Why? This extra condition doesn't help you, and why your link shows nothing, it behaves exactly as I'd expect, ^ is identical to superscript, you're just making an implicit mistake of thinking +2 is somehow covered by ^ and would be part of the superscript, but it wouldn't, that's a different source of ambiguity
What would help is an example where parens aren't needed, but nonetheless slash would mean something else vs horizontal line, like in the original example
That's how you show semantic "completely different"
The math notation doesn't need parens. The computer notation needs parens. This alone is simple obvious proof that they are different notations, at least in my understanding of what a notation is.
-3^2 in the math notation doesn't need parens only because of operator precedence.
The fact that the computer ^ requires parens in more cases like -3^(2+2) is irrelevant for this and doesn't allow you justifying different precedence rules (and your downgrading from "completely different" to "different" isn't a proof, just "tautology". Hey, they also look different, so they are different!)
Why? This extra condition doesn't help you, and why your link shows nothing, it behaves exactly as I'd expect, ^ is identical to superscript, you're just making an implicit mistake of thinking +2 is somehow covered by ^ and would be part of the superscript, but it wouldn't, that's a different source of ambiguity
What would help is an example where parens aren't needed, but nonetheless slash would mean something else vs horizontal line, like in the original example
That's how you show semantic "completely different"