugh disappointment–the keys felt like you were pushing cow tits. It’s like announcing the 100th anniversary edition of the Cadillac, only to find you have a Chevy Chevette suspension. Quite an inept move on HP’s part :smack:.
My HP 15C still works fine. It’s close to 30 years old now.
I had an HP 15c that I bought in the college bookstore around 1985 but I lost it about twenty years ago. But I was able to buy the “limited edition” version that HP sold a couple of years ago. There’s also an iPhone app that mimics a 15c but it’s about thirty bucks.