Date: Mar 14, 2006 10:37 AM
Author: magidin@math.berkeley.edu
Subject: Re: Reason for operator precedence
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