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Using "=" vs ":="

• To: mathgroup at smc.vnet.net
• Subject: [mg70664] Using "=" vs ":="
• From: misha <iamisha1 at comcast.net>
• Date: Sun, 22 Oct 2006 01:20:22 -0400 (EDT)

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

• Follow-Ups:
  • Re: Using "=" vs ":="
    • From: Murray Eisenberg <murray@math.umass.edu>