Re: Using "=" vs ":="

• To: mathgroup at smc.vnet.net
• Subject: [mg70692] Re: Using "=" vs ":="
• From: Dave Seaman <dseaman at no.such.host>
• Date: Mon, 23 Oct 2006 02:50:50 -0400 (EDT)
• Organization: Information Technology at Purdue
• References: <ehf1ks\$5ds\$1@smc.vnet.net>

```On Sun, 22 Oct 2006 06:04:12 +0000 (UTC), 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...

Actually, there's a problem.  Function evaluation is represented by
square brackets in Mathematica, not by parentheses.  What you wrote
involves multiplication of a simple variable called Sin by the expression
(x^2+y^2).

> 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?

It's exactly what you told it, since (x^2+y^2) evaluates to 5 here.

> 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?

There is a difference, but I don't think it's relevant to your question.
Try it with square brackets and then with parentheses, and compare
results.

--
Dave Seaman
U.S. Court of Appeals to review three issues
concerning case of Mumia Abu-Jamal.
<http://www.mumia2000.org/>

```

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