Re: Using "=" vs ":="

*To*: mathgroup at smc.vnet.net*Subject*: [mg70694] Re: Using "=" vs ":="*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Mon, 23 Oct 2006 02:50:54 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*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? This has nothing to do with Set vs. SetDelayed. You are using the wrong syntax. See "Your First Mathematica Calculations" at http://documents.wolfram.com/mathematica/GettingStarted/StartingOut/YourFirstMathematicaCalculations.html *Built-in functions are capitalized. Arguments to functions are wrapped with /square/ brackets. Sin[x]* In[1]:= f[x_, y_] := 1 - Sin[x^2 + y^2] In[2]:= f[x, y] Out[2]= 2 2 1 - Sin[x + y ] In[3]:= f[1, 2] Out[3]= 1 - Sin[5] In[4]:= N[%] Out[4]= 1.95892 > 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 > For example, In[5]:= g = Random[] Out[5]= 0.624668 In[6]:= {g, g, g} Out[6]= {0.624668, 0.624668, 0.624668} In[7]:= h := Random[] In[8]:= {h, h, h} Out[8]= {0.17459, 0.0433796, 0.504572} Regards, Jean-Marc