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Re: Simplify problem

• To: mathgroup at smc.vnet.net
• Subject: [mg95805] Re: Simplify problem
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 28 Jan 2009 06:26:35 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <glmstk$mm3$1@smc.vnet.net>

In article <glmstk$mm3$1 at smc.vnet.net>, tidy512 at googlemail.com wrote:

> I am using Simplify / FullSimplify etc. to simplify some equations
> I have, but I am unable to coerce Mathematica into automatically
> giving me the form I require for some of the sub-expressions, e.g.
> 
> I'd like
> 
> 1/Sqrt[1 + 1/x]
> 
> to be automatically converted to
> 
> Sqrt[x/(1 + x)]
> 
> 'x' is always of type Real and greater-than 0 btw.
> 
> I would appreciate any help or tips anyone can provide on this.

Broadly speaking, Mathematica mainly uses *LeafCount* to assess the 
complexity of expressions. For instance, of two expressions, the one 
with the lowest value for *LeafCount* will be deemed as simpler than the 
other.

In[2]:= 1/Sqrt[1 + 1/x] // LeafCount

Out[2]= 9

In[3]:= Sqrt[x/(1 + x)] // LeafCount

Out[3]= 11

So Simmplify/FullSimplify is not going to go from the first from to the 
second except if one can modify/write appropriately the complexity 
function used by FullSimplify. See

http://reference.wolfram.com/mathematica/ref/ComplexityFunction.html

Regards,
--Jean-Marc