RE: Using "=" vs ":="

• To: mathgroup at smc.vnet.net
• Subject: [mg70683] RE: [mg70664] Using "=" vs ":="
• From: "David Park" <djmp at earthlink.net>
• Date: Mon, 23 Oct 2006 02:50:09 -0400 (EDT)

```Misha,

The problem is not '=' vs. ':='.
The problem is Sin(x^2+y^2) vs. Sin[x^2+y^2].

The first form is not a function but just a multiplication.

David Park

From: misha [mailto:iamisha1 at comcast.net]
To: mathgroup at smc.vnet.net

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...
Then,
In[2]:= f[x,y]
Out[2]:=1-Sin(x^2+y^2)
Still no problem...
Then,
In[3]:=f[1,2]
Out[3]:=1-5 Sin

Huh?

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)
....
In[3]:=f[1,2]
Out[3]:=1-Sin[5]

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

Thanks!
Misha

```

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