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Re: Using "=" vs ":="

• To: mathgroup at smc.vnet.net
• Subject: [mg70697] Re: Using "=" vs ":="
• From: Peter Pein <petsie at dordos.net>
• Date: Mon, 23 Oct 2006 02:51:08 -0400 (EDT)
• References: <ehf1ks$5ds$1@smc.vnet.net>

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...
> 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
> 
Hi Misha,

try to use Mathematica syntax while using Mathematica. Sin is just a 
variable (multilyed by x²+y²) in your example.

The second part of your posting is inconsistent:
Out[3] should be 1-5 Sin, if you entered f[x_,y_]=1-Sin(x²+y²)


In[1]:= f[x_,y_]:=1-Sin[x^2+y^2] (* "=" or ":=" doesn't matter in this 
case *)
In[2]:= f[1,2]
Out[2]= 1-Sin[5]

Peter

P.S.: if you don't have access to brackets on your keyboard either buy a 
new one or use Sin@(x²+y²). ;-)