
Re: Reason for operator precedence
Posted:
Mar 14, 2006 10:37 AM


In article <4416a498$1_4@news.peopletelecom.com.au>, Tony <ignorethis@nowhere.com> wrote: >Hi all. > >Hope this isn't a silly question. > >I was wondering what the reason is for having multiple levels of operator >precedence?
So that polynomials and rational functions can be written easily. That's essentially the main reason.
>Phrased another way, why is it that we don't just evaluate everything from >left to right?
>Having multiple levels of precedence obviously adds complexity, so I assume >there must be some payback. However, I don't see what it is.
So, by "evaluting left to right", I assume that you mean that something like
2 + 3 * 5
would evaluate to 25, since 2 plus 3 is five, and then multiplying that by 5 yields 25.
A general quadratic polynomial, using standard operator percedence, is written as:
ax^2 + bx + c
And it can be written in other orders easily if you want:
c + bx + ax^2
bx + c + ax^2
etc.
How would you have to write it if you simply evaluated left to right? The smallest number of parenthesis I can come up with is:
axx + (bx + c)
which may obscure the degree. If you want to put in the square, you would need to do something like
bx + c + (a(x^2)).
Higher degree polynomials would be even harder.
 ====================================================================== "It's not denial. I'm just very selective about what I accept as reality."  Calvin ("Calvin and Hobbes") ======================================================================
Arturo Magidin magidin@math.berkeley.edu

