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Re: Using "=" vs ":="

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  • Subject: [mg70688] Re: Using "=" vs ":="
  • From: Bill Rowe <readnewsciv at>
  • Date: Mon, 23 Oct 2006 02:50:26 -0400 (EDT)

On 10/22/06 at 1:20 AM, iamisha1 at (misha) wrote:

>I'm going through Mathematic by Example, 2nd ed., (Abell and
>Braselton), and have come across something that puzzles me.

>Chapter 2, Section 2, Example 8 Define f(x,y)=1-sin(x^2+y^2)

>So I first try,
>In[1]:= f[x_, y_]:=1-Sin(x^2+y^2)
>No problem so far...

The line of code above is valid Mathematica syntax but almost 
certainly isn't what you think. It defines f[x,y] as 1 minus the 
product of something called Sin and the expression x^2+y^2. That 
is the characters '(' and ')' do not delimit arguments for 
functions. Instead you need to use square brackets. I am 
reasonably certain what you wanted is

f[x_, y_]:= 1-Sin[x^2+y^2]

>In[2]:= f[x,y]
>Still no problem...

Yes, this would not show an issue since x and y don't have 
defined values. Hence, Mathematica returns a symbolic answer 
showing an implicit multiplication. If you do



you can see the result is not how you are interpreting it.

>Out[3]:=1-5 Sin


See comments above

>I noticed that rather than using ":=" to "simply define" this
>function, as opposed to (just) "=" to "define and compute" this
>function, I get different subsequent behavior.  Specifically, doing
>the above with just "=", works fine.

>In[1]:= f[x_, y_]=1-Sin(x^2+y^2)

I am not sure what you did here but I am certain what you have 
posted is incomplete. That is


1 - Sin*(x^2 + y^2)


1 - 5*Sin

>My question is, Why?  What's the difference between ":=" and "=" for
>defining functions?

The difference is when evaluation of the right hand side occurs. 
For "=", evaluation occurs before the assignment is made. For 
":=" evaluation is delayed and occurs when you evaluate the 
function at some later point.
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