>>>>Was there ever a conclusion here as to what is correct?
>>>>
>>>>I would of done it like this:
>>>>(-2)^2 = 4
>>>>
>>>
>>>try:
>>>
>>>?5-2^2
>>>
>>>?-2^2
>>>
>>>obviously VFP and Excel has a bug.
>>
>>
>>Metin,
>>
>>This is not algebra
>>
>>The minus sign in the first expression is a binary operator.
>>In the second expression, it's a unary operator
>>
>>The unary minus has higher precedence than the exponent
>>The binary minus has lower precedence than the exponent
>>
>>No bug
>
>you say
>
>?5-2^2
>
>different than
>
>?-2^2+5
>
>that can't acceptable...

Metin,

I'll try to explain to a top 1% mathematician about computer languages - not algebra
I do not claim that this is complete - it's meant to help you understand

If there are words you do not understand, try to find them here : http://www.thefreedictionary.com

Operators
--------------
The arity (http://en.wikipedia.org/wiki/Arity) of an operator is the number of arguments it takes
eg multiplication takes two arguments, a * b could be written as *(a, b)

A unary operator takes 1 argument and its arity is 1
a binary operator takes 2 arguments and its aritry is 2
a ternary operator takes 2 arguments and its arity is 3
a n-ary operator takes n arguments and its arity is n

In essence, an operator with arity n is a function taking n arguments and returning exactly ONE result

Prefix/postfix/infix
Notation and operators:
In a prefix notation, the operator is written before the argument, example from C#: ++i
In a postfix notation, the operator is written after the argument, example 3! (where ! is factorial, ie 3 * 2 * 1)
In an Infix notation, the operator is written between the arguments, eg : 1 + 2 or a * b


Precedence
The operators are assigned a precedence (sort of priority). Operators with higher precedence are evaluated before those with a lower precedence
This is by convention. Without them we would be forced to write fully parenthesized expressions
1 + 2 + 3 * 4 will be evaluated ((1+2) + (3*4))

associativity
If an operator is associative, eg (1+2)+3 = 1 + (2 + 3), it will be assigned a Left or a Right associativity
Why is Left/Right needed ? Addition - for example - is an binary operator (Arity = 2, takes 2 arguments)

1 + 2 - 3
Since an operator is in essence a function that takes n arguments, would we write
Plus(1, Minus(2, 3)) or 1 + (2-3)
or
Minus(Plus(1,2),3) or (1+2) - 3

So, the associativity comes into play with operators of equal precedence (+ and -, * and -)

unary minus                    Right
exponent                          Right (vfp = Left)
multiplication, division  Left
addition, subtraction     Left 

In the expressions below the minus sign is a unary operator, ie takes one argument
[ remember that unary minus has higher precedence ]

-3
-2^2

If we wrote it with functions

Negate(3)
Exponent(Negate(2), 2)

Here, it takes two arguments and is a binary operator

0 - 3
0 - 2 ^2

With functions

Subtract(0, 3)
Subtract(0, Exponent(2,2))

How do we know that a minus is a unary operator ?
A unary minus comes at the beginning of an expression or immediately after a left parenthesis

Ok, time to do some work now