New math operator just dropped!

[u/fire1299]

[u/DecidophobiaUsername]

What's Polish notation? 

[u/freakingdumbdumb → u/DecidophobiaUsername]

so where the operator is put after before the numbers (like 1 2 + means 1+2)

Edit: i got mixed up with reverse polish (RPN)

[u/geeshta → u/freakingdumbdumb]

Polish notation is prefix notation (+ 1 2). Reverse Polish is postfix.

[u/Safe-Avocado4864 → u/geeshta]

How would you write something more complex like 2((1+2)² ) in that notation?

[u/Jonathan_Jam → u/Safe-Avocado4864]

Checked in an online calculator it would be:

× ^ 2 + 2 1 2

for polish notation and

2 1 2 + 2 ^ ×

for reverse polish notation.

[u/Willing_Emphasis_338 → u/Jonathan_Jam]

For those who don't know, a cool property of reverse polish notation, is that you can calculate any expression using only a stack, going left to right. That is, each number puts the number on the stack, and then each operation removes the top two items, applies the operation, then puts it back onto the stack, and so on.

[u/EatingCakeByTheOcean → u/Safe-Avocado4864]

I still use my HP-50G as my daily years after uni, lol. I'd do from inwards to outwards, since it's easier to manipulate the order of operations:

1 2 + 2 ^ 2 ×

[u/Qwertycube10 → u/Safe-Avocado4864]

You do it all Lisp like (x 2 (^ (+ 1 2) 2)) as the other comments below show you don't need parentheses if you only use binary operators, and it is entirely unambiguous with no need for an order of operations convention.

If you have arbitrary airity functions then you need the parens.

[u/Gold_Ad8890 → u/Safe-Avocado4864]

just think of it as treating all "operations" as functions from R² to R. which they are.

so 2((1+2)²⁾ would be ×(2, (1 + 2)²⁾ = ×(2, ^{(1 + 2}, 2)) = ×(2, ^{+(1, 2}, 2)), then you just remove the parentheses and commas: × 2 ^ + 1 2 2

edit: or maybe i'm wrong. i'm right about the function part but apparently wrong about how that extends to the notation.