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MathGroup Archive 2006

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Re: Using "=" vs ":="

  • To: mathgroup at
  • Subject: [mg70692] Re: Using "=" vs ":="
  • From: Dave Seaman <dseaman at>
  • Date: Mon, 23 Oct 2006 02:50:50 -0400 (EDT)
  • Organization: Information Technology at Purdue
  • References: <ehf1ks$5ds$>

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

> 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

Dave Seaman
U.S. Court of Appeals to review three issues 
concerning case of Mumia Abu-Jamal.

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