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Re: Using "=" vs ":="


There's an error in your definition of f.  It should be:

   f[x_, y_]:=1-Sin[x^2+y^2]

The punctuation around the argument of Sin should be square brackets, 
not parentheses.

For the definition you gave, both of Mathematica's outputs are correct 
and consistent.  In fact, Sin(x^2+y^2) to Mathematica means the product 
of Sin and the expression x^2+y^2.  So your f[x,y] showed this product 
again; your f[1,2] evaluated x^2+y^2 to be 5, and the product of Sin and 
5 is 5 Sin.

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
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
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University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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