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Implications

March 2005: Chris Chiasson

One thing that the Mathematica book does not cover, as an issue of scoping, is the set of ''implications'' of the coding principles:

"Mathematica is a system built on a fairly small set of very powerful principles. This book describes those principles, but by no means spells out all of their implications. In particular, while the book describes the elements that go into Mathematica programs, it does not give detailed examples of complete programs. For those, you should look at other publications." - Stephen Wolfram, The Mathematica Book

When I was beginning to learn Mathematica (I wonder if I am still beginning), one of the problems I had involved thinking in terms of things like definitions and function calls. Mathematica does not seem to have these. Mathematica has an expression engine with pattern matching. When someone types

In[1]:=   f[x_]=x!

Out[1]:=

this really only sets up a replacement rule

{f[x_]->x!}

that Mathematica will use whenever it finds an expression that fits the pattern f[x_].

I am sure others could expand and revise from this point, which is why I think it would be a good topic for the Mathematica Wiki.

August 2005: Mark Knutson
Agreed. I noticed this and as a programmer, found the notion of a function definition as a pattern to be matched to be intriguing. I think the Maeder book on Mathematica Programming gives some perspective here as well, but I admit I am only just beginning to consider the broader implications of this. The generalizations used to implement the 'everything is an expression' is another concept I find intriguing. Sorry I don't have more to add than that--at this point, at least.

October 2005: SarahF
See the discussion tab for this page for some basics on function definitions in Mathematica. Much more could be said...

November 15th 2005: STH

I find the following attributes and idioms to be very suggestive of the essence of how Mathematica and mathematics are related.

• Flat
• Orderless
• OneIdentity
• Optional
• Listable

• 
  In[3]:=   x_ + y_.//FullForm
  
  Out[3]:=

In[4]:=   Attributes[Plus]

Out[4]:=

In[5]:=   DefaultValues[Plus]

Out[5]:=

• 
  In[6]:=   x_ * y_.//FullForm
  
  Out[6]:=

In[7]:=   Attributes[Times]

Out[7]:=

In[8]:=   DefaultValues[Times]

Out[8]:=

• 
  In[9]:=   x_ ^ y_.//FullForm
  
  Out[9]:=

In[10]:=   Attributes[Power]

Out[10]:=

In[11]:=   DefaultValues[Power]

Out[11]:=

Contributors to this Page

The 5 contributors to this page (ordered by date of first contribution):

	User	Latest Contribution	# Contributions
1.	ChrisChiasson	Wed 20 Sep 2006 21:15:48	13
2.	riemann	Sun 19 Jun 2005 11:20:19	2
3.	MarkKnutson	Mon 29 Aug 2005 10:19:16	1
4.	SarahF	Tue 18 Oct 2005 14:40:28	2
5.	hattons	Tue 15 Nov 2005 22:09:12	2

This page was created by ChrisChiasson on Mon 14 Mar 2005 23:15:58 and last updated by ChrisChiasson on Wed 20 Sep 2006 21:15:48