[bc_programming]

This issue seems like partly an artifact of the invented binary operator ^. In math exponents are superscripts and there's no binary operator- it's part of the term. But for text on computers, binary operators ended up being fabricated for the things you couldn't represent directly. The caret is common and was the first one to appear, but doubled multiplication signs is another one. Traditionally, binary operators have lower precedence than unary operators since the unary minus is considered part of the term, so the exponent turning into an operator mucks things up if it's still implemented to adhere to that logic.

You sort of see the same issue with division. The forward slash is a completely invented binary operator since the actual division symbol was often not present- and let's be real nobody uses the binary division operator when writing formulae. It's supposed to represent the dividing line in a fraction, similar to how division is usually represented in a formula as a fraction of two other expressions. It's got lower precedence than anything in either term- but, if you just replace the dividing line with a forward slash to input the formula into a computer, you'll get incorrect results, because it's replacing what is part of a complete term (the division line) with a new binary operator inserted between sets of terms, which is now subject to precedence rules.

[MrJohz]

I suspect it's more likely an artifact of how the number is lexed. `-3^2` probably gets lexed into Number(-3), Operator(^), Number(2), which results in the aforementioned precedence issues. The reason for parsing the operator with the number is that it makes it easier to handle the case where you just write a negative number as a literal value into a cell.

Source: I've written an Excel clone before. I don't believe it has the same bug, but if it does, that will be how it's crept in.

EDIT: looking at some of the descriptions of the bug, it seems like it happens when handling variables (i.e. cell references) as well, which makes it seem like a pure precedence issue and not a parsing issue. So I've got no idea, presumably someone simply messed up the precedence order.

[tsimionescu]

It's almost certainly a precedence issue. It's much easier to consider that unary operators have precedence over binary operators, and just learn the precedence rules for each class, rather than a global precedence rule. Plus, there's no conflict with math notation, as there is no exponentiation operator in math.

[fn-mote]

In my country we teach the same rules in math class. Blaming it on “unary vs binary” was a stretch. Next you’re going to blame it on the lexer for producing the -3 as a single term instead of two. (Which WOULD explain something, but… fix it?!)

In my country we use a horizontal line with a dot above and below to indicate in-line division in lower grades. Exactly like the computer /.

It’s not like there was no precedent here.

[mark-r]

I also learned the line with a dot above and below in my country, the USA. But that was a very long time ago, math teaching has changed immeasurably since my time.

In Unicode it's U+00F7: https://www.compart.com/en/unicode/U+00F7