Fun with Exponents

[Veggiesama]

I was explaining how exponents work to a young friend of mine, and I happened to have MapTool loaded at the time, so I punched this in:

Code: Select all

[-5^2]

Order of operations states you should do exponents first, so the above problem can be rewritten as -(5^2) = -(25).

MapTool returns a positive 25. Wrong!

-5^2 is not the same as (-5)^2. In other words,

Code: Select all

[if(-5^2 == (-5)^2, "TRUE", "FALSE")]

should return FALSE, not TRUE.

[aliasmask]

I think stating it as -5^2 is the same thing as -1*5^2 where the multiplication is done first. Now if you do 1-5^2 it is done as you expect where 5^2 is first then the subtraction. So, I think MT has it right.

edit: unless you're saying the exponent trumps multiplication too? After testing, it does.. so, you're right.

[Veggiesama]

Yeah, from Wikipedia:

1. terms inside brackets
2. exponents and roots
3. multiplication and division
4. addition and subtraction

On the other hand, Wiki goes on to say:
"Unfortunately, there exist differing conventions concerning the unary operator − (usually read "minus"). In written or printed mathematics, the expression −3^2 is interpreted to mean −(3^2) = −9, but in some applications and programming languages, notably the application Microsoft Office Excel and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus (negation) has higher precedence than exponentiation, so in those languages −3^2 will be interpreted as (−3)^2 = 9. In any case where there is a possibility that the notation might be misinterpreted, it is advisable to use parentheses to clarify which interpretation is intended."

I learn something new every day, I guess.

[DrVesuvius]

I think the confusion comes from the fact that in the expression "-5^2", the minus sign isn't really an operator, but an inherent part of the discrete number "-5".

[Azhrei]

I think the confusion comes from the fact that in the expression "-5^2", the minus sign isn't really an operator, but an inherent part of the discrete number "-5".

Um, that depends.

In many languages it would be classified as a unary operator if it were followed by a variable name or other expression. If the definition of "expression" includes any integer value, then it can be a unary operator in front of an integer.

The distinction comes about because of the way an LR(1) parser works. I looked at the grammar used by the MT parser and I don't see any specification of precedence so I can't tell. It might be that the order of the items in the file specifies the precedence...

[AidyBaby]

I think the confusion comes from the fact that in the expression "-5^2", the minus sign isn't really an operator, but an inherent part of the discrete number "-5".

Yep, how else (simply put) would you square -5?

[Veggiesama]

(-5)^2

^_^

[whited]

I looked at the grammar used by the MT parser and I don't see any specification of precedence so I can't tell. It might be that the order of the items in the file specifies the precedence...

I've been reading up on ANTLR lately - how the rules are nested is how the precedence is defined. The MT parser grammar reads "-5^2" as (-5)^2

That is, unary operators "-", "+" and "!" are higher precedence than "^" because they are nested deeper in the grammar rules.